<?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>lra2aa.out</source>

<heading><![CDATA[
Prover9 (64) version 2026-3T, March 2026.
Process 844980 was started by veroff on b146-03,
Tue Apr 14 12:00:22 2026
The command was "prover9 -f lra2aa.in".
]]></heading>

<proof number="1" length="13508" max_count="65">

<comments><![CDATA[
% Proof 1 at 2077.20 (+ 0.13) seconds: "aa1".
% Length of proof: 13508 (0 new hints)
% Level of proof: 685
% Maximum clause weight: 65.000
% Given clauses in run: 14272
% Given clauses in proof: 13490 (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) * (z * z) = x * (y * (z * z))
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_r")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="35" type="assumption">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("aK1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" 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="37" 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="38" 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="39" 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="40" 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="41" 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="42" 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="43" 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="44" 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="45" 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="46" 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="47" 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="48" 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="49" 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="50" 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="51" 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="52" 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="53" 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="54" 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="55" 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="56" 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="57" 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="58" 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="59" 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="60" 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="61" 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="62" 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="63" 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="64" 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="65" 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="66" 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="67">
    <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="69">
    <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="71">
    <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="72">
    <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="73">
    <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="74">
    <literal><![CDATA[
      x * (x \ (1 * y)) = y
    ]]></literal>
    <justification jstring="[para(10(a,2),7(a,1))].">
      <j1 rule="para" parents="10 7"/>
    </justification>
  </clause>

  <clause id="75">
    <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="76">
    <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="77">
    <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="78">
    <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="79">
    <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="80">
    <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="81">
    <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="82">
    <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="83">
    <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="84">
    <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="85">
    <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="86">
    <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="87">
    <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="88">
    <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="89">
    <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="90">
    <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="91">
    <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="92">
    <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="93">
    <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="94">
    <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="95">
    <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="96">
    <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="97">
    <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="98">
    <literal><![CDATA[
      (x * 1) \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 18"/>
      <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="106">
    <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="107">
    <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="108">
    <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="109">
    <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="110">
    <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="111">
    <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="112">
    <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="113">
    <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="114">
    <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="115">
    <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="116">
    <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="117">
    <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="118">
    <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="119">
    <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="120">
    <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="121">
    <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="122">
    <literal><![CDATA[
      ((x * x) * (y * (z * u))) \ ((((x * x) * y) * z) * u) = a((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      ((x * x) * (y * z)) \ (((x * x) * y) * (z * u)) = L(u,z,(x * x) * y)
    ]]></literal>
    <justification jstring="[para(33(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="124">
    <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="125">
    <literal><![CDATA[
      x * ((x \ y) * (z * z)) = y * (z * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      (x / y) * (y * (z * z)) = x * (z * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x
    ]]></literal>
    <justification jstring="[para(35(a,2),8(a,1,2))].">
      <j1 rule="para" parents="35 8"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      1 * z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),36(a,1))].">
      <j1 rule="para" parents="7 36"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),36(b,1))].">
      <j1 rule="para" parents="7 36"/>
    </justification>
  </clause>

  <clause id="131">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(8(a,1),36(a,1))].">
      <j1 rule="para" parents="8 36"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,1),36(a,1))].">
      <j1 rule="para" parents="10 36"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * x != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(7(a,1),37(a,1))].">
      <j1 rule="para" parents="7 37"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(8(a,1),37(b,1))].">
      <j1 rule="para" parents="8 37"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),37(a,1))].">
      <j1 rule="para" parents="12 37"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / u != y
    ]]></literal>
    <literal><![CDATA[
      x * u = z
    ]]></literal>
    <justification jstring="[para(11(a,1),39(a,1))].">
      <j1 rule="para" parents="11 39"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(9(a,1),40(a,1))].">
      <j1 rule="para" parents="9 40"/>
    </justification>
  </clause>

  <clause id="138">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(7(a,1),45(a,2))].">
      <j1 rule="para" parents="7 45"/>
    </justification>
  </clause>

  <clause id="140">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="10 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(8(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(8(a,1),46(a,2))].">
      <j1 rule="para" parents="8 46"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(10(a,1),46(a,2))].">
      <j1 rule="para" parents="10 46"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      ((x * y) * z) / z != u * y
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(11(a,2),46(a,2)),flip(a)].">
      <j1 rule="para" parents="11 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(12(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="12 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      (x * y) / z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></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="147">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="11 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></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="149">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(22(a,2),49(a,1))].">
      <j1 rule="para" parents="22 49"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      x \ (y * z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(9(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="9 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      x \ ((y * z) * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y * (z * u) = x
    ]]></literal>
    <justification jstring="[para(14(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="14 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      L(L(x,y,z),u,w) != L(v5,y,z)
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(30(a,1),52(a,1))].">
      <j1 rule="para" parents="30 52"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      L(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,35,a)].">
      <j1 rule="hyper" parents="54 35"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,12,a)].">
      <j1 rule="hyper" parents="59 12"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(59,a,10,a)].">
      <j1 rule="hyper" parents="59 10"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(60,a,10,a)].">
      <j1 rule="hyper" parents="60 10"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(60,a,9,a)].">
      <j1 rule="hyper" parents="60 9"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      ((x / y) * y) / z = x / z
    ]]></literal>
    <justification jstring="[hyper(61,a,12,a)].">
      <j1 rule="hyper" parents="61 12"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      (x * (x \ y)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a)].">
      <j1 rule="hyper" parents="63 10"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      x \ (y * 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,8,a)].">
      <j1 rule="hyper" parents="64 8"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,12,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 12 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      (x / y) * y = z * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="65 12 10"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      (x / y) * y = x * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="65 12 8"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      (x / y) * y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(65,a,12,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="65 12 7"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      (x * y) / y = x * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,11,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="65 11 8"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10,a,b,9,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 10 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,10,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="65 10 8"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      x * (x \ y) = 1 * y
    ]]></literal>
    <justification jstring="[hyper(65,a,10,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="65 10 7"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,67,a,b,8,a)].">
      <j1 rule="hyper" parents="65 67 8"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),67(a,1,1))].">
      <j1 rule="para" parents="10 67"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),67(a,1,1))].">
      <j1 rule="para" parents="12 67"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(67(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="67 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,69,a)].">
      <j1 rule="hyper" parents="65 16 69"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      a(K(x,y),z,u) = w \ w
    ]]></literal>
    <justification jstring="[hyper(65,a,69,a,b,35,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 69 35"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      x \ x = 1 * 1
    ]]></literal>
    <justification jstring="[hyper(65,a,69,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="65 69 8"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(69(a,2),7(a,1,1))].">
      <j1 rule="para" parents="69 7"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(69(a,2),8(a,1,2))].">
      <j1 rule="para" parents="69 8"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      a(K(x,y),z,u) = w / w
    ]]></literal>
    <justification jstring="[hyper(65,a,79,a,b,35,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 79 35"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      x * (y / y) = x
    ]]></literal>
    <justification jstring="[para(79(a,2),8(a,1,2))].">
      <j1 rule="para" parents="79 8"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),80(a,1,2))].">
      <j1 rule="para" parents="10 80"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),80(a,1,2))].">
      <j1 rule="para" parents="12 80"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(80(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="80 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(44,a,27,a,b,112,a(flip))].">
      <j1 rule="hyper" parents="44 27 112"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,25,a,b,112,a(flip))].">
      <j1 rule="hyper" parents="43 25 112"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,112,a(flip))].">
      <j1 rule="hyper" parents="42 23 112"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      x / (y \ x) = z / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,82,a,b,82,a(flip))].">
      <j1 rule="hyper" parents="65 82 82"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,82,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 82 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,82,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="65 82 10"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(59,a,82,a)].">
      <j1 rule="hyper" parents="59 82"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(38,a,20,a(flip),b,82,a),flip(a)].">
      <j1 rule="hyper" parents="38 20 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),82(a,1,2))].">
      <j1 rule="para" parents="18 82"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),82(a,1,2))].">
      <j1 rule="para" parents="22 82"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(82(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="82 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(82(a,2),82(a,1,2))].">
      <j1 rule="para" parents="82 82"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      (x / y) \ x = y / 1
    ]]></literal>
    <justification jstring="[hyper(65,a,85,a,b,80,a(flip))].">
      <j1 rule="hyper" parents="65 85 80"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,85,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="65 85 10"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      x * ((y / z) \ y) = x * z
    ]]></literal>
    <justification jstring="[hyper(60,a,85,a)].">
      <j1 rule="hyper" parents="60 85"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(38,a,82,a,b,85,a(flip))].">
      <j1 rule="hyper" parents="38 82 85"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(85(a,1),41(a,1))].">
      <j1 rule="para" parents="85 41"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(85(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="85 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,22,a,b,169,a)].">
      <j1 rule="hyper" parents="65 22 169"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,203,a)].">
      <j1 rule="hyper" parents="56 203"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      T(x,a(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[para(35(a,2),203(a,1,2))].">
      <j1 rule="para" parents="35 203"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(203(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="203 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,2),138(a,1,1))].">
      <j1 rule="para" parents="10 138"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      ((1 / x) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,2),138(a,1,1))].">
      <j1 rule="para" parents="12 138"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      x \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(175(a,2),138(a,1))].">
      <j1 rule="para" parents="175 138"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,2),141(a,1,2))].">
      <j1 rule="para" parents="10 141"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(10(a,2),142(a,1,2))].">
      <j1 rule="para" parents="10 142"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x * K(y,y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(173(a,2),142(a,1,2))].">
      <j1 rule="para" parents="173 142"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(153(a,1),52(a,2))].">
      <j1 rule="para" parents="153 52"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(173(a,1),153(a,1,3))].">
      <j1 rule="para" parents="173 153"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      T(x,L(L(x,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,25,a,b,184,a(flip))].">
      <j1 rule="hyper" parents="43 25 184"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      T(x,L(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,184,a(flip))].">
      <j1 rule="hyper" parents="42 23 184"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      (x \ 1) * (x * x) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,34,a(flip),b,73,a(flip))].">
      <j1 rule="hyper" parents="36 34 73"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      (x * ((x \ 1) * y)) \ y = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(73(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="73 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      x * (x \ y) = y * (z * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,75,a,b,10,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="65 75 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></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="225">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(75(a,1),18(a,2,2))].">
      <j1 rule="para" parents="75 18"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),20(a,2,1))].">
      <j1 rule="para" parents="83 20"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      (x * x) * (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,33,a,b,84,a(flip))].">
      <j1 rule="hyper" parents="37 33 84"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(84(a,1),18(a,2,2))].">
      <j1 rule="para" parents="84 18"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      x * T(y / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,113,a,b,12,a)].">
      <j1 rule="hyper" parents="65 113 12"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,113,a,b,10,a)].">
      <j1 rule="hyper" parents="65 113 10"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      x \ (y * T(z,y)) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,113,a)].">
      <j1 rule="hyper" parents="64 113"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,113,a)].">
      <j1 rule="hyper" parents="60 113"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,113,a)].">
      <j1 rule="hyper" parents="59 113"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,12,a(flip),b,113,a),flip(a)].">
      <j1 rule="hyper" parents="36 12 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(37,a,12,a,b,113,a(flip))].">
      <j1 rule="hyper" parents="37 12 113"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,10,a,b,113,a(flip))].">
      <j1 rule="hyper" parents="36 10 113"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(113(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="113 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(113(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="113 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="113 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),113(a,1,2))].">
      <j1 rule="para" parents="23 113"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),113(a,1,2))].">
      <j1 rule="para" parents="25 113"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),113(a,1,2))].">
      <j1 rule="para" parents="27 113"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) * z) = (y * (x * x)) * z
    ]]></literal>
    <justification jstring="[para(113(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),36(a,1))].">
      <j1 rule="para" parents="113 36"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(113(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="113 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(113(a,2),46(a,2)),flip(a)].">
      <j1 rule="para" parents="113 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(185(a,1),113(a,1,2))].">
      <j1 rule="para" parents="185 113"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      L(x,y,z) * x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(184(a,1),113(a,1,2))].">
      <j1 rule="para" parents="184 113"/>
    </justification>
  </clause>

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

  <clause id="251">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      T(x / y,y \ x) = x / y
    ]]></literal>
    <justification jstring="[para(115(a,1),185(a,1,2))].">
      <j1 rule="para" parents="115 185"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(163(a,1),46(a,1))].">
      <j1 rule="para" parents="163 46"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(163(a,2),141(a,1))].">
      <j1 rule="para" parents="163 141"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(164(a,1),46(a,1))].">
      <j1 rule="para" parents="164 46"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(165(a,2),141(a,1))].">
      <j1 rule="para" parents="165 141"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(167(a,2),141(a,1))].">
      <j1 rule="para" parents="167 141"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(167(a,2),142(a,1))].">
      <j1 rule="para" parents="167 142"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a,b,170,a),flip(a)].">
      <j1 rule="hyper" parents="65 18 170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,170,a)].">
      <j1 rule="hyper" parents="65 16 170"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a,b,171,a),flip(a)].">
      <j1 rule="hyper" parents="65 18 171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,16,a,b,171,a)].">
      <j1 rule="hyper" parents="65 16 171"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,20,a,b,180,a),flip(a)].">
      <j1 rule="hyper" parents="65 20 180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20,a,b,181,a),flip(a)].">
      <j1 rule="hyper" parents="65 20 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      K(T(x,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,186,a)].">
      <j1 rule="hyper" parents="57 186"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),194(a,1,1))].">
      <j1 rule="para" parents="10 194"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      (x * T(x,y)) / x = T(x,y)
    ]]></literal>
    <justification jstring="[para(185(a,1),194(a,1,2))].">
      <j1 rule="para" parents="185 194"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(197(a,2),182(a,1))].">
      <j1 rule="para" parents="197 182"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      x / (x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,12,a,b,221,a)].">
      <j1 rule="hyper" parents="37 12 221"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      (x \ 1) \ x = x * x
    ]]></literal>
    <justification jstring="[hyper(36,a,10,a,b,221,a)].">
      <j1 rule="hyper" parents="36 10 221"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      (x * x) \ x = 1 / x
    ]]></literal>
    <justification jstring="[hyper(36,a,10,a,b,227,a)].">
      <j1 rule="hyper" parents="36 10 227"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(235(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="235 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(235(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="235 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      K(x,(y * x) / y) = 1
    ]]></literal>
    <justification jstring="[para(235(a,1),267(a,1,1))].">
      <j1 rule="para" parents="235 267"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      (1 / x) * (1 / x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[para(85(a,1),272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="85 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,276,a)].">
      <j1 rule="hyper" parents="58 276"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),278(a,1,2,1))].">
      <j1 rule="para" parents="10 278"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      T(x,y / (y / x)) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),278(a,1,2,1))].">
      <j1 rule="para" parents="12 278"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      (x / (x / y)) * y = y * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(281(a,1),113(a,1,2))].">
      <j1 rule="para" parents="281 113"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(113(a,1),140(a,1)),flip(b)].">
      <j1 rule="para" parents="113 140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,1),150(a,1,2))].">
      <j1 rule="para" parents="10 150"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      (K(x,y) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(41,a,14,a(flip),b,174,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 14 174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(174(a,2),172(a,1)),flip(b)].">
      <j1 rule="para" parents="174 172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(194(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="194 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),258(a,1,1))].">
      <j1 rule="para" parents="10 258"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(113(a,2),258(a,1,1))].">
      <j1 rule="para" parents="113 258"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(164(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="164 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      (x * (y * z)) * a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(14(a,2),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="18 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9(a,2),260(a,1,2))].">
      <j1 rule="para" parents="9 260"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(11(a,1),270(a,1,1))].">
      <j1 rule="para" parents="11 270"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(194(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="194 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      x \ (y * T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(236(a,1),270(a,1,1))].">
      <j1 rule="para" parents="236 270"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(115(a,2),300(a,1))].">
      <j1 rule="para" parents="115 300"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(167(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="167 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      x \ (1 * y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(168(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="168 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      (x / y) \ (z * (z \ x)) = y
    ]]></literal>
    <justification jstring="[para(12(a,1),76(a,1,2,2,2))].">
      <j1 rule="para" parents="12 76"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(18(a,2),76(a,1,2,2))].">
      <j1 rule="para" parents="18 76"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(78(a,1),18(a,2,2))].">
      <j1 rule="para" parents="78 18"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[para(20(a,2),87(a,1,1,1))].">
      <j1 rule="para" parents="20 87"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(88(a,1),20(a,2,1))].">
      <j1 rule="para" parents="88 20"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[para(82(a,1),88(a,1,1,1,1))].">
      <j1 rule="para" parents="82 88"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,93,a,b,10,a)].">
      <j1 rule="hyper" parents="65 93 10"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),93(a,1,1))].">
      <j1 rule="para" parents="10 93"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),93(a,1,1))].">
      <j1 rule="para" parents="12 93"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      (x * y) / (x * K(x,y)) = R(y,x,K(x,y))
    ]]></literal>
    <justification jstring="[para(93(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="93 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(93(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="93 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      x / T(y,y \ z) = x / ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(62,a,114,a)].">
      <j1 rule="hyper" parents="62 114"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,114,a)].">
      <j1 rule="hyper" parents="59 114"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,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="321">
    <literal><![CDATA[
      T(x,(x \ y) \ y) = x
    ]]></literal>
    <justification jstring="[para(114(a,1),185(a,1,2))].">
      <j1 rule="para" parents="114 185"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      T((x \ y) \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(56,a,321,a)].">
      <j1 rule="hyper" parents="56 321"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      ((x \ y) \ y) * x = x * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(321(a,1),113(a,1,2))].">
      <j1 rule="para" parents="321 113"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),129(b,1))].">
      <j1 rule="para" parents="7 129"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(161(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="161 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(162(a,2),45(a,1))].">
      <j1 rule="para" parents="162 45"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(166(a,2),45(a,1))].">
      <j1 rule="para" parents="166 45"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(166(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="166 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(166(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="166 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(166(a,2),260(a,1))].">
      <j1 rule="para" parents="166 260"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      x \ ((y / (x \ y)) * z) = z
    ]]></literal>
    <justification jstring="[hyper(146,a,188,a),flip(a)].">
      <j1 rule="hyper" parents="146 188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(189(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="189 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(190(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="190 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(190(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="190 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,12,a(flip),b,199,a),flip(a)].">
      <j1 rule="hyper" parents="325 12 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(199(a,2),145(a,1))].">
      <j1 rule="para" parents="199 145"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * x = x * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(219(a,1),113(a,1,2))].">
      <j1 rule="para" parents="219 113"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(231(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="231 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      (x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(231(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="231 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      (x / y) * (y \ x) = (y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(254(a,1),113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,262,a(flip))].">
      <j1 rule="hyper" parents="145 262"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      K(x,1 / x) / (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,264,a(flip))].">
      <j1 rule="hyper" parents="145 264"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(311(a,1),20(a,2,1))].">
      <j1 rule="para" parents="311 20"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(268(a,1),337(a,1,2,1))].">
      <j1 rule="para" parents="268 337"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      x \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),98(a,1,1))].">
      <j1 rule="para" parents="8 98"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(332,a,349,a),flip(a)].">
      <j1 rule="hyper" parents="332 349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(349(a,1),300(a,1))].">
      <j1 rule="para" parents="349 300"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(212,a,99,a),flip(a)].">
      <j1 rule="hyper" parents="212 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      L(x \ 1,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(325,a,273,a(flip),b,225,a),flip(a)].">
      <j1 rule="hyper" parents="325 273 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(325,a,171,a(flip),b,225,a),flip(a)].">
      <j1 rule="hyper" parents="325 171 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,159,a(flip),b,225,a),flip(a)].">
      <j1 rule="hyper" parents="325 159 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(216,a,225,a),flip(a)].">
      <j1 rule="hyper" parents="216 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(59,a,225,a)].">
      <j1 rule="hyper" parents="59 225"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(202,a,225,a(flip))].">
      <j1 rule="hyper" parents="202 225"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),225(a,2,1))].">
      <j1 rule="para" parents="12 225"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="225 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(195,a,226,a(flip))].">
      <j1 rule="hyper" parents="195 226"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),226(a,2,2))].">
      <j1 rule="para" parents="10 226"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      T(x,y) * z != x * y
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(113(a,1),246(a,2))].">
      <j1 rule="para" parents="113 246"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(163(a,2),255(a,1))].">
      <j1 rule="para" parents="163 255"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,2),257(a,1,1))].">
      <j1 rule="para" parents="12 257"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),292(a,1,2))].">
      <j1 rule="para" parents="23 292"/>
    </justification>
  </clause>

  <clause id="373">
    <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),292(a,1,2))].">
      <j1 rule="para" parents="25 292"/>
    </justification>
  </clause>

  <clause id="374">
    <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),292(a,1,2))].">
      <j1 rule="para" parents="27 292"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(164(a,2),296(a,1,1))].">
      <j1 rule="para" parents="164 296"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),303(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="10 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(153(a,1),362(a,1,2))].">
      <j1 rule="para" parents="153 362"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(362(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="362 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(82(a,1),365(a,1,1,1))].">
      <j1 rule="para" parents="82 365"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),376(a,1,1))].">
      <j1 rule="para" parents="11 376"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(82(a,1),376(a,1,1))].">
      <j1 rule="para" parents="82 376"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      K(x,y) = (y * x) \ ((y \ (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),94(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      K(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * x = y
    ]]></literal>
    <justification jstring="[para(94(a,1),172(a,1)),flip(b)].">
      <j1 rule="para" parents="94 172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(113(a,2),94(a,1,2))].">
      <j1 rule="para" parents="113 94"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(262(a,2),95(a,1,1))].">
      <j1 rule="para" parents="262 95"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(96(a,1),172(a,1)),flip(b)].">
      <j1 rule="para" parents="96 172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(116(a,1),301(a,1))].">
      <j1 rule="para" parents="116 301"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(132,a,18,a,b,171,a(flip))].">
      <j1 rule="hyper" parents="132 18 171"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(132,a,18,a,b,170,a(flip))].">
      <j1 rule="hyper" parents="132 18 170"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      x \ (y * (z * z)) = (x \ y) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,155,a(flip),b,34,a(flip))].">
      <j1 rule="hyper" parents="132 155 34"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      (x * x) \ (y * z) = ((x * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(132,a,155,a(flip),b,33,a(flip))].">
      <j1 rule="hyper" parents="132 155 33"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      ((x * x) * y) \ z = y \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,78,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="132 78 33"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      ((x * x) * y) \ (x * x) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,75,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="132 75 33"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      (x \ 1) * (y * y) = x \ (y * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,73,a(flip),b,34,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 73 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      ((x * x) \ 1) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,73,a(flip),b,33,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 73 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(135,a,20,a,b,180,a(flip))].">
      <j1 rule="hyper" parents="135 20 180"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      L(x,y \ 1,y) / ((y \ 1) * x) = y
    ]]></literal>
    <justification jstring="[hyper(135,a,18,a,b,170,a(flip))].">
      <j1 rule="hyper" parents="135 18 170"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      (x / (y * y)) / z = x / (z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(135,a,88,a(flip),b,34,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="135 88 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      (x * x) * (1 / y) = (x * x) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,84,a(flip),b,33,a),flip(a)].">
      <j1 rule="hyper" parents="135 84 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      L(x \ 1,x,y) * (((y * x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(136,a,225,a,b,82,a)].">
      <j1 rule="hyper" parents="136 225 82"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(136,a,198,a,b,190,a)].">
      <j1 rule="hyper" parents="136 198 190"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="136 31 20"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      x * (((y / x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(136,a,85,a(flip),b,82,a)].">
      <j1 rule="hyper" parents="136 85 82"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="136 29 20"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="136 27 20"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y \ u = z
    ]]></literal>
    <justification jstring="[para(405(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="405 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,114,a,b,85,a)].">
      <j1 rule="hyper" parents="137 114 85"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="137 30 18"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="137 29 18"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,18,a,b,159,a(flip))].">
      <j1 rule="hyper" parents="137 18 159"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 25 18"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      (x / ((y / z) * z)) * y = x
    ]]></literal>
    <justification jstring="[hyper(137,a,12,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="137 12 85"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(20(a,2),417(a,1,1))].">
      <j1 rule="para" parents="20 417"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / u = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(201,a,153,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="201 153 18"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      (x \ 1) * (x \ 1) = (x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(201,a,82,a(flip),b,273,a),flip(a)].">
      <j1 rule="hyper" parents="201 82 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(223(a,1),45(a,1))].">
      <j1 rule="para" parents="223 45"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),241(a,1,2,1))].">
      <j1 rule="para" parents="22 241"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(235(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="235 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(275,a,251,a)].">
      <j1 rule="hyper" parents="275 251"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(275,a,274,a)].">
      <j1 rule="hyper" parents="275 274"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(314(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="314 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(201,a,85,a(flip),b,360,a),flip(a)].">
      <j1 rule="hyper" parents="201 85 360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,170,a(flip),b,360,a),flip(a)].">
      <j1 rule="hyper" parents="65 170 360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      (K(x,y) \ z) \ 1 = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,159,a(flip),b,360,a),flip(a)].">
      <j1 rule="hyper" parents="65 159 360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,431,a,b,385,a)].">
      <j1 rule="hyper" parents="41 431 385"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      ((x * x) \ y) \ 1 = y \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,159,a(flip),b,394,a),flip(a)].">
      <j1 rule="hyper" parents="65 159 394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      1 / (x \ (y * y)) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(201,a,159,a(flip),b,394,a(flip))].">
      <j1 rule="hyper" parents="201 159 394"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      ((x * x) / y) \ 1 = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(135,a,85,a(flip),b,395,a),flip(a)].">
      <j1 rule="hyper" parents="135 85 395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      (x * x) \ T(y,(x * x) \ 1) = y * ((x * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(292,a,396,a),flip(a)].">
      <j1 rule="hyper" parents="292 396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      (x * x) \ ((x * x) / y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(140,a,402,a)].">
      <j1 rule="hyper" parents="140 402"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      (x * x) * ((1 / y) * z) = ((x * x) / y) * z
    ]]></literal>
    <justification jstring="[para(402(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="402 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,343,a(flip),b,430,a),flip(a)].">
      <j1 rule="hyper" parents="325 343 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(135,a,346,a(flip),b,430,a)].">
      <j1 rule="hyper" parents="135 346 430"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      K(x \ 1,x) \ (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(132,a,343,a(flip),b,430,a)].">
      <j1 rule="hyper" parents="132 343 430"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(284,a,100,a),flip(a)].">
      <j1 rule="hyper" parents="284 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(135,a,156,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="135 156 100"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,154,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="65 154 100"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      L(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,33,a,b,100,a),flip(a)].">
      <j1 rule="hyper" parents="36 33 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) * z)),x,y) = z
    ]]></literal>
    <justification jstring="[hyper(36,a,78,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="36 78 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      ((x * y) * (L(z,y,x) * u)) \ ((x * (y * z)) * u) = a(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(100(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="100 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="450">
    <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="451">
    <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="452">
    <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="453">
    <literal><![CDATA[
      ((x * (y * z)) * L(u,z,y)) / (y * (z * u)) = R(x,y * z,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(100(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="100 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="454">
    <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="455">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(100(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="100 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="100 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="457">
    <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),93(a,1,1))].">
      <j1 rule="para" parents="100 93"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(262(a,2),100(a,1,1))].">
      <j1 rule="para" parents="262 100"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      (x * (y * z)) * L(u,L(z,y,x),x * y) = (x * y) * (L(z,y,x) * u)
    ]]></literal>
    <justification jstring="[para(100(a,1),100(a,1,1))].">
      <j1 rule="para" parents="100 100"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      a(x * x,y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,447,a)].">
      <j1 rule="hyper" parents="55 447"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      L(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(447(a,1),52(a,2))].">
      <j1 rule="para" parents="447 52"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      L(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(277(a,1),447(a,1,3))].">
      <j1 rule="para" parents="277 447"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      L(x,y,(z \ 1) / z) = x
    ]]></literal>
    <justification jstring="[para(420(a,1),447(a,1,3))].">
      <j1 rule="para" parents="420 447"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      L(x,a(y * y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(460(a,2),350(a,1,2))].">
      <j1 rule="para" parents="460 350"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      (((x \ 1) / x) * y) * z = ((x \ 1) / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,463,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 463 18"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(325,a,237,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="325 237 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,232,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="325 232 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(325,a,170,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="325 170 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,159,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="325 159 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(216,a,102,a),flip(a)].">
      <j1 rule="hyper" parents="216 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = K(x,y) * u
    ]]></literal>
    <justification jstring="[hyper(137,a,153,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="137 153 102"/>
    </justification>
  </clause>

  <clause id="472">
    <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="473">
    <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="474">
    <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="475">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(102(a,2),304(a,1))].">
      <j1 rule="para" parents="102 304"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      L(x \ K(y \ z,y),x,z) = (z * x) \ ((y \ z) * y)
    ]]></literal>
    <justification jstring="[para(313(a,1),102(a,2,2))].">
      <j1 rule="para" parents="313 102"/>
    </justification>
  </clause>

  <clause id="477">
    <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="478">
    <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="479">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,466,a(flip),b,153,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 466 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,311,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="132 311 109"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(132,a,155,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="132 155 109"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(132,a,154,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="132 154 109"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,10,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="132 10 109"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,156,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="65 156 109"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,34,a(flip),b,109,a),flip(a)].">
      <j1 rule="hyper" parents="37 34 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      R(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(37,a,33,a(flip),b,109,a),flip(a)].">
      <j1 rule="hyper" parents="37 33 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,109,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="132 109 100"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),46(a,1))].">
      <j1 rule="para" parents="109 46"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="109 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),485(a,1,3))].">
      <j1 rule="para" parents="7 485"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      R(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(277(a,1),485(a,1,3))].">
      <j1 rule="para" parents="277 485"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      R(x,y,1) = z \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,9,a,b,491,a),flip(a)].">
      <j1 rule="hyper" parents="325 9 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(491(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="491 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,180,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="325 180 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),110(a,2,2))].">
      <j1 rule="para" parents="10 110"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),110(a,2,2))].">
      <j1 rule="para" parents="12 110"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="110 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(110(a,2),115(a,1,1))].">
      <j1 rule="para" parents="110 115"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      R((x \ 1) / y,y,x) = K(x \ 1,x) / (y * x)
    ]]></literal>
    <justification jstring="[para(262(a,2),110(a,2,1))].">
      <j1 rule="para" parents="262 110"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      (x * L(y,z,u)) / (L(y,z,u) * y) = R(x / y,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(249(a,2),110(a,2,2)),flip(a)].">
      <j1 rule="para" parents="249 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(109(a,1),110(a,2,1))].">
      <j1 rule="para" parents="109 110"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),110(a,2,2))].">
      <j1 rule="para" parents="109 110"/>
    </justification>
  </clause>

  <clause id="506">
    <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),192(a,1,2,1))].">
      <j1 rule="para" parents="100 192"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),193(a,1,1,2))].">
      <j1 rule="para" parents="12 193"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,30,a,b,261,a)].">
      <j1 rule="hyper" parents="132 30 261"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      ((x \ (1 / x)) \ 1) * y = (x \ (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,462,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 462 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      (K(x,y) \ 1) * z = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(132,a,153,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 153 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="65 233 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      (K(x,y) \ 1) * (K(x,y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(36,a,153,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="36 153 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      ((x \ 1) * y) / L(y,x \ 1,x) = R(1 / x,x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(201,a,261,a(flip),b,365,a)].">
      <j1 rule="hyper" parents="201 261 365"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      L(x,y \ 1,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(261(a,1),45(a,1))].">
      <j1 rule="para" parents="261 45"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(385(a,1),510(a,1,1)),flip(a)].">
      <j1 rule="para" parents="385 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[para(385(a,1),512(a,1,1))].">
      <j1 rule="para" parents="385 512"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[para(433(a,1),512(a,1,1))].">
      <j1 rule="para" parents="433 512"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,30,a,b,263,a)].">
      <j1 rule="hyper" parents="132 30 263"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(265(a,1),144(a,1,1))].">
      <j1 rule="para" parents="265 144"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(9(a,1),299(a,1,2,2,2))].">
      <j1 rule="para" parents="9 299"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      (K(x,y) * z) \ u = z \ (K(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(216,a,308,a),flip(a)].">
      <j1 rule="hyper" parents="216 308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ u) = K(y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(137,a,308,a(flip),b,153,a(flip))].">
      <j1 rule="hyper" parents="137 308 153"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(308(a,1),25(a,2,1))].">
      <j1 rule="para" parents="308 25"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(308(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="308 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(308(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="308 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      L(x,y,z) != (z * y) \ u
    ]]></literal>
    <literal><![CDATA[
      y \ (z \ u) = x
    ]]></literal>
    <justification jstring="[para(308(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="308 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(85(a,1),308(a,1,1))].">
      <j1 rule="para" parents="85 308"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(82(a,1),327(a,1,1,1))].">
      <j1 rule="para" parents="82 327"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(194(a,1),327(a,1,1,1))].">
      <j1 rule="para" parents="194 327"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),328(a,1,1))].">
      <j1 rule="para" parents="11 328"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(82(a,1),328(a,1,1))].">
      <j1 rule="para" parents="82 328"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(161(a,1),328(a,1,1))].">
      <j1 rule="para" parents="161 328"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      x \ y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x \ y) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),329(a,1,2))].">
      <j1 rule="para" parents="10 329"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x * (u * (u \ y)) = z
    ]]></literal>
    <justification jstring="[para(77(a,1),331(a,1,2))].">
      <j1 rule="para" parents="77 331"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      x * (y / (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(190(a,2),331(a,1,2))].">
      <j1 rule="para" parents="190 331"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(198(a,2),331(a,1,2))].">
      <j1 rule="para" parents="198 331"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(261(a,1),331(a,1))].">
      <j1 rule="para" parents="261 331"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(102(a,2),336(a,1))].">
      <j1 rule="para" parents="102 336"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(12(a,2),370(a,1,1))].">
      <j1 rule="para" parents="12 370"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(161(a,1),370(a,1,1))].">
      <j1 rule="para" parents="161 370"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(110(a,2),375(a,1))].">
      <j1 rule="para" parents="110 375"/>
    </justification>
  </clause>

  <clause id="542">
    <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),381(a,1))].">
      <j1 rule="para" parents="27 381"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(444(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="444 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      T((x \ 1) \ y,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(468(a,1),184(a,1,2))].">
      <j1 rule="para" parents="468 184"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      R(x / y,y,T(z,x)) \ (z * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,232,a(flip),b,482,a)].">
      <j1 rule="hyper" parents="65 232 482"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(407(a,1),520(a,1))].">
      <j1 rule="para" parents="407 520"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(155(a,2),530(a,1))].">
      <j1 rule="para" parents="155 530"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(156(a,2),530(a,1))].">
      <j1 rule="para" parents="156 530"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),531(a,1,2))].">
      <j1 rule="para" parents="10 531"/>
    </justification>
  </clause>

  <clause id="550">
    <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),531(a,1,2))].">
      <j1 rule="para" parents="14 531"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      x * ((y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(z \ 1,z,y) = u
    ]]></literal>
    <justification jstring="[para(362(a,1),536(a,1,2,1))].">
      <j1 rule="para" parents="362 536"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(246,a,119,a),flip(a)].">
      <j1 rule="hyper" parents="246 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      ((x * x) \ (y / z)) * z = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,12,a(flip),b,119,a),flip(a)].">
      <j1 rule="hyper" parents="132 12 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      ((x * x) \ y) \ z = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,156,a(flip),b,119,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 156 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      (x * x) * ((((x * x) \ y) * z) * u) = (y * z) * u
    ]]></literal>
    <justification jstring="[para(119(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="119 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      ((x * x) * y) / z = (x * x) * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),120(a,1,1,2))].">
      <j1 rule="para" parents="12 120"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      (x \ (y \ 1)) * (z * z) = x \ (y \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(132,a,395,a(flip),b,125,a),flip(a)].">
      <j1 rule="hyper" parents="132 395 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      x \ (y * (z * (u * u))) = (x \ (y * z)) * (u * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,34,a(flip),b,125,a)].">
      <j1 rule="hyper" parents="132 34 125"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      (x \ (y / (z * z))) * (z * z) = x \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,12,a(flip),b,125,a),flip(a)].">
      <j1 rule="hyper" parents="132 12 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      ((x * y) \ x) * (y * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,100,a,b,125,a),flip(a)].">
      <j1 rule="hyper" parents="36 100 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      (x \ y) * ((y \ x) * (y \ x)) = L(y \ x,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),560(a,1,1,1))].">
      <j1 rule="para" parents="10 560"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      (x * (y * (z * z))) / (u * (z * z)) = (x * y) / u
    ]]></literal>
    <justification jstring="[hyper(135,a,34,a(flip),b,126,a)].">
      <j1 rule="hyper" parents="135 34 126"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      (x / (y / (z * z))) * y = x * (z * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),126(a,1,2))].">
      <j1 rule="para" parents="12 126"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      (x / (y \ 1)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[para(221(a,1),126(a,1,2))].">
      <j1 rule="para" parents="221 126"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      T(x / (y \ 1),y) = y \ (x * (y * y))
    ]]></literal>
    <justification jstring="[hyper(284,a,564,a)].">
      <j1 rule="hyper" parents="284 564"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      (x * (y * y)) / y = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,564,a)].">
      <j1 rule="hyper" parents="145 564"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      T(x / (x \ 1),x) = x * x
    ]]></literal>
    <justification jstring="[hyper(246,a,564,a(flip))].">
      <j1 rule="hyper" parents="246 564"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,309,a(flip),b,566,a(flip))].">
      <j1 rule="hyper" parents="136 309 566"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      (x / y) * (y \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,158,a(flip),b,566,a(flip))].">
      <j1 rule="hyper" parents="136 158 566"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      (x * y) / (y * y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,87,a(flip),b,566,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 87 566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      R(x,x \ y,x \ y) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(528,a,568,a),flip(a)].">
      <j1 rule="hyper" parents="528 568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      R(x / y,y,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(327,a,568,a),flip(a)].">
      <j1 rule="hyper" parents="327 568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      (x * y) \ R(x,y,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(140,a,568,a)].">
      <j1 rule="hyper" parents="140 568"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      L(R(x,y,y),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(135,a,29,a(flip),b,568,a)].">
      <j1 rule="hyper" parents="135 29 568"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      x * ((y * y) \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,485,a(flip),b,572,a),flip(a)].">
      <j1 rule="hyper" parents="65 485 572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      R(T(x / y,z),y,y) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(572(a,1),27(a,2,1))].">
      <j1 rule="para" parents="572 27"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * y) = y * y
    ]]></literal>
    <justification jstring="[para(572(a,1),482(a,1,1))].">
      <j1 rule="para" parents="572 482"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      x / ((y \ x) * (y \ x)) = y * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,569,a),flip(a)].">
      <j1 rule="hyper" parents="334 569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * x)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(284,a,569,a),flip(a)].">
      <j1 rule="hyper" parents="284 569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      (x * x) \ 1 = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(132,a,271,a(flip),b,575,a),flip(a)].">
      <j1 rule="hyper" parents="132 271 575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      (x \ (x \ 1)) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[para(580(a,1),396(a,1,1))].">
      <j1 rule="para" parents="580 396"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      x * (y \ (y \ 1)) = x / (y * y)
    ]]></literal>
    <justification jstring="[para(580(a,1),575(a,1,2))].">
      <j1 rule="para" parents="580 575"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) * (z * z) = x * ((y * y) \ (z * z))
    ]]></literal>
    <justification jstring="[para(581(a,1),34(a,2,2))].">
      <j1 rule="para" parents="581 34"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,100,a(flip),b,242,a)].">
      <j1 rule="hyper" parents="65 100 242"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,242,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="132 242 100"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),242(a,1,2,1))].">
      <j1 rule="para" parents="22 242"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(235(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="235 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(114(a,1),242(a,1,2,1))].">
      <j1 rule="para" parents="114 242"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,109,a(flip),b,243,a),flip(a)].">
      <j1 rule="hyper" parents="325 109 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,109,a(flip),b,243,a)].">
      <j1 rule="hyper" parents="132 109 243"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(235(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="235 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(114(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="114 243"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      T(x / (y \ 1),y) = (y \ x) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(245,a,564,a,b,125,a)].">
      <j1 rule="hyper" parents="245 564 125"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(245,a,337,a,b,405,a)].">
      <j1 rule="hyper" parents="245 337 405"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      T(x \ 1,x * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(245,a,221,a,b,227,a)].">
      <j1 rule="hyper" parents="245 221 227"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      ((x * x) \ y) * (z * (x * x)) = T(y * z,x * x)
    ]]></literal>
    <justification jstring="[hyper(245,a,34,a,b,119,a),flip(a)].">
      <j1 rule="hyper" parents="245 34 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(245,a,233,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="245 233 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      ((x * x) \ y) \ y = T(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,156,a(flip),b,119,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 156 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a(flip),b,599,a)].">
      <j1 rule="hyper" parents="65 25 599"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(599(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="599 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(599(a,1),242(a,1,2))].">
      <j1 rule="para" parents="599 242"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(599(a,2),243(a,1,2,1))].">
      <j1 rule="para" parents="599 243"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,274,a,b,601,a)].">
      <j1 rule="hyper" parents="42 274 601"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      x * L(T(y,y * x),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(601(a,1),242(a,1,2,1))].">
      <j1 rule="para" parents="601 242"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[hyper(325,a,85,a(flip),b,596,a),flip(a)].">
      <j1 rule="hyper" parents="325 85 596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(606(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="606 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(275,a,252,a)].">
      <j1 rule="hyper" parents="275 252"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      x * L(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(252(a,1),292(a,1,2))].">
      <j1 rule="para" parents="252 292"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(275,a,253,a)].">
      <j1 rule="hyper" parents="275 253"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(226(a,1),253(a,1,1))].">
      <j1 rule="para" parents="226 253"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),253(a,1,1))].">
      <j1 rule="para" parents="110 253"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(310(a,1),253(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      T(x * (y \ 1),y) = R(y \ x,y,y)
    ]]></literal>
    <justification jstring="[para(572(a,1),253(a,1,1))].">
      <j1 rule="para" parents="572 253"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,614,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 614 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(614(a,1),292(a,1,2))].">
      <j1 rule="para" parents="614 292"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),618(a,2,1))].">
      <j1 rule="para" parents="9 618"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) * x = x * R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,621,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 621 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(284,a,287,a),flip(a)].">
      <j1 rule="hyper" parents="284 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      K(x,y) \ (z * u) = (K(x,y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(132,a,155,a(flip),b,287,a(flip))].">
      <j1 rule="hyper" parents="132 155 287"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,109,a,b,287,a(flip))].">
      <j1 rule="hyper" parents="37 109 287"/>
    </justification>
  </clause>

  <clause id="626">
    <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(287(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="287 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(287(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="287 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(287(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="287 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(287(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="287 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      ((K(x,y) * (z * u)) * w) / (u * w) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(287(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="287 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      x \ (K(y,z) * (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * u,x) = w
    ]]></literal>
    <justification jstring="[para(287(a,1),301(a,1,2))].">
      <j1 rule="para" parents="287 301"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * u) = (K(x,y) / z) * u
    ]]></literal>
    <justification jstring="[para(430(a,1),287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="430 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(440(a,1),287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="440 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,y) * a(K(w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(325,a,127,a,b,625,a),flip(a)].">
      <j1 rule="hyper" parents="325 127 625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      R(K(x,y),z,u) = w / (K(x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,82,a,b,625,a),flip(a)].">
      <j1 rule="hyper" parents="325 82 625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(625(a,1),27(a,2,1))].">
      <j1 rule="para" parents="625 27"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(635(a,2),294(a,1)),flip(b)].">
      <j1 rule="para" parents="635 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      T(T(x,x \ y),z) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(245,a,319,a,b,113,a)].">
      <j1 rule="hyper" parents="245 319 113"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,(x \ y) \ y) = u
    ]]></literal>
    <justification jstring="[para(319(a,2),316(a,1,1))].">
      <j1 rule="para" parents="319 316"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,94,a(flip),b,382,a)].">
      <j1 rule="hyper" parents="325 94 382"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),643(a,1,1,2))].">
      <j1 rule="para" parents="12 643"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      T(x,y * y) / (y * y) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(135,a,22,a,b,390,a(flip))].">
      <j1 rule="hyper" parents="135 22 390"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      (x * x) \ (x * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(273(a,1),391(a,2,1))].">
      <j1 rule="para" parents="273 391"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      x * ((1 / x) \ y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(330,a,647,a),flip(a)].">
      <j1 rule="hyper" parents="330 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      L(x \ y,x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,102,a,b,647,a)].">
      <j1 rule="hyper" parents="65 102 647"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a,b,647,a),flip(a)].">
      <j1 rule="hyper" parents="65 18 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(132,a,18,a,b,647,a(flip))].">
      <j1 rule="hyper" parents="132 18 647"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      x \ ((x * x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,76,a(flip),b,647,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 76 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      (1 / x) * (x \ y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),647(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      ((1 / x) * y) \ 1 = (x * y) \ (x * x)
    ]]></literal>
    <justification jstring="[para(647(a,1),434(a,1,1))].">
      <j1 rule="para" parents="647 434"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      L(T(x,y),y,y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),649(a,1,1))].">
      <j1 rule="para" parents="22 649"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      L(T(x \ y,z),x,x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(649(a,1),25(a,2,1))].">
      <j1 rule="para" parents="649 25"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(649(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="649 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(649(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="649 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      L(x,y / x,y / x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[para(85(a,1),649(a,1,1))].">
      <j1 rule="para" parents="85 649"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      L(x \ y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(650(a,1),331(a,1))].">
      <j1 rule="para" parents="650 331"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      (1 / L(x,y,z)) \ L(x,L(x,y,z),L(x,y,z)) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,249,a(flip),b,651,a),flip(a)].">
      <j1 rule="hyper" parents="325 249 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      (1 / x) \ y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x) = y
    ]]></literal>
    <justification jstring="[para(651(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="651 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(82(a,1),648(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      (x \ 1) * (1 / x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,342,a(flip),b,653,a)].">
      <j1 rule="hyper" parents="65 342 653"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      (x \ 1) * (1 / x) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,580,a(flip),b,664,a),flip(a)].">
      <j1 rule="hyper" parents="325 580 664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      (K(x,y) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),419(a,1,1,2))].">
      <j1 rule="para" parents="12 419"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      (K(x,y) * z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(419(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="419 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(419(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="419 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      (K(x,y) * z) * u != w * v5
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * (z * u)) / v5 = w
    ]]></literal>
    <justification jstring="[para(419(a,1),370(a,1,1))].">
      <j1 rule="para" parents="419 370"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,250,a(flip),b,424,a),flip(a)].">
      <j1 rule="hyper" parents="135 250 424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(425(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="425 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(426(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="426 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      (K(x,y) \ z) \ u = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(336,a,470,a),flip(a)].">
      <j1 rule="hyper" parents="336 470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x * K(y,z)) \ (K(y,z) * u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(113(a,1),470(a,1,1))].">
      <j1 rule="para" parents="113 470"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      (K(x,y) \ z) \ z = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(245,a,471,a(flip),b,155,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 471 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(341,a,677,a)].">
      <j1 rule="hyper" parents="341 677"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(430(a,1),479(a,1,1))].">
      <j1 rule="para" parents="430 479"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(65,a,442,a(flip),b,515,a),flip(a)].">
      <j1 rule="hyper" parents="65 442 515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(515(a,1),148(a,1))].">
      <j1 rule="para" parents="515 148"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      K(x,x \ 1) * x = (1 / x) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(136,a,680,a(flip),b,570,a),flip(a)].">
      <j1 rule="hyper" parents="136 680 570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,680,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 680 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      (K(x,y) \ z) * (z \ u) = K(x,y) \ u
    ]]></literal>
    <justification jstring="[hyper(137,a,159,a(flip),b,521,a(flip))].">
      <j1 rule="hyper" parents="137 159 521"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      T(x * y,(x \ 1) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(56,a,544,a)].">
      <j1 rule="hyper" parents="56 544"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      K(x * x,(x * x) \ y) = T(y,x * x) \ y
    ]]></literal>
    <justification jstring="[para(552(a,1),95(a,1,1)),flip(a)].">
      <j1 rule="para" parents="552 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      ((x * x) \ y) / z = (x * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,553,a)].">
      <j1 rule="hyper" parents="145 553"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      (x * x) \ ((x * y) / z) = ((1 / x) * y) / z
    ]]></literal>
    <justification jstring="[hyper(135,a,647,a(flip),b,553,a),flip(a)].">
      <j1 rule="hyper" parents="135 647 553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      (x * (y * y)) \ ((y * y) * z) = T(x,y * y) \ z
    ]]></literal>
    <justification jstring="[para(22(a,2),554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ u = (y * z) \ ((x * x) * u)
    ]]></literal>
    <justification jstring="[para(391(a,1),554(a,1,1))].">
      <j1 rule="para" parents="391 554"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      (x * y) \ ((x * x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(647(a,1),554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="647 554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      (x * x) * (y / (x * y)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,20,a,b,556,a),flip(a)].">
      <j1 rule="hyper" parents="65 20 556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      (x * x) * ((x \ y) / y) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),693(a,1,2,2))].">
      <j1 rule="para" parents="10 693"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      (x \ y) / (z * z) = x \ (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(145,a,559,a)].">
      <j1 rule="hyper" parents="145 559"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      (x * (y * y)) / z = x / (z / (y * y))
    ]]></literal>
    <justification jstring="[hyper(145,a,563,a)].">
      <j1 rule="hyper" parents="145 563"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      (x * (y * (z * z))) / u = (x * y) / (u / (z * z))
    ]]></literal>
    <justification jstring="[hyper(135,a,34,a(flip),b,563,a)].">
      <j1 rule="hyper" parents="135 34 563"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      (x * (y * y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / (y * y)) = u
    ]]></literal>
    <justification jstring="[para(563(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="563 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      (K(x,y) \ 1) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(624(a,1),305(a,1))].">
      <j1 rule="para" parents="624 305"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      L(x \ y,x,y) = ((1 / y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,102,a,b,654,a)].">
      <j1 rule="hyper" parents="325 102 654"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      (K(x,y) * z) / u != K(x,y) * w
    ]]></literal>
    <literal><![CDATA[
      z / u = w
    ]]></literal>
    <justification jstring="[para(666(a,2),45(a,1))].">
      <j1 rule="para" parents="666 45"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      K(x,x \ 1) * x = L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,650,a(flip),b,682,a),flip(a)].">
      <j1 rule="hyper" parents="325 650 682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      x \ (y / ((z \ 1) * (z \ 1))) = (x \ y) / ((z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(420(a,1),695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="420 695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      (x * y) / (z * z) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(136,a,87,a(flip),b,696,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 87 696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      (x \ (y * (z / (u * u)))) * (u * u) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(704(a,1),559(a,1,1,2))].">
      <j1 rule="para" parents="704 559"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),89(a,1,1,2))].">
      <j1 rule="para" parents="10 89"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      (x * y) * a(x,y / z,z) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),89(a,1,1,2))].">
      <j1 rule="para" parents="12 89"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(89(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="89 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      x * a(y,z,z \ (y \ x)) = (y * z) * (z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(78(a,1),89(a,1,1))].">
      <j1 rule="para" parents="78 89"/>
    </justification>
  </clause>

  <clause id="711">
    <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(89(a,1),102(a,2,1))].">
      <j1 rule="para" parents="89 102"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      ((x * x) \ y) * ((y \ (x * x)) * z) = L(z,y \ (x * x),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,391,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="65 391 101"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      L(T(x,y),y,z / y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(113(a,1),103(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      (((x \ 1) / x) * y) / z = ((x \ 1) / x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(201,a,463,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="201 463 104"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),106(a,2,2))].">
      <j1 rule="para" parents="10 106"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      R(R(x,y,y \ z),u,w) * z = (R(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(136,a,31,a,b,108,a)].">
      <j1 rule="hyper" parents="136 31 108"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(136,a,29,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="136 29 108"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      T(R(x,y,y \ z),z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ ((x * y) * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),376(a,1,1))].">
      <j1 rule="para" parents="108 376"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      L(x,y \ 1,y) \ x = a(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(261(a,1),222(a,1,1))].">
      <j1 rule="para" parents="261 222"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(265(a,1),224(a,1,2))].">
      <j1 rule="para" parents="265 224"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(148,a,720,a)].">
      <j1 rule="hyper" parents="148 720"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(721(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="721 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,364,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="137 364 18"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),372(a,1,2,1))].">
      <j1 rule="para" parents="22 372"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,242,a(flip),b,414,a),flip(a)].">
      <j1 rule="hyper" parents="65 242 414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      (x * ((x \ y) * y)) / y = L(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,414,a(flip),b,249,a)].">
      <j1 rule="hyper" parents="135 414 249"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,242,a(flip),b,414,a(flip))].">
      <j1 rule="hyper" parents="132 242 414"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      x * ((x \ y) * z) != y * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(414(a,1),45(a,1))].">
      <j1 rule="para" parents="414 45"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(414(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="414 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,156,a(flip),b,445,a),flip(a)].">
      <j1 rule="hyper" parents="245 156 445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,242,a(flip),b,445,a(flip))].">
      <j1 rule="hyper" parents="132 242 445"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(469(a,1),25(a,2,1))].">
      <j1 rule="para" parents="469 25"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(469(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="469 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(469(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="469 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      L(L(x \ 1,x,y) \ z,(y * x) \ y,y * x) = y \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(225(a,2),469(a,1,1,1))].">
      <j1 rule="para" parents="225 469"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      ((x \ 1) / x) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(137,a,463,a(flip),b,472,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 463 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(82(a,1),480(a,1,1,1))].">
      <j1 rule="para" parents="82 480"/>
    </justification>
  </clause>

  <clause id="739">
    <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),481(a,1,1))].">
      <j1 rule="para" parents="29 481"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      x \ (y * (z \ (1 / z))) = (x \ y) * (z \ (1 / z))
    ]]></literal>
    <justification jstring="[para(492(a,1),481(a,1,1))].">
      <j1 rule="para" parents="492 481"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(132,a,484,a(flip),b,243,a)].">
      <j1 rule="hyper" parents="132 484 243"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(496(a,2),296(a,1))].">
      <j1 rule="para" parents="496 296"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(497(a,1),27(a,2,1))].">
      <j1 rule="para" parents="497 27"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(497(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="497 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(497(a,1),253(a,1,1)),flip(a)].">
      <j1 rule="para" parents="497 253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      (x \ (1 / x)) \ 1 = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(132,a,492,a(flip),b,571,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 492 571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[hyper(135,a,576,a(flip),b,568,a)].">
      <j1 rule="hyper" parents="135 576 568"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      ((x * y) / (z * y)) * z = z * R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,615,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 615 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),615(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,655,a(flip),b,656,a)].">
      <j1 rule="hyper" parents="65 655 656"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,656,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="132 656 650"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      (((x * y) * z) / (x * z)) * x = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,749,a,b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 749 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(181(a,1),749(a,2,1)),flip(a)].">
      <j1 rule="para" parents="181 749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(749(a,2),274(a,1,1))].">
      <j1 rule="para" parents="749 274"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,755,a)].">
      <j1 rule="hyper" parents="65 27 755"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(755(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="755 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),756(a,1,1,2))].">
      <j1 rule="para" parents="12 756"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(203(a,1),758(a,1,1))].">
      <j1 rule="para" parents="203 758"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(135,a,759,a(flip),b,266,a)].">
      <j1 rule="hyper" parents="135 759 266"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,264,a,b,760,a),flip(a)].">
      <j1 rule="hyper" parents="325 264 760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) != v5
    ]]></literal>
    <literal><![CDATA[
      (R(x,u,w) * y) * z = v5
    ]]></literal>
    <justification jstring="[para(31(a,1),291(a,1,1))].">
      <j1 rule="para" parents="31 291"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,1),298(a,1,2))].">
      <j1 rule="para" parents="25 298"/>
    </justification>
  </clause>

  <clause id="768">
    <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),298(a,1,2))].">
      <j1 rule="para" parents="29 298"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      (x * x) * (((1 / y) * z) * u) = (((x * x) / y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,439,a(flip),b,120,a),flip(a)].">
      <j1 rule="hyper" parents="136 439 120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      ((1 / x) * y) \ ((z * z) \ u) = (((z * z) / x) * y) \ u
    ]]></literal>
    <justification jstring="[para(439(a,1),393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="439 393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="771">
    <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(93(a,1),455(a,1,1)),flip(a)].">
      <j1 rule="para" parents="93 455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="113 456"/>
    </justification>
  </clause>

  <clause id="774">
    <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),456(a,1,2,2))].">
      <j1 rule="para" parents="100 456"/>
    </justification>
  </clause>

  <clause id="775">
    <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(89(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="89 456"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      (x * y) * T(z,y) != u * (z * y)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),489(a,2,2))].">
      <j1 rule="para" parents="113 489"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (x \ (1 / x)) \ y = ((1 / x) \ x) * y
    ]]></literal>
    <justification jstring="[para(746(a,1),509(a,1,1)),flip(a)].">
      <j1 rule="para" parents="746 509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(z \ L(u,y,x),z,x * y) = w
    ]]></literal>
    <justification jstring="[para(100(a,1),543(a,1,2))].">
      <j1 rule="para" parents="100 543"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) \ 1) = y \ (x * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(132,a,578,a(flip),b,582,a),flip(a)].">
      <j1 rule="hyper" parents="132 578 582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      L(R(1 / x,x,y),z,u) * (x * y) = (x * y) * L((x * y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(226(a,2),587(a,1,1,1))].">
      <j1 rule="para" parents="226 587"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      L(R(x / y,y,z),u,w) * (y * z) = (y * z) * L((y * z) \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(110(a,2),587(a,1,1,1))].">
      <j1 rule="para" parents="110 587"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      L(R(1 / x,x,x \ y),z,u) * y = y * L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(366(a,2),587(a,1,1,1))].">
      <j1 rule="para" parents="366 587"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,588,a),flip(a)].">
      <j1 rule="hyper" parents="145 588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(135,a,100,a(flip),b,588,a),flip(a)].">
      <j1 rule="hyper" parents="135 100 588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      R(R(1 / x,x,y),z,u) * (x * y) = (x * y) * R((x * y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(226(a,2),592(a,1,1,1))].">
      <j1 rule="para" parents="226 592"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      R(R(x / y,y,z),u,w) * (y * z) = (y * z) * R((y * z) \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(110(a,2),592(a,1,1,1))].">
      <j1 rule="para" parents="110 592"/>
    </justification>
  </clause>

  <clause id="788">
    <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(315(a,1),592(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="315 592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(291,a,593,a)].">
      <j1 rule="hyper" parents="291 593"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,593,a),flip(a)].">
      <j1 rule="hyper" parents="145 593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      (((x * y) / x) * z) * (z \ x) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,484,a(flip),b,593,a)].">
      <j1 rule="hyper" parents="65 484 593"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      (x * R(y,z,z \ x)) / (z \ x) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(135,a,593,a(flip),b,484,a(flip))].">
      <j1 rule="hyper" parents="135 593 484"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(611(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="611 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(308(a,1),611(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="308 611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(468(a,1),611(a,1,1,2))].">
      <j1 rule="para" parents="468 611"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(613(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="613 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      x * T(K(y,z) * u,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (u * x) = w
    ]]></literal>
    <justification jstring="[para(623(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="623 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      K(x,y) * (((1 / z) * u) / w) = ((K(x,y) / z) * u) / w
    ]]></literal>
    <justification jstring="[para(632(a,1),666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="632 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      R(K(x,y),z,u) * w = K(x,y) * (a(K(v5,v6),v7,v8) * w)
    ]]></literal>
    <justification jstring="[hyper(136,a,634,a,b,419,a)].">
      <j1 rule="hyper" parents="136 634 419"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (x \ 1) * (x \ (((x \ 1) \ y) / y)) = R(x \ 1,x \ 1,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,694,a(flip),b,663,a),flip(a)].">
      <j1 rule="hyper" parents="65 694 663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(275,a,670,a)].">
      <j1 rule="hyper" parents="275 670"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(137,a,670,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 670 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,683,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 683 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      ((1 / x) * y) \ L(z,x,x) = (x * y) \ (x * (x * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),692(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x
    ]]></literal>
    <justification jstring="[para(102(a,1),784(a,2,1,2))].">
      <j1 rule="para" parents="102 784"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(363(a,1),784(a,2,1,2))].">
      <j1 rule="para" parents="363 784"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(469(a,1),784(a,2,1,2))].">
      <j1 rule="para" parents="469 784"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,495,a(flip),b,790,a),flip(a)].">
      <j1 rule="hyper" parents="65 495 790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,790,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="136 790 20"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(790(a,2),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="790 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(310(a,1),790(a,2,1,2))].">
      <j1 rule="para" parents="310 790"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(495(a,1),790(a,2,1,2))].">
      <j1 rule="para" parents="495 790"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ ((x * z) * (z \ y)) = w
    ]]></literal>
    <justification jstring="[para(90(a,1),531(a,1,2))].">
      <j1 rule="para" parents="90 531"/>
    </justification>
  </clause>

  <clause id="816">
    <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),373(a,1,2,1))].">
      <j1 rule="para" parents="22 373"/>
    </justification>
  </clause>

  <clause id="817">
    <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(114(a,1),373(a,1,2,1))].">
      <j1 rule="para" parents="114 373"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      (x \ y) * L(T((x \ y) \ y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(x,z),u,w) * (x \ y) = v5
    ]]></literal>
    <justification jstring="[para(320(a,1),373(a,1,2,1))].">
      <j1 rule="para" parents="320 373"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(310(a,1),409(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="310 409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(102(a,1),416(a,1,2,1))].">
      <j1 rule="para" parents="102 416"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(308(a,1),416(a,1,2,1))].">
      <j1 rule="para" parents="308 416"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      L(x,y,y) * a(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,89,a(flip),b,454,a),flip(a)].">
      <j1 rule="hyper" parents="36 89 454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      (x * x) * ((L(y,x,x) * z) * u) = ((x * (x * y)) * z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,454,a(flip),b,120,a),flip(a)].">
      <j1 rule="hyper" parents="136 454 120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(140,a,822,a)].">
      <j1 rule="hyper" parents="140 822"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(376,a,498,a),flip(a)].">
      <j1 rule="hyper" parents="376 498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      T((K(x,y) * z) \ u,w) = T(z \ (K(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(216,a,523,a),flip(a)].">
      <j1 rule="hyper" parents="216 523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="827">
    <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(523(a,1),298(a,1,2))].">
      <j1 rule="para" parents="523 298"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(194(a,1),545(a,1,1,1))].">
      <j1 rule="para" parents="194 545"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(572(a,1),574(a,1,1,1))].">
      <j1 rule="para" parents="572 574"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      L(x * ((y \ x) \ 1),z,u) / ((y \ x) \ 1) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(571(a,1),574(a,1,1,1))].">
      <j1 rule="para" parents="571 574"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      (x \ L(y,x,x)) * (x * x) = x * T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(36,a,125,a,b,584,a)].">
      <j1 rule="hyper" parents="36 125 584"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      x * (y * R(T(z,x * y),u,w)) = L(R(z,u,w),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(27(a,2),584(a,1,2,2))].">
      <j1 rule="para" parents="27 584"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (x * T(y,x * x)) / (x * x) = x \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,585,a(flip),b,390,a(flip))].">
      <j1 rule="hyper" parents="135 585 390"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      (x * y) * z != (u * x) * y
    ]]></literal>
    <literal><![CDATA[
      R(T(u,x * y),x,y) = z
    ]]></literal>
    <justification jstring="[para(590(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="590 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(z,x * y),x,y) = u
    ]]></literal>
    <justification jstring="[para(590(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="590 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[para(756(a,1),590(a,1,2))].">
      <j1 rule="para" parents="756 590"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(327,a,837,a),flip(a)].">
      <j1 rule="hyper" parents="327 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(132,a,73,a(flip),b,837,a)].">
      <j1 rule="hyper" parents="132 73 837"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(262(a,2),840(a,1,1))].">
      <j1 rule="para" parents="262 840"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      K(x \ 1,x) \ x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,114,a(flip),b,841,a),flip(a)].">
      <j1 rule="hyper" parents="325 114 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(135,a,841,a(flip),b,515,a(flip))].">
      <j1 rule="hyper" parents="135 841 515"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,515,a(flip),b,842,a)].">
      <j1 rule="hyper" parents="65 515 842"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      L(x,x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,702,a(flip),b,846,a)].">
      <j1 rule="hyper" parents="65 702 846"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      1 / L(x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,702,a(flip),b,846,a(flip))].">
      <j1 rule="hyper" parents="201 702 846"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,846,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 846 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(846(a,1),471(a,1,1))].">
      <j1 rule="para" parents="846 471"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,319,a,b,850,a),flip(a)].">
      <j1 rule="hyper" parents="325 319 850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,852,a(flip),b,262,a),flip(a)].">
      <j1 rule="hyper" parents="134 852 262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(852(a,1),520(a,1))].">
      <j1 rule="para" parents="852 520"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,25,a,b,610,a),flip(a)].">
      <j1 rule="hyper" parents="325 25 610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * T((x \ z) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(82(a,1),671(a,1,1,1))].">
      <j1 rule="para" parents="82 671"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(135,a,706,a(flip),b,113,a)].">
      <j1 rule="hyper" parents="135 706 113"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      (x * y) \ ((x * z) * (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(706(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="706 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,838,a(flip),b,707,a)].">
      <j1 rule="hyper" parents="132 838 707"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a(flip),b,713,a)].">
      <j1 rule="hyper" parents="65 25 713"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(359(a,1),728(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="359 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(469(a,1),728(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="469 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      (x \ 1) \ (L(y,L(x,x,x),x \ 1) * 1) = ((x \ 1) \ 1) * T(y,1)
    ]]></literal>
    <justification jstring="[para(848(a,2),728(a,1,2,1,2))].">
      <j1 rule="para" parents="848 728"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      (x / y) \ ((x \ (x / y)) * x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(363(a,1),732(a,1,2,1))].">
      <j1 rule="para" parents="363 732"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),741(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),795(a,2,1,2,1))].">
      <j1 rule="para" parents="12 795"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(22(a,2),795(a,2,1,2))].">
      <j1 rule="para" parents="22 795"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      (x * (y * (x \ 1))) / x = (x * (y / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(495(a,1),810(a,1,1,2))].">
      <j1 rule="para" parents="495 810"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      R(R(T(x / y,y * z),u,w),y,z) = R((y * z) \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(825(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="825 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      x * (T(y,x * x) / (x * x)) = x \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,704,a(flip),b,833,a)].">
      <j1 rule="hyper" parents="65 704 833"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(363(a,1),861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="363 861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      (1 / x) \ (y * (x \ (1 / x))) = T(y / x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,492,a(flip),b,866,a),flip(a)].">
      <j1 rule="hyper" parents="65 492 866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      x * ((x * x) \ y) = x \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(645(a,1),871(a,1,2))].">
      <j1 rule="para" parents="645 871"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      L((x * x) * y,x,x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,157,a(flip),b,874,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 157 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * x = x * L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(30(a,1),339(a,1,1))].">
      <j1 rule="para" parents="30 339"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      (x * x) \ T(y,(x * x) \ 1) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,575,a(flip),b,437,a),flip(a)].">
      <j1 rule="hyper" parents="325 575 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      (x * x) \ T(y,x \ (x \ 1)) = y / (x * x)
    ]]></literal>
    <justification jstring="[para(580(a,1),877(a,1,2,2))].">
      <j1 rule="para" parents="580 877"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      (x * x) * (y * (z / (x * x))) = T(y * z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(137,a,704,a(flip),b,878,a)].">
      <j1 rule="hyper" parents="137 704 878"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      (1 / x) \ (y / (x * x)) = x \ T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(132,a,878,a(flip),b,653,a)].">
      <j1 rule="hyper" parents="132 878 653"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = ((x \ 1) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(737(a,1),465(a,1,1))].">
      <j1 rule="para" parents="737 465"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      x \ (y * (z * (u * (w * w)))) = (x \ (y * (z * u))) * (w * w)
    ]]></literal>
    <justification jstring="[para(34(a,1),558(a,1,2,2))].">
      <j1 rule="para" parents="34 558"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      ((x * y) * (z * (u * u))) / ((y * z) * (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,20,a,b,562,a),flip(a)].">
      <j1 rule="hyper" parents="325 20 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      T(x * (y / (z * z)),z * z) = ((z * z) \ x) * y
    ]]></literal>
    <justification jstring="[para(12(a,1),598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[para(221(a,1),598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="221 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      ((((x * x) \ y) * z) * u) \ w = ((y * z) * u) \ ((x * x) * w)
    ]]></literal>
    <justification jstring="[para(391(a,1),691(a,1,1,1))].">
      <j1 rule="para" parents="391 691"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) \ ((((x * y) \ 1) * x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      a((x * y) \ 1,x,y) = z
    ]]></literal>
    <justification jstring="[para(262(a,2),709(a,1,1))].">
      <j1 rule="para" parents="262 709"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / z = ((x \ 1) / x) * (y / z)
    ]]></literal>
    <justification jstring="[para(737(a,1),714(a,1,1))].">
      <j1 rule="para" parents="737 714"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,423,a(flip),b,747,a),flip(a)].">
      <j1 rule="hyper" parents="325 423 747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),751(a,1,2,1))].">
      <j1 rule="para" parents="8 751"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),751(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),802(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 802"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,398,a,b,803,a)].">
      <j1 rule="hyper" parents="65 398 803"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,382,a,b,862,a),flip(a)].">
      <j1 rule="hyper" parents="132 382 862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,94,a(flip),b,865,a)].">
      <j1 rule="hyper" parents="65 94 865"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,94,a(flip),b,865,a(flip))].">
      <j1 rule="hyper" parents="132 94 865"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y / x),y) = z
    ]]></literal>
    <justification jstring="[para(897(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="897 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(148,a,872,a),flip(a)].">
      <j1 rule="hyper" parents="148 872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      ((1 / x) \ y) * (x \ (1 / x)) = T(y / x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,740,a(flip),b,873,a)].">
      <j1 rule="hyper" parents="65 740 873"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = (x \ 1) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,737,a(flip),b,881,a),flip(a)].">
      <j1 rule="hyper" parents="325 737 881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / z = (x \ 1) * (x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(325,a,737,a(flip),b,888,a),flip(a)].">
      <j1 rule="hyper" parents="325 737 888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[para(891(a,1),384(a,1,2))].">
      <j1 rule="para" parents="891 384"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(225(a,2),895(a,1,1,1))].">
      <j1 rule="para" parents="225 895"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(262(a,2),899(a,1,2))].">
      <j1 rule="para" parents="262 899"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      (x * y) * z != x * (y * L(u,w,v5))
    ]]></literal>
    <literal><![CDATA[
      L(L(u,y,x),w,v5) = z
    ]]></literal>
    <justification jstring="[para(412(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="412 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(225(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="225 412"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(308(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="308 412"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(225(a,1),413(a,1,2,1))].">
      <j1 rule="para" parents="225 413"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(308(a,1),413(a,1,2,1))].">
      <j1 rule="para" parents="308 413"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,633,a,b,458,a)].">
      <j1 rule="hyper" parents="36 633 458"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * (x * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,517,a,b,458,a)].">
      <j1 rule="hyper" parents="36 517 458"/>
    </justification>
  </clause>

  <clause id="913">
    <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(523(a,1),458(a,1,2))].">
      <j1 rule="para" parents="523 458"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(331,a,911,a),flip(a)].">
      <j1 rule="hyper" parents="331 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(214,a,911,a),flip(a)].">
      <j1 rule="hyper" parents="214 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      x \ L(x * ((x \ 1) * y),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(261(a,2),508(a,1,2,1))].">
      <j1 rule="para" parents="261 508"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(468(a,1),508(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="468 508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(358(a,1),518(a,1,2,1))].">
      <j1 rule="para" parents="358 518"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      (1 / x) \ R((x * x) \ y,z,u) = x * R(x \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,524,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="132 524 650"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      K(x \ 1,x) * R(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(524(a,1),458(a,1,2))].">
      <j1 rule="para" parents="524 458"/>
    </justification>
  </clause>

  <clause id="924">
    <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(525(a,1),298(a,1,2))].">
      <j1 rule="para" parents="525 298"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = (R(x,y,y) \ (x * y)) * ((y \ 1) * ((x * y) \ R(x,y,y)))
    ]]></literal>
    <justification jstring="[para(573(a,1),561(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="573 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(137,a,733,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="137 733 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,743,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="136 743 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[para(366(a,1),792(a,1,1,2))].">
      <j1 rule="para" parents="366 792"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(904(a,2),404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="904 404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,30,a,b,117,a)].">
      <j1 rule="hyper" parents="325 30 117"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      (x / (y * y)) * (z * z) = x * ((y * y) \ (z * z))
    ]]></literal>
    <justification jstring="[para(582(a,1),583(a,1,1))].">
      <j1 rule="para" parents="582 583"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      (x / (y * y)) * (z * z) = x * (((y * y) \ z) * z)
    ]]></literal>
    <justification jstring="[para(391(a,1),935(a,2,2))].">
      <j1 rule="para" parents="391 935"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      (x \ (y / (z * z))) * (u * u) = (x \ y) * (((z * z) \ u) * u)
    ]]></literal>
    <justification jstring="[para(695(a,1),936(a,1,1))].">
      <j1 rule="para" parents="695 936"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (x \ y) / ((z \ 1) / z) = x \ (y / ((z \ 1) / z))
    ]]></literal>
    <justification jstring="[para(420(a,1),703(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="420 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      R(T(x,y),z,z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * z) * (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(27(a,2),718(a,1))].">
      <j1 rule="para" parents="27 718"/>
    </justification>
  </clause>

  <clause id="940">
    <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(102(a,1),767(a,1,2,1))].">
      <j1 rule="para" parents="102 767"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * x) * ((((1 / y) * z) * u) * w) = ((((x * x) / y) * z) * u) * w
    ]]></literal>
    <justification jstring="[hyper(136,a,769,a(flip),b,120,a),flip(a)].">
      <j1 rule="hyper" parents="136 769 120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,587,a(flip),b,829,a),flip(a)].">
      <j1 rule="hyper" parents="325 587 829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      T(x * (y * z),z \ (z \ 1)) = (z * z) * (x * (y * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(570(a,1),879(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="570 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),918(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ (x \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(78(a,1),918(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,589,a(flip),b,944,a)].">
      <j1 rule="hyper" parents="65 589 944"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,944,a(flip),b,589,a(flip))].">
      <j1 rule="hyper" parents="132 944 589"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      (x \ 1) \ (x \ L(x,y,z)) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,946,a(flip),b,242,a)].">
      <j1 rule="hyper" parents="132 946 242"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,803,a(flip),b,928,a),flip(a)].">
      <j1 rule="hyper" parents="325 803 928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(85(a,1),942(a,1,1,1,2))].">
      <j1 rule="para" parents="85 942"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(140,a,945,a),flip(a)].">
      <j1 rule="hyper" parents="140 945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      (x \ 1) * L(L(T(x,x \ 1),y,z),u,w) = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(948(a,1),945(a,1,2,1))].">
      <j1 rule="para" parents="948 945"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      ((x * x) * ((y * z) * u)) / (z * u) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),124(a,1,1))].">
      <j1 rule="para" parents="33 124"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,413,a(flip),b,604,a)].">
      <j1 rule="hyper" parents="65 413 604"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(243(a,1),955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="243 955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(549,a,956,a),flip(a)].">
      <j1 rule="hyper" parents="549 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(548,a,956,a)].">
      <j1 rule="hyper" parents="548 956"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(421,a,956,a),flip(a)].">
      <j1 rule="hyper" parents="421 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(331,a,956,a),flip(a)].">
      <j1 rule="hyper" parents="331 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,156,a(flip),b,956,a)].">
      <j1 rule="hyper" parents="132 156 956"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(132,a,75,a(flip),b,956,a),flip(a)].">
      <j1 rule="hyper" parents="132 75 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(132,a,84,a(flip),b,956,a(flip))].">
      <j1 rule="hyper" parents="132 84 956"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (x \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,959,a)].">
      <j1 rule="hyper" parents="145 959"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      R(x,y,z) \ (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(140,a,959,a)].">
      <j1 rule="hyper" parents="140 959"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,594,a,b,959,a)].">
      <j1 rule="hyper" parents="65 594 959"/>
    </justification>
  </clause>

  <clause id="968">
    <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(959(a,1),619(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="959 619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(137,a,962,a(flip),b,388,a),flip(a)].">
      <j1 rule="hyper" parents="137 962 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(964(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="964 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(192(a,1),957(a,1,2,2))].">
      <j1 rule="para" parents="192 957"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      x \ ((x * x) * (R(1 / x,y,z) * u)) = R(1 / x,y,z) * ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,652,a,b,958,a)].">
      <j1 rule="hyper" parents="65 652 958"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(484(a,1),958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="484 958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,592,a(flip),b,963,a),flip(a)].">
      <j1 rule="hyper" parents="325 592 963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) = a(1 / x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(722,a,975,a),flip(a)].">
      <j1 rule="hyper" parents="722 975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(975(a,1),722(a,1))].">
      <j1 rule="para" parents="975 722"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(715(a,1),974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="715 974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(287(a,1),630(a,1,1))].">
      <j1 rule="para" parents="287 630"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      R((x * (y \ z)) / z,u,w) * z = (R(x / y,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(496(a,1),716(a,1,1,1))].">
      <j1 rule="para" parents="496 716"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,734,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="137 734 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,734,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 734 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ z,u,w)) = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,735,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="137 735 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,744,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="136 744 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,408,a(flip),b,757,a),flip(a)].">
      <j1 rule="hyper" parents="65 408 757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(371,a,987,a)].">
      <j1 rule="hyper" parents="371 987"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(785(a,2),48(a,1))].">
      <j1 rule="para" parents="785 48"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = (x * y) * R(L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(100(a,1),789(a,1,1,1,1))].">
      <j1 rule="para" parents="100 789"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(171(a,1),807(a,2,1,2))].">
      <j1 rule="para" parents="171 807"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ u)) / z)) = w
    ]]></literal>
    <justification jstring="[para(807(a,1),298(a,1,2))].">
      <j1 rule="para" parents="807 298"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(137,a,808,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="137 808 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(226(a,1),811(a,1,1,1,2))].">
      <j1 rule="para" parents="226 811"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      ((x * ((y * z) / (u * z))) / x) * (u * z) = (((x * (y / u)) / x) * u) * z
    ]]></literal>
    <justification jstring="[para(110(a,1),811(a,1,1,1,2))].">
      <j1 rule="para" parents="110 811"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = ((x * (y / (u * z))) / x) * (u * z)
    ]]></literal>
    <justification jstring="[para(310(a,1),811(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="310 811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,426,a(flip),b,868,a),flip(a)].">
      <j1 rule="hyper" parents="325 426 868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      ((x * y) * (z * (u * u))) / (y * (z * (u * u))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(34(a,1),883(a,1,2))].">
      <j1 rule="para" parents="34 883"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      (x * x) * (((y * z) * u) / (z * u)) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,556,a(flip),b,954,a)].">
      <j1 rule="hyper" parents="65 556 954"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,666,a(flip),b,981,a)].">
      <j1 rule="hyper" parents="65 666 981"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(132,a,991,a(flip),b,263,a)].">
      <j1 rule="hyper" parents="132 991 263"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      R(x,y,z * (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(490,a,998,a)].">
      <j1 rule="hyper" parents="490 998"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      R(x,y,z / (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1002(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 1002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      R(x,y,z * (u * (w * w))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(34(a,1),1002(a,1,3))].">
      <j1 rule="para" parents="34 1002"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      R(x,y,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(221(a,1),1002(a,1,3)),flip(a)].">
      <j1 rule="para" parents="221 1002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      R(x,y,z \ (u / (w * w))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(559(a,1),1002(a,1,3)),flip(a)].">
      <j1 rule="para" parents="559 1002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1005,a(flip),b,1005,a),flip(a)].">
      <j1 rule="hyper" parents="325 1005 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,568,a,b,1005,a)].">
      <j1 rule="hyper" parents="65 568 1005"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      R(x / y,y,x) = 1 / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,347,a(flip),b,1005,a),flip(a)].">
      <j1 rule="hyper" parents="65 347 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      R(x,x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(130,a,571,a(flip),b,1005,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 571 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      R(x / y,y,x) \ 1 = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1005(a,1),480(a,1,1))].">
      <j1 rule="para" parents="1005 480"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      R(x,y,x * y) \ 1 = y * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(1005(a,1),483(a,1,1))].">
      <j1 rule="para" parents="1005 483"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,114,a,b,1010,a),flip(a)].">
      <j1 rule="hyper" parents="325 114 1010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[hyper(44,a,756,a,b,1013,a)].">
      <j1 rule="hyper" parents="44 756 1013"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1013(a,1),379(a,1,1))].">
      <j1 rule="para" parents="1013 379"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      T(x,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(262(a,2),1014(a,1,2))].">
      <j1 rule="para" parents="262 1014"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      R(x,y,z * (u \ 1)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(570(a,1),1003(a,1,3))].">
      <j1 rule="para" parents="570 1003"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,1007,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="136 1007 20"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      T(x,x \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,262,a,b,1015,a)].">
      <j1 rule="hyper" parents="137 262 1015"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,319,a(flip),b,1019,a)].">
      <j1 rule="hyper" parents="65 319 1019"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,1019,a(flip),b,319,a(flip))].">
      <j1 rule="hyper" parents="132 1019 319"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,485,a(flip),b,1017,a),flip(a)].">
      <j1 rule="hyper" parents="65 485 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = R(x,y,L(z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(946(a,1),1017(a,1,3))].">
      <j1 rule="para" parents="946 1017"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(262(a,2),1022(a,1,3))].">
      <j1 rule="para" parents="262 1022"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,1025,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 1025 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(1025(a,1),379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1025 379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(1025(a,1),481(a,1,1))].">
      <j1 rule="para" parents="1025 481"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(854(a,1),1025(a,1,3))].">
      <j1 rule="para" parents="854 1025"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(136,a,1030,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 1030 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(1030(a,1),481(a,1,1))].">
      <j1 rule="para" parents="1030 481"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      R(L(x,y,z),x \ 1,x \ L(x,y,z)) \ 1 = (x \ 1) * ((L(x,y,z) * (x \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(946(a,1),1012(a,1,1,3))].">
      <j1 rule="para" parents="946 1012"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      R(x,y,z * (u \ (w * w))) = R(x,y,z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(395(a,1),1004(a,1,3,2))].">
      <j1 rule="para" parents="395 1004"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      R(x,y,z * L(u \ w,u \ w,u)) = R(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(561(a,1),1004(a,1,3,2))].">
      <j1 rule="para" parents="561 1004"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      R(x,y,z \ (u \ 1)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(271(a,1),1006(a,1,3,2))].">
      <j1 rule="para" parents="271 1006"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      R(x,y,z \ (u * (w \ 1))) = R(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(570(a,1),1006(a,1,3,2))].">
      <j1 rule="para" parents="570 1006"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      R(K(x,y) \ z,z \ 1,z) = (K(x,y) \ 1) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(685(a,1),1008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="685 1008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(249(a,1),1023(a,2,3))].">
      <j1 rule="para" parents="249 1023"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(455,a,1027,a)].">
      <j1 rule="hyper" parents="455 1027"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(1019(a,1),1027(a,2,2))].">
      <j1 rule="para" parents="1019 1027"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(411(a,1),1041(a,1,1)),flip(a)].">
      <j1 rule="para" parents="411 1041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,312,a(flip),b,1031,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 312 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1044(a,1),1031(a,2,2))].">
      <j1 rule="para" parents="1044 1031"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1044(a,1),1032(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1044 1032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      R(x,y,z * (u \ (w * w))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1017,a(flip),b,1034,a),flip(a)].">
      <j1 rule="hyper" parents="325 1017 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      R((x * x) * y,z,u) = (x * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      R((x * x) * y,z,u) * w = (x * x) * (R(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(136,a,1049,a,b,120,a)].">
      <j1 rule="hyper" parents="136 1049 120"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      (x * x) \ R((x * x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,1049,a,b,xx)].">
      <j1 rule="hyper" parents="132 1049"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      R(((x \ 1) * (x \ 1)) * y,z,u) = ((x \ 1) / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(420(a,1),1049(a,2,1))].">
      <j1 rule="para" parents="420 1049"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      R((x * x) \ y,z,u) = (x * x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1052(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      (1 / x) \ R((x * x) \ y,z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,1054,a,b,653,a)].">
      <j1 rule="hyper" parents="132 1054 653"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      (x * x) * (R(1 / y,z,u) * w) = R((x * x) / y,z,u) * w
    ]]></literal>
    <justification jstring="[para(402(a,1),1050(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="402 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),1000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 1000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) * v5 = K(x,y) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(136,a,1057,a,b,419,a)].">
      <j1 rule="hyper" parents="136 1057 419"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(680(a,1),1057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="680 1057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      K(x,x \ 1) * (R(x \ 1,y,z) * u) = R(1 / x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,1060,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 1060 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1018(a,1),46(a,1))].">
      <j1 rule="para" parents="1018 46"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      R(K(x,y) \ z,z \ 1,z) = K(x,y) \ ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,510,a(flip),b,1038,a),flip(a)].">
      <j1 rule="hyper" parents="325 510 1038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * y)) * (z * z) = L(L(z,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,558,a(flip),b,451,a)].">
      <j1 rule="hyper" parents="65 558 451"/>
    </justification>
  </clause>

  <clause id="1065">
    <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),488(a,1,1))].">
      <j1 rule="para" parents="100 488"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(y \ z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(102(a,1),768(a,1,2,1))].">
      <j1 rule="para" parents="102 768"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,423,a(flip),b,819,a),flip(a)].">
      <j1 rule="hyper" parents="325 423 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * (u * u)))) = L(z,y,x) * (u * u)
    ]]></literal>
    <justification jstring="[para(18(a,2),882(a,2,1))].">
      <j1 rule="para" parents="18 882"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      L(x * (y * y),z,u) = L(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(456,a,1068,a)].">
      <j1 rule="hyper" parents="456 1068"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      L((x / (y * y)) * (y * y),z,u) = (y * y) * L((y * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,587,a(flip),b,1069,a),flip(a)].">
      <j1 rule="hyper" parents="325 587 1069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      L(x * ((y \ 1) * (y \ 1)),z,u) = L(x,z,u) * ((y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(420(a,1),1069(a,2,2))].">
      <j1 rule="para" parents="420 1069"/>
    </justification>
  </clause>

  <clause id="1072">
    <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(529,a,909,a)].">
      <j1 rule="hyper" parents="529 909"/>
    </justification>
  </clause>

  <clause id="1073">
    <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),909(a,1,1))].">
      <j1 rule="para" parents="100 909"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      x * R(x \ (x \ y),z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1055,a(flip),b,921,a),flip(a)].">
      <j1 rule="hyper" parents="65 1055 921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      R((x \ y) / x,z,u) = (x \ R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,1074,a(flip),b,592,a),flip(a)].">
      <j1 rule="hyper" parents="135 1074 592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      x \ R(x * y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1074(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      x * R(x \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(69(a,1),1074(a,1,2,1,2))].">
      <j1 rule="para" parents="69 1074"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      x \ R(x,x,y) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(620,a,1077,a),flip(a)].">
      <j1 rule="hyper" parents="620 1077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      x \ (x \ R(x,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,1077,a)].">
      <j1 rule="hyper" parents="140 1077"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      R(1 / x,y,z) * x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,592,a,b,1077,a)].">
      <j1 rule="hyper" parents="65 592 1077"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,966,a(flip),b,1077,a),flip(a)].">
      <j1 rule="hyper" parents="65 966 1077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      (x * R(y \ 1,z,u)) / (y \ R(y,z,u)) = R(x / y,y,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(201,a,1077,a(flip),b,482,a)].">
      <j1 rule="hyper" parents="201 1077 482"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      x \ R(x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(1077(a,1),620(a,1))].">
      <j1 rule="para" parents="1077 620"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1077(a,1),909(a,2,2))].">
      <j1 rule="para" parents="1077 909"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      x \ R(x,x,x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),1078(a,2,1,2))].">
      <j1 rule="para" parents="10 1078"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      (x / y) \ R(x / y,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1078(a,2,1,2))].">
      <j1 rule="para" parents="12 1078"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      x * R(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1079(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1079 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      x * (((x \ y) / y) * x) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(148,a,1085,a)].">
      <j1 rule="hyper" parents="148 1085"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      x * (((x \ y) / y) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(1085(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1085 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      x \ R(x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) / y) * x = z
    ]]></literal>
    <justification jstring="[para(1088(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1088 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(140,a,926,a)].">
      <j1 rule="hyper" parents="140 926"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,423,a(flip),b,927,a),flip(a)].">
      <j1 rule="hyper" parents="325 423 927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      (x * x) * (((y * x) \ y) * (x * (x \ 1))) = T(L(x,x,y),x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(560(a,1),943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="560 943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(67(a,1),984(a,2,2,1))].">
      <j1 rule="para" parents="67 984"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1001(a,1,2,1,2))].">
      <j1 rule="para" parents="8 1001"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      R(((x \ 1) / x) * y,z,u) = ((x \ 1) / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(420(a,1),1053(a,1,1,1))].">
      <j1 rule="para" parents="420 1053"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      R(((x \ 1) / x) * y,z,u) = (x \ 1) * (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,737,a(flip),b,1096,a),flip(a)].">
      <j1 rule="hyper" parents="325 737 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      R((x \ 1) * (x \ y),z,u) = (x \ 1) * (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(737(a,1),1097(a,1,1))].">
      <j1 rule="para" parents="737 1097"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1067(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(115(a,1),1067(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="115 1067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(423(a,1),1067(a,1,1))].">
      <j1 rule="para" parents="423 1067"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,821,a(flip),b,1100,a)].">
      <j1 rule="hyper" parents="65 821 1100"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,820,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="65 820 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,724,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="65 724 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(82(a,1),1104(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 1104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      ((x \ R(1 / y,y,x)) * x) * (y * x) = x * ((y * x) * T((y * x) \ 1,x))
    ]]></literal>
    <justification jstring="[para(226(a,2),1104(a,1,1,1,2))].">
      <j1 rule="para" parents="226 1104"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(236(a,1),1103(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="236 1103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(245,a,1107,a(flip),b,233,a(flip))].">
      <j1 rule="hyper" parents="245 1107 233"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,1108,a,b,xx)].">
      <j1 rule="hyper" parents="135 1108"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(132,a,1108,a,b,313,a)].">
      <j1 rule="hyper" parents="132 1108 313"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1108(a,2),81(a,1,2,1))].">
      <j1 rule="para" parents="1108 81"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(86(a,1),1109(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="86 1109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      x * (T(y * x,x) / x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1111(a,1,2,1,1,1))].">
      <j1 rule="para" parents="9 1111"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(426(a,1),1112(a,1,2,1,2))].">
      <j1 rule="para" parents="426 1112"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(784(a,2),1112(a,1,2,1,2))].">
      <j1 rule="para" parents="784 1112"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1110(a,1,2,1,1))].">
      <j1 rule="para" parents="9 1110"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      L(x * ((y \ 1) / y),z,u) = L(x,z,u) * ((y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(420(a,1),1071(a,1,1,2))].">
      <j1 rule="para" parents="420 1071"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),1091(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),1091(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[hyper(137,a,896,a,b,1119,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 896 1119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1122(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * x),z) = (y * x) * K(z \ (z / K(x,y)),z)
    ]]></literal>
    <justification jstring="[para(16(a,2),1122(a,2,2,1,2,2))].">
      <j1 rule="para" parents="16 1122"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * K(u \ (u / L(z,y,x)),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),1122(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 1122"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(423(a,1),1092(a,1,1))].">
      <j1 rule="para" parents="423 1092"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z)
    ]]></literal>
    <justification jstring="[hyper(835,a,1099,a)].">
      <j1 rule="hyper" parents="835 1099"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1099(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(423(a,1),1099(a,2,1))].">
      <j1 rule="para" parents="423 1099"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(424(a,1),1129(a,1,1))].">
      <j1 rule="para" parents="424 1129"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(327,a,1131,a),flip(a)].">
      <j1 rule="hyper" parents="327 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      (x * T(T(y,x),z)) * T(y,x) = (y * x) * T(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,234,a(flip),b,1131,a),flip(a)].">
      <j1 rule="hyper" parents="325 234 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,154,a(flip),b,1131,a),flip(a)].">
      <j1 rule="hyper" parents="325 154 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(140,a,1131,a)].">
      <j1 rule="hyper" parents="140 1131"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,83,a(flip),b,1131,a),flip(a)].">
      <j1 rule="hyper" parents="135 83 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(115(a,1),1131(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="115 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1138(a,1),334(a,1))].">
      <j1 rule="para" parents="1138 334"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,113,a(flip),b,1135,a),flip(a)].">
      <j1 rule="hyper" parents="135 113 1135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(140,a,1141,a),flip(a)].">
      <j1 rule="hyper" parents="140 1141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(241(a,1),1134(a,1,1))].">
      <j1 rule="para" parents="241 1134"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,250,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="65 250 1139"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(235(a,1),1139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="235 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(540,a,1144,a)].">
      <j1 rule="hyper" parents="540 1144"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      (x * (y / x)) * (x \ y) = y * (y / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,155,a(flip),b,1144,a),flip(a)].">
      <j1 rule="hyper" parents="325 155 1144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      ((x / y) * (x / (x / y))) * y = x * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(536,a,1147,a)].">
      <j1 rule="hyper" parents="536 1147"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / y) = u
    ]]></literal>
    <justification jstring="[para(1146(a,1),375(a,1))].">
      <j1 rule="para" parents="1146 375"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(235(a,1),1128(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="235 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      T((K(x,y) * z) \ (K(x,y) * (u * z)),K(x,y)) = R(T(u,K(x,y) * z),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(287(a,1),1150(a,1,1,2))].">
      <j1 rule="para" parents="287 1150"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1136(a,1),1150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1136 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(113(a,1),1152(a,1,1,2))].">
      <j1 rule="para" parents="113 1152"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) / (y / z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),1149(a,1,1,1))].">
      <j1 rule="para" parents="11 1149"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(325,a,821,a(flip),b,1101,a),flip(a)].">
      <j1 rule="hyper" parents="325 821 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),1101(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1101(a,1),529(a,1))].">
      <j1 rule="para" parents="1101 529"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,821,a(flip),b,1156,a)].">
      <j1 rule="hyper" parents="65 821 1156"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(862(a,1),1105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="862 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),1159(a,2,2))].">
      <j1 rule="para" parents="94 1159"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1160(a,1,1,1))].">
      <j1 rule="para" parents="9 1160"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1161(a,2,2,1))].">
      <j1 rule="para" parents="9 1161"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(551,a,1162,a)].">
      <j1 rule="hyper" parents="551 1162"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      (x * y) \ (y * K(x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,1163,a)].">
      <j1 rule="hyper" parents="140 1163"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      T(x,y) * T((y \ (x * y)) \ (y \ z),u) = y \ ((x * y) * T((x * y) \ z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),1120(a,1,1))].">
      <j1 rule="para" parents="22 1120"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      ((x * y) / z) * T(((x * y) / z) \ x,u) = (x * (y * T(y \ z,u))) / z
    ]]></literal>
    <justification jstring="[hyper(135,a,820,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="135 820 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,113,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="135 113 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1127(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1127"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,1171,a),flip(a)].">
      <j1 rule="hyper" parents="145 1171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(898,a,1172,a)].">
      <j1 rule="hyper" parents="898 1172"/>
    </justification>
  </clause>

  <clause id="1174">
    <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),1173(a,1,1,2,2))].">
      <j1 rule="para" parents="20 1173"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,821,a(flip),b,1130,a)].">
      <j1 rule="hyper" parents="65 821 1130"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(245,a,1130,a(flip),b,821,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 1130 821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1176(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(132,a,1177,a,b,xx)].">
      <j1 rule="hyper" parents="132 1177"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1178(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1112(a,1),1179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1112 1179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(148,a,1180,a),flip(a)].">
      <j1 rule="hyper" parents="148 1180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1115,a(flip),b,1180,a)].">
      <j1 rule="hyper" parents="65 1115 1180"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1145(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(540,a,1183,a)].">
      <j1 rule="hyper" parents="540 1183"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(371,a,1183,a),flip(a)].">
      <j1 rule="hyper" parents="371 1183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,83,a(flip),b,1183,a),flip(a)].">
      <j1 rule="hyper" parents="135 83 1183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      (1 / x) * ((y * ((z / x) \ z)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(199(a,2),1186(a,1,2,1))].">
      <j1 rule="para" parents="199 1186"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(82(a,1),1155(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 1155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(y * T(y \ (z / x),u),x) = w
    ]]></literal>
    <justification jstring="[para(1155(a,1),301(a,1,2))].">
      <j1 rule="para" parents="1155 301"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(905(a,2),1155(a,1,1))].">
      <j1 rule="para" parents="905 1155"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(69(a,1),1191(a,2,2,2,1,2))].">
      <j1 rule="para" parents="69 1191"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,233,a(flip),b,1193,a),flip(a)].">
      <j1 rule="hyper" parents="325 233 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,7,a(flip),b,1194,a),flip(a)].">
      <j1 rule="hyper" parents="37 7 1194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(262(a,2),1194(a,2,2))].">
      <j1 rule="para" parents="262 1194"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1197(a,1),1027(a,2,2))].">
      <j1 rule="para" parents="1197 1027"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / (y \ 1) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(540,a,1199,a)].">
      <j1 rule="hyper" parents="540 1199"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,1199,a),flip(a)].">
      <j1 rule="hyper" parents="327 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(211,a,1199,a),flip(a)].">
      <j1 rule="hyper" parents="211 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / ((x \ 1) * y) = R(1 / (1 / x),x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1202(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1202 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1154,a,1201,a)].">
      <j1 rule="hyper" parents="1154 1201"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1208(a,1),1027(a,2,2))].">
      <j1 rule="para" parents="1208 1027"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,1043,a,b,1198,a),flip(a)].">
      <j1 rule="hyper" parents="37 1043 1198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(132,a,1210,a(flip),b,905,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 1210 905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      (x * y) / ((y \ 1) \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = (x * (1 / y)) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,1199,a(flip),b,1213,a)].">
      <j1 rule="hyper" parents="136 1199 1213"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1008,a(flip),b,1215,a),flip(a)].">
      <j1 rule="hyper" parents="65 1008 1215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(327,a,1216,a),flip(a)].">
      <j1 rule="hyper" parents="327 1216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1218(a,1),27(a,2,1))].">
      <j1 rule="para" parents="1218 27"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,1219,a(flip),b,1216,a),flip(a)].">
      <j1 rule="hyper" parents="135 1219 1216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(673,a,1220,a),flip(a)].">
      <j1 rule="hyper" parents="673 1220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(671,a,1220,a)].">
      <j1 rule="hyper" parents="671 1220"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) = ((1 / x) * T(y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,424,a(flip),b,1220,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 424 1220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(73(a,1),1221(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="73 1221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(1221(a,1),1113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1221 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,896,a,b,1224,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 896 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),1222(a,2,1,1))].">
      <j1 rule="para" parents="12 1222"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1222(a,1),1102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1222 1102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1175,a(flip),b,1225,a),flip(a)].">
      <j1 rule="hyper" parents="325 1175 1225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,1122,a(flip),b,1227,a)].">
      <j1 rule="hyper" parents="65 1122 1227"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(584(a,1),238(a,1,1))].">
      <j1 rule="para" parents="584 238"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,717,a(flip),b,783,a)].">
      <j1 rule="hyper" parents="65 717 783"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(587(a,1),1232(a,1,1))].">
      <j1 rule="para" parents="587 1232"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(915(a,1),1233(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="915 1233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(137,a,809,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="137 809 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(85(a,1),951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="85 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1236(a,2,1,1))].">
      <j1 rule="para" parents="7 1236"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(85(a,1),1237(a,1,2,1))].">
      <j1 rule="para" parents="85 1237"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,191,a(flip),b,1238,a(flip))].">
      <j1 rule="hyper" parents="136 191 1238"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      (R(x / y,z,u) * y) * (y \ w) = w * R(w \ (x * (y \ w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(797,a,982,a),flip(a)].">
      <j1 rule="hyper" parents="797 982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(140,a,983,a)].">
      <j1 rule="hyper" parents="140 983"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(140,a,985,a)].">
      <j1 rule="hyper" parents="140 985"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ y,z,u)) = y * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),985(a,2,2,1))].">
      <j1 rule="para" parents="22 985"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = y * (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(589(a,1),1243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="589 1243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,1244,a),flip(a)].">
      <j1 rule="hyper" parents="373 1244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,242,a(flip),b,1244,a(flip))].">
      <j1 rule="hyper" parents="132 242 1244"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(132,a,10,a(flip),b,1245,a),flip(a)].">
      <j1 rule="hyper" parents="132 10 1245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1248">
    <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(36,a,414,a(flip),b,1245,a),flip(a)].">
      <j1 rule="hyper" parents="36 414 1245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1245(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) * (x * x)) = L(x \ 1,y,z) * x
    ]]></literal>
    <justification jstring="[para(272(a,1),1245(a,1,2,2))].">
      <j1 rule="para" parents="272 1245"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),1246(a,2,2))].">
      <j1 rule="para" parents="22 1246"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(1247(a,1),77(a,1,2,2))].">
      <j1 rule="para" parents="1247 77"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(1247(a,1),299(a,1,2,2))].">
      <j1 rule="para" parents="1247 299"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(140,a,1249,a)].">
      <j1 rule="hyper" parents="140 1249"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,156,a(flip),b,1249,a)].">
      <j1 rule="hyper" parents="135 156 1249"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,156,a(flip),b,1249,a)].">
      <j1 rule="hyper" parents="132 156 1249"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(132,a,75,a(flip),b,1249,a),flip(a)].">
      <j1 rule="hyper" parents="132 75 1249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1258">
    <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(132,a,1249,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="132 1249 93"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z) \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,365,a,b,1257,a)].">
      <j1 rule="hyper" parents="65 365 1257"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1257(a,1),1017(a,1,3))].">
      <j1 rule="para" parents="1257 1017"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      x * (L(x,y,z) * (L(x,u,w) \ 1)) = L(x,y,z) * (L(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(1257(a,1),1249(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1257 1249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ y) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(85(a,1),1252(a,1,2,2))].">
      <j1 rule="para" parents="85 1252"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ 1) * u)) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(389(a,1),1252(a,1,2,2))].">
      <j1 rule="para" parents="389 1252"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1254(a,1),997(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1254 997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1255(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1255 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ (L(x,u,w) * v5) = L(x,u,w) * (L(L(x,u,w),y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(30(a,1),1256(a,1,1))].">
      <j1 rule="para" parents="30 1256"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      R(x,y,z * (u * (L(u,w,v5) \ u))) = R(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1256(a,1),1048(a,1,3,2))].">
      <j1 rule="para" parents="1256 1048"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      R(x,y,z * L(z,u,u)) = R(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(824(a,1),1260(a,1,3)),flip(a)].">
      <j1 rule="para" parents="824 1260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      x * (L(x,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = w
    ]]></literal>
    <justification jstring="[para(9(a,1),1253(a,1,2,2))].">
      <j1 rule="para" parents="9 1253"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ x) = u
    ]]></literal>
    <justification jstring="[para(262(a,2),1265(a,1,2))].">
      <j1 rule="para" parents="262 1265"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      y * (L(y,z,u) \ ((y \ L(y,z,u)) * x)) = w
    ]]></literal>
    <justification jstring="[para(101(a,1),1265(a,1))].">
      <j1 rule="para" parents="101 1265"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) * (x * x),y,z) = L(x \ 1,y,z) * x
    ]]></literal>
    <justification jstring="[para(1069(a,2),1250(a,1,2))].">
      <j1 rule="para" parents="1069 1250"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      L(x \ 1,y,z) * x = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(221(a,1),1272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="221 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),1264(a,2,1))].">
      <j1 rule="para" parents="11 1264"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,1274,a(flip),b,426,a),flip(a)].">
      <j1 rule="hyper" parents="136 1274 426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,242,a,b,1275,a)].">
      <j1 rule="hyper" parents="36 242 1275"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),986(a,2,1,1,1))].">
      <j1 rule="para" parents="7 986"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,592,a(flip),b,1277,a),flip(a)].">
      <j1 rule="hyper" parents="325 592 1277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(592(a,1),1278(a,1,1))].">
      <j1 rule="para" parents="592 1278"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,1279,a),flip(a)].">
      <j1 rule="hyper" parents="145 1279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <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),1280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 1280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,413,a(flip),b,990,a),flip(a)].">
      <j1 rule="hyper" parents="325 413 990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      (((x * y) / (x * z)) * x) * z = x * (z * R(z \ y,x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1282(a,1,1,1,1,2))].">
      <j1 rule="para" parents="10 1282"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(113(a,1),1282(a,1,1,1,1,2))].">
      <j1 rule="para" parents="113 1282"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      x \ ((((x * y) / (x * z)) * x) * z) = z * R(z \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(530,a,1283,a)].">
      <j1 rule="hyper" parents="530 1283"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      x \ ((x * x) * y) = y * R(y \ (x * y),x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1285(a,1,2,1,1))].">
      <j1 rule="para" parents="11 1285"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      x * R(x \ (y * x),y,x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,652,a(flip),b,1286,a),flip(a)].">
      <j1 rule="hyper" parents="65 652 1286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      x * R(T(y,x),y,x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(22(a,2),1287(a,1,2,1))].">
      <j1 rule="para" parents="22 1287"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      R(x,x,y) * y = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(374,a,1288,a)].">
      <j1 rule="hyper" parents="374 1288"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      R(x,x,y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,1288,a(flip),b,243,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="135 1288 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      x \ R(x,x \ 1,y) = x * (((1 / (x \ 1)) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(137,a,1290,a(flip),b,1079,a),flip(a)].">
      <j1 rule="hyper" parents="137 1290 1079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      x \ (((1 / x) \ y) / y) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[para(1290(a,1),1078(a,1,2))].">
      <j1 rule="para" parents="1290 1078"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      (x / ((y \ 1) * x)) * (y \ 1) = (y \ 1) \ ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(82(a,1),1292(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 1292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      x \ (((1 / x) \ ((x \ 1) * y)) / ((x \ 1) * y)) = (((x \ 1) * y) / L(y,x \ 1,x)) * x
    ]]></literal>
    <justification jstring="[para(261(a,1),1292(a,2,1,2))].">
      <j1 rule="para" parents="261 1292"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      L(T(x / (y * x),y),y,y) = (1 / y) * (y \ (((1 / y) \ x) / x))
    ]]></literal>
    <justification jstring="[para(1292(a,2),655(a,2,2))].">
      <j1 rule="para" parents="1292 655"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      x \ R(x,x \ 1,y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),1291(a,2,2,1,1))].">
      <j1 rule="para" parents="82 1291"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      x * R(1 / x,x,x \ y) = x \ R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(366(a,2),1296(a,2,2)),flip(a)].">
      <j1 rule="para" parents="366 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ ((z \ u) / u)) = R(x,y,(u / ((z \ 1) * u)) * z)
    ]]></literal>
    <justification jstring="[para(1293(a,1),1017(a,1,3))].">
      <j1 rule="para" parents="1293 1017"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(243(a,1),1284(a,2,2))].">
      <j1 rule="para" parents="243 1284"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      L(R(x \ 1,x,y),x,x) = (1 / x) * (x \ (((1 / x) \ y) / y))
    ]]></literal>
    <justification jstring="[para(614(a,1),1295(a,1,1))].">
      <j1 rule="para" parents="614 1295"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      (1 / x) * (x \ (((1 / x) \ y) / y)) = R((1 / x) * 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,657,a(flip),b,1301,a),flip(a)].">
      <j1 rule="hyper" parents="65 657 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      (1 / x) * (x \ (((1 / x) \ y) / y)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1302(a,2,1))].">
      <j1 rule="para" parents="8 1302"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      (x * x) \ (((1 / x) \ y) / y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,653,a(flip),b,1303,a)].">
      <j1 rule="hyper" parents="65 653 1303"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(140,a,993,a)].">
      <j1 rule="hyper" parents="140 993"/>
    </justification>
  </clause>

  <clause id="1306">
    <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(109(a,1),994(a,1,2))].">
      <j1 rule="para" parents="109 994"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),1070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      L((x * x) \ y,z,u) = (x * x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(140,a,1307,a),flip(a)].">
      <j1 rule="hyper" parents="140 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,1307,a(flip),b,908,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 1307 908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      x * L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,1307,a(flip),b,907,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 1307 907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      L((x * x) * y,z,u) = (x * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1307(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      x \ (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,1310,a)].">
      <j1 rule="hyper" parents="140 1310"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (x \ 1) * (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,944,a(flip),b,1310,a(flip))].">
      <j1 rule="hyper" parents="137 944 1310"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      x \ L(x,x,y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(225(a,1),1310(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1310(a,1),1233(a,1,1))].">
      <j1 rule="para" parents="1310 1233"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1310(a,1),1239(a,1,1))].">
      <j1 rule="para" parents="1310 1239"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      x * L(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1312(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1312 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      x \ (L(x,y,z) * (x \ L(x,u,w))) = L(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1312(a,1),1246(a,2,2))].">
      <j1 rule="para" parents="1312 1246"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      L((x * x) \ y,z,u) \ w = L(y,z,u) \ ((x * x) * w)
    ]]></literal>
    <justification jstring="[para(1308(a,2),554(a,1,1))].">
      <j1 rule="para" parents="1308 554"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      L(x \ (x \ y),z,u) = x \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(140,a,1309,a),flip(a)].">
      <j1 rule="hyper" parents="140 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,y,z) \ x),y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,69,a(flip),b,1309,a),flip(a)].">
      <j1 rule="hyper" parents="132 69 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      x \ L(x * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1309(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      (x / y) * L((x / y) \ y,z,u) = (x / y) \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(85(a,1),1309(a,1,2,1,2))].">
      <j1 rule="para" parents="85 1309"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      x \ L(x * (x * y),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(71(a,1),1309(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      (x * (y \ 1)) * L((x * (y \ 1)) \ (y * y),z,u) = (x * (y \ 1)) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(577(a,1),1309(a,1,2,1,2))].">
      <j1 rule="para" parents="577 1309"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = x \ L((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(652(a,1),1309(a,1,2,1,2))].">
      <j1 rule="para" parents="652 1309"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      x * L(R(x \ 1,y,z),u,w) = x \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1079(a,1),1309(a,1,2,1))].">
      <j1 rule="para" parents="1079 1309"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      L((x * x) * y,z,u) * w = (x * x) * (L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(136,a,1311,a,b,120,a)].">
      <j1 rule="hyper" parents="136 1311 120"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      x \ L((x * x) * y,z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,1311,a,b,648,a)].">
      <j1 rule="hyper" parents="132 1311 648"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      L((x * x) * y,z,u) \ w = L(y,z,u) \ ((x * x) \ w)
    ]]></literal>
    <justification jstring="[para(1311(a,2),393(a,1,1))].">
      <j1 rule="para" parents="1311 393"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      (x \ 1) * (x \ L(x,y,z)) = x \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1312,a,b,1313,a),flip(a)].">
      <j1 rule="hyper" parents="325 1312 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((x \ y) \ L(x \ y,x \ y,x)) = y \ (x * 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,469,a(flip),b,1313,a),flip(a)].">
      <j1 rule="hyper" parents="325 469 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      L(x \ 1,y,z) \ ((x \ L(x,y,z)) * x) = x * x
    ]]></literal>
    <justification jstring="[para(1316(a,1),577(a,1,1))].">
      <j1 rule="para" parents="1316 577"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      R(x,y,(z \ L(z,u,w)) * z) = R(x,y,L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(1316(a,1),1017(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1316 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1320(a,2),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1320 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      L(x * (y * x),z,u) = x * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(137,a,586,a(flip),b,1322,a),flip(a)].">
      <j1 rule="hyper" parents="137 586 1322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,919,a,b,1322,a)].">
      <j1 rule="hyper" parents="65 919 1322"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      L(x,y,z) \ L(x * L(x,y,z),u,w) = L(x,y,z) * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(249(a,1),1322(a,1,2,1))].">
      <j1 rule="para" parents="249 1322"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      L(x * (x * y),z,u) = x * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(148,a,1324,a),flip(a)].">
      <j1 rule="hyper" parents="148 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      (x \ 1) * (x * (x * y)) = x * L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,389,a(flip),b,1324,a)].">
      <j1 rule="hyper" parents="65 389 1324"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      (x \ 1) * (x * (y * x)) = L(y,x \ 1,x) * x
    ]]></literal>
    <justification jstring="[hyper(514,a,1337,a)].">
      <j1 rule="hyper" parents="514 1337"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      x * (x * L(T(y,x),z,u)) = L(x * (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(242(a,2),1337(a,2,2)),flip(a)].">
      <j1 rule="para" parents="242 1337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      K(x,x \ 1) * (x * L(y,x \ 1,x)) = L(x * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1341(a,1),912(a,1,2))].">
      <j1 rule="para" parents="1341 912"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      K(x,x \ 1) * (L(y,x \ 1,x) * x) = L(y * x,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1342(a,1),912(a,1,2))].">
      <j1 rule="para" parents="1342 912"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      R(x,x \ 1,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,379,a,b,1332,a(flip))].">
      <j1 rule="hyper" parents="41 379 1332"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ R(x,u,w)) = R(x,u,w) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(965(a,1),1315(a,2,2,1))].">
      <j1 rule="para" parents="965 1315"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      L(x * (y * y),z,u) \ ((y * y) * w) = L(T(x,y * y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(22(a,2),1319(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      L((x * x) * y,z,u) \ (w * v5) = L(y,z,u) \ (((x * x) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(391(a,1),1331(a,2,2))].">
      <j1 rule="para" parents="391 1331"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(1317,a,1338,a)].">
      <j1 rule="hyper" parents="1317 1338"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      R(1 / x,x,L(x \ 1,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,365,a,b,1350,a)].">
      <j1 rule="hyper" parents="41 365 1350"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T(x,L(x \ 1,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(245,a,1350,a(flip),b,946,a)].">
      <j1 rule="hyper" parents="245 1350 946"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(357(a,1),1352(a,1,2))].">
      <j1 rule="para" parents="357 1352"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(359(a,1),1352(a,1,2))].">
      <j1 rule="para" parents="359 1352"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,114,a,b,1354,a),flip(a)].">
      <j1 rule="hyper" parents="325 114 1354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),1354(a,1,2))].">
      <j1 rule="para" parents="82 1354"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1354(a,1),988(a,1,1,1))].">
      <j1 rule="para" parents="1354 988"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(1356(a,1),761(a,1,1))].">
      <j1 rule="para" parents="1356 761"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      1 / T(x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,1357,a,b,xx)].">
      <j1 rule="hyper" parents="201 1357"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,845,a(flip),b,1360,a),flip(a)].">
      <j1 rule="hyper" parents="65 845 1360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(386,a,1365,a),flip(a)].">
      <j1 rule="hyper" parents="386 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(136,a,1365,a(flip),b,441,a)].">
      <j1 rule="hyper" parents="136 1365 441"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(132,a,1365,a(flip),b,264,a(flip))].">
      <j1 rule="hyper" parents="132 1365 264"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),1365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1371">
    <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(1366(a,2),821(a,1,1))].">
      <j1 rule="para" parents="1366 821"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1366(a,2),1234(a,2,1))].">
      <j1 rule="para" parents="1366 1234"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1366(a,2),1256(a,1,2))].">
      <j1 rule="para" parents="1366 1256"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(136,a,1367,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 1367 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1367(a,1),471(a,1,1))].">
      <j1 rule="para" parents="1367 471"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[para(357(a,1),1351(a,1,3))].">
      <j1 rule="para" parents="357 1351"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1378(a,1),365(a,1,1))].">
      <j1 rule="para" parents="1378 365"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(137,a,1366,a,b,1379,a)].">
      <j1 rule="hyper" parents="137 1366 1379"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(1381(a,1),1031(a,2,2))].">
      <j1 rule="para" parents="1381 1031"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(85(a,1),1355(a,1,2))].">
      <j1 rule="para" parents="85 1355"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(681,a,1375,a)].">
      <j1 rule="hyper" parents="681 1375"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(327,a,1382,a),flip(a)].">
      <j1 rule="hyper" parents="327 1382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,1212,a(flip),b,1384,a(flip))].">
      <j1 rule="hyper" parents="201 1212 1384"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1358(a,1),115(a,1,1))].">
      <j1 rule="para" parents="1358 115"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(200(a,1),1388(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="200 1388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(202,a,1392,a)].">
      <j1 rule="hyper" parents="202 1392"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(137,a,1394,a,b,xx)].">
      <j1 rule="hyper" parents="137 1394"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(82(a,1),1395(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="82 1395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1396(a,2,2,2,2))].">
      <j1 rule="para" parents="9 1396"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1329,a(flip),b,1326,a),flip(a)].">
      <j1 rule="hyper" parents="325 1329 1326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x \ 1,x) = L(x * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,853,a(flip),b,1344,a)].">
      <j1 rule="hyper" parents="65 853 1344"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ w) = w * R(w \ (y * (x \ w)),z,u)
    ]]></literal>
    <justification jstring="[para(592(a,1),1240(a,1,1))].">
      <j1 rule="para" parents="592 1240"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1241(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (x \ z),u,w) = x \ (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),1241(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1087,a,1401,a)].">
      <j1 rule="hyper" parents="1087 1401"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      (x \ y) * (x \ (y * R(y \ x,z,u))) = R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,1401,a(flip),b,1077,a(flip))].">
      <j1 rule="hyper" parents="137 1401 1077"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1401(a,1),1087(a,1))].">
      <j1 rule="para" parents="1401 1087"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ (y * R(y \ x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(1404(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1404 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      (x \ (y \ x)) * (x \ (R(y,z,u) * (y \ x))) = R(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(594(a,1),1404(a,1,2,2))].">
      <j1 rule="para" parents="594 1404"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1242(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1409">
    <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(14(a,2),1242(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14 1242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1317,a,1408,a)].">
      <j1 rule="hyper" parents="1317 1408"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      x * ((x \ y) \ L(x \ y,z,u)) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,1310,a(flip),b,1408,a(flip))].">
      <j1 rule="hyper" parents="137 1310 1408"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      (x \ y) * (x \ (y * L(y \ x,z,u))) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,1408,a(flip),b,1310,a(flip))].">
      <j1 rule="hyper" parents="137 1408 1310"/>
    </justification>
  </clause>

  <clause id="1413">
    <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)),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ x,z,u)) = T(y,x) \ L(x \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      ((x \ y) \ 1) * (x \ (y * L(y \ x,x \ y,x))) = y \ (x * 1)
    ]]></literal>
    <justification jstring="[para(1410(a,1),1333(a,1,2))].">
      <j1 rule="para" parents="1410 1333"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ (y * L(y \ x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(1412(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1412 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      ((x \ y) \ 1) * (x \ (x * ((x \ y) * (y \ x)))) = y \ (x * 1)
    ]]></literal>
    <justification jstring="[para(414(a,1),1415(a,1,2,2))].">
      <j1 rule="para" parents="414 1415"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((x \ y) * (y \ x)) = y \ (x * 1)
    ]]></literal>
    <justification jstring="[hyper(520,a,1417,a)].">
      <j1 rule="hyper" parents="520 1417"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((x \ y) * (y \ x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,160,a(flip),b,1418,a),flip(a)].">
      <j1 rule="hyper" parents="325 160 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      R(x \ y,(x \ y) \ 1,(x \ y) * (y \ x)) = ((x \ y) * (y \ x)) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(201,a,1419,a(flip),b,379,a),flip(a)].">
      <j1 rule="hyper" parents="201 1419 379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1005(a,1),1259(a,1,1))].">
      <j1 rule="para" parents="1005 1259"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * L(T(x,L(x,y,z) \ 1),u,w)) = L(x,u,w) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(242(a,2),1261(a,1,2))].">
      <j1 rule="para" parents="242 1261"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1305(a,1,2,2,1))].">
      <j1 rule="para" parents="10 1305"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(429,a,1424,a)].">
      <j1 rule="hyper" parents="429 1424"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1424(a,1),429(a,1))].">
      <j1 rule="para" parents="1424 429"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      ((x * x) * (y * z)) \ ((x * x) * (y * (z * u))) = L(u,z,(x * x) * y)
    ]]></literal>
    <justification jstring="[para(33(a,1),123(a,1,2))].">
      <j1 rule="para" parents="33 123"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,14,a,b,477,a)].">
      <j1 rule="hyper" parents="325 14 477"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(287(a,1),628(a,1,2))].">
      <j1 rule="para" parents="287 628"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * y)) * (z * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(L(z,z,y),y * z,x) = u
    ]]></literal>
    <justification jstring="[para(558(a,1),774(a,1))].">
      <j1 rule="para" parents="558 774"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (L(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,408,a(flip),b,781,a),flip(a)].">
      <j1 rule="hyper" parents="65 408 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(587(a,1),1431(a,2,1))].">
      <j1 rule="para" parents="587 1431"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,908,a(flip),b,1432,a)].">
      <j1 rule="hyper" parents="65 908 1432"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(245,a,907,a(flip),b,1432,a(flip))].">
      <j1 rule="hyper" parents="245 907 1432"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,1434,a)].">
      <j1 rule="hyper" parents="57 1434"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      x * ((x * y) * L((x * y) \ y,z,u)) = (x * L(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1433(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 1433"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(915(a,1),1433(a,2,1,2))].">
      <j1 rule="para" parents="915 1433"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x \ L(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(1310(a,1),1433(a,2,1))].">
      <j1 rule="para" parents="1310 1433"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * u) = x * L(x \ (u * u),y,z)
    ]]></literal>
    <justification jstring="[para(1307(a,1),1438(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1307 1438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1372(a,1),1437(a,1,2))].">
      <j1 rule="para" parents="1372 1437"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1366(a,2),1440(a,2,1))].">
      <j1 rule="para" parents="1366 1440"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,1376,a,b,1441,a),flip(a)].">
      <j1 rule="hyper" parents="36 1376 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),1441(a,1,2,2))].">
      <j1 rule="para" parents="22 1441"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(681,a,1442,a)].">
      <j1 rule="hyper" parents="681 1442"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,177,a(flip),b,1442,a(flip))].">
      <j1 rule="hyper" parents="137 177 1442"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      (1 / (1 / x)) \ y != K(x,x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(1442(a,1),45(a,1))].">
      <j1 rule="para" parents="1442 45"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(1446(a,1),1031(a,2,2))].">
      <j1 rule="para" parents="1446 1031"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,157,a(flip),b,1445,a(flip))].">
      <j1 rule="hyper" parents="137 157 1445"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(540,a,1448,a)].">
      <j1 rule="hyper" parents="540 1448"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(855,a,1443,a),flip(a)].">
      <j1 rule="hyper" parents="855 1443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,10,a(flip),b,1451,a),flip(a)].">
      <j1 rule="hyper" parents="132 10 1451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(681,a,1452,a)].">
      <j1 rule="hyper" parents="681 1452"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(245,a,287,a,b,1444,a)].">
      <j1 rule="hyper" parents="245 287 1444"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(765,a,786,a),flip(a)].">
      <j1 rule="hyper" parents="765 786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(592(a,1),1456(a,2,1))].">
      <j1 rule="para" parents="592 1456"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,910,a(flip),b,1457,a)].">
      <j1 rule="hyper" parents="65 910 1457"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(245,a,909,a(flip),b,1457,a(flip))].">
      <j1 rule="hyper" parents="245 909 1457"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(594(a,1),1459(a,1,2))].">
      <j1 rule="para" parents="594 1459"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[para(1077(a,1),1459(a,1,2))].">
      <j1 rule="para" parents="1077 1459"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,1463,a(flip),b,114,a(flip))].">
      <j1 rule="hyper" parents="201 1463 114"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,1463,a(flip),b,114,a(flip))].">
      <j1 rule="hyper" parents="137 1463 114"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      R(1 / x,y,z) / (1 / x) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,963,a(flip),b,1464,a),flip(a)].">
      <j1 rule="hyper" parents="325 963 1464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      x * (R(x,y,z) / x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,1464,a,b,xx)].">
      <j1 rule="hyper" parents="137 1464"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      ((x \ 1) \ R(x \ 1,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,1081,a,b,1464,a)].">
      <j1 rule="hyper" parents="136 1081 1464"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ 1) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,1081,a(flip),b,1464,a)].">
      <j1 rule="hyper" parents="136 1081 1464"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(1464(a,1),504(a,1,1))].">
      <j1 rule="para" parents="1464 504"/>
    </justification>
  </clause>

  <clause id="1472">
    <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(1465(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1465 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(1468(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1468 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1461(a,1),756(a,1,1))].">
      <j1 rule="para" parents="1461 756"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(38,a,362,a,b,1467,a)].">
      <j1 rule="hyper" parents="38 362 1467"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      L(x \ 1,x,(x \ y) / y) = 1 / x
    ]]></literal>
    <justification jstring="[para(366(a,1),1477(a,1,3))].">
      <j1 rule="para" parents="366 1477"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (((x \ y) / y) * x) * (1 / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(137,a,1478,a(flip),b,225,a(flip))].">
      <j1 rule="hyper" parents="137 1478 225"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1458(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 1458"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      R(x,T(y,x),T(K(z,u),y * x)) \ ((K(z,u) * y) * x) = T(y,x) * T(K(z,u),y * x)
    ]]></literal>
    <justification jstring="[para(287(a,2),828(a,1,2))].">
      <j1 rule="para" parents="287 828"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(814(a,1),893(a,1,1))].">
      <j1 rule="para" parents="814 893"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      T(L(x,x,y),x \ (x \ 1)) = (x * x) * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),1093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      L(T(x,x \ (x \ 1)),x,y) = (x * x) * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,25,a,b,1483,a)].">
      <j1 rule="hyper" parents="65 25 1483"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u * u) = L(x,y,(u * u) * z)
    ]]></literal>
    <justification jstring="[hyper(774,a,1427,a)].">
      <j1 rule="hyper" parents="774 1427"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      L(x,y,(z * z) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(461,a,1486,a),flip(a)].">
      <j1 rule="hyper" parents="461 1486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1487(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(227(a,1),1487(a,1,3)),flip(a)].">
      <j1 rule="para" parents="227 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      L(x,y,z * (z * u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(100(a,1),1487(a,1,3))].">
      <j1 rule="para" parents="100 1487"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      L(x,y,((z * z) \ u) * w) = L(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(119(a,1),1487(a,1,3)),flip(a)].">
      <j1 rule="para" parents="119 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      L(x,y,(z * (z * u)) * w) = L(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(454(a,1),1487(a,1,3))].">
      <j1 rule="para" parents="454 1487"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      L(x,y,T(z * (u * w),w \ (w \ 1))) = L(x,y,z * (u * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(943(a,2),1487(a,1,3))].">
      <j1 rule="para" parents="943 1487"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      L(x,y,L((z * z) \ u,w,v5)) = L(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1307(a,1),1487(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1307 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      ((1 / x) * y) * L(z,y,x) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,1490,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 1490 18"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,659,a(flip),b,1490,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 659 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,1 / x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(132,a,1490,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="132 1490 650"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      L(x,y,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),1490(a,1,3)),flip(a)].">
      <j1 rule="para" parents="82 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      L(x \ ((y \ 1) \ z),x,y) = ((y \ 1) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,308,a(flip),b,1499,a),flip(a)].">
      <j1 rule="hyper" parents="65 308 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      ((x \ 1) * y) * L(z,y,x) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,1499,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 1499 18"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      L(x,y,z) != ((z \ 1) * y) \ u
    ]]></literal>
    <literal><![CDATA[
      y \ ((z \ 1) \ u) = x
    ]]></literal>
    <justification jstring="[para(1499(a,1),526(a,1))].">
      <j1 rule="para" parents="1499 526"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      (x \ 1) \ (L(y,L(x,x,x),x) * 1) = ((x \ 1) \ 1) * T(y,1)
    ]]></literal>
    <justification jstring="[para(1499(a,1),864(a,1,2,1))].">
      <j1 rule="para" parents="1499 864"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      L(x,y,(1 / z) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(647(a,1),1489(a,1,3))].">
      <j1 rule="para" parents="647 1489"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(82(a,1),1505(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="82 1505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      L(x,y,z \ L(z,z,u)) = L(x,y,(z \ 1) * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(1314(a,2),1506(a,2,3)),flip(a)].">
      <j1 rule="para" parents="1314 1506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      L(x,y,L(T(z,u),u,u) * w) = L(x,y,(u * (z * u)) * w)
    ]]></literal>
    <justification jstring="[para(240(a,1),1492(a,1,3,1))].">
      <j1 rule="para" parents="240 1492"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      K(x,x \ 1) * y != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      x \ L(z,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(1498(a,1),1447(a,1)),flip(a)].">
      <j1 rule="para" parents="1498 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(538,a,1501,a),flip(a)].">
      <j1 rule="hyper" parents="538 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      (x * y) \ (x * ((x \ 1) \ z)) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,102,a(flip),b,1501,a)].">
      <j1 rule="hyper" parents="65 102 1501"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      L(x,y,L(1 / z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(273(a,1),1495(a,1,3,1))].">
      <j1 rule="para" parents="273 1495"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      L(x,y,L((1 / z) * u,w,v5)) = L(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(647(a,1),1495(a,1,3,1))].">
      <j1 rule="para" parents="647 1495"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(82(a,1),1512(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="82 1512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      L(x,y,z) \ (x * ((x \ 1) \ u)) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(1313(a,1),1510(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1313 1510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ 1) * z) = (x * y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1511(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      L(x \ 1,y,z) \ ((x \ 1) * u) = L(x,y,z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1515(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(177(a,1),1515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="177 1515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,1518,a(flip),b,1518,a),flip(a)].">
      <j1 rule="hyper" parents="325 1518 1518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      L(x \ y,x \ y,x) \ (x \ y) = (y \ x) \ ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(359(a,1),1518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="359 1518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      L(R(x,y,(x * y) \ 1),z,u) \ R(x,y,(x * y) \ 1) = L(y * ((x * y) \ 1),z,u) \ (R(x,y,(x * y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(483(a,1),1518(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="483 1518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ u) = L(x,y,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(1265,a,1517,a)].">
      <j1 rule="hyper" parents="1265 1517"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1256,a(flip),b,1522,a),flip(a)].">
      <j1 rule="hyper" parents="325 1256 1522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,1252,a(flip),b,1523,a),flip(a)].">
      <j1 rule="hyper" parents="132 1252 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x \ y,x) \ z) = ((x \ y) \ 1) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(359(a,1),1523(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="359 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      (x \ 1) * ((x \ 1) * (L(x \ 1,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(1256(a,1),1523(a,1,2))].">
      <j1 rule="para" parents="1256 1523"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,1518,a(flip),b,1524,a),flip(a)].">
      <j1 rule="hyper" parents="65 1518 1524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(137,a,1518,a(flip),b,1524,a(flip))].">
      <j1 rule="hyper" parents="137 1518 1524"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) != (x \ 1) \ w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(1524(a,2),49(a,1))].">
      <j1 rule="para" parents="1524 49"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,1422,a,b,1527,a)].">
      <j1 rule="hyper" parents="41 1422 1527"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      (x \ 1) \ L(x,y,z) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1530(a,1),365(a,1,1))].">
      <j1 rule="para" parents="1530 365"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      R(x,y,(z \ u) * L(z \ u,z \ u,z)) = R(x,y,(u \ z) \ ((z \ u) \ 1))
    ]]></literal>
    <justification jstring="[para(1520(a,1),1260(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1520 1260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1509,a,683,a)].">
      <j1 rule="hyper" parents="1509 683"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,389,a,b,1534,a),flip(a)].">
      <j1 rule="hyper" parents="40 389 1534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1497,a(flip),b,1535,a),flip(a)].">
      <j1 rule="hyper" parents="65 1497 1535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,1 / T(y,y \ z),(y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(317(a,2),1535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="317 1535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1536(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1536 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      x \ R(1 / (1 / x),y,z) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,1538,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="132 1538 261"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(774,a,1429,a)].">
      <j1 rule="hyper" parents="774 1429"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(216,a,1540,a),flip(a)].">
      <j1 rule="hyper" parents="216 1540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(1540(a,1),216(a,1))].">
      <j1 rule="para" parents="1540 216"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      L(x,y,K(z,u) * K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,153,a(flip),b,1541,a),flip(a)].">
      <j1 rule="hyper" parents="325 153 1541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      L(x,y,T(z,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1226(a,2),1541(a,1,3))].">
      <j1 rule="para" parents="1226 1541"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      L(T(x,y),z,T(u,w)) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,25,a(flip),b,1545,a),flip(a)].">
      <j1 rule="hyper" parents="325 25 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ 1))) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1494,a(flip),b,1545,a)].">
      <j1 rule="hyper" parents="65 1494 1545"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,y) = (T(y,z) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,308,a(flip),b,1545,a),flip(a)].">
      <j1 rule="hyper" parents="65 308 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      (T(x,y) * z) * L(u,z,x) = T(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(137,a,1545,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 1545 18"/>
    </justification>
  </clause>

  <clause id="1550">
    <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),1545(a,1,3))].">
      <j1 rule="para" parents="25 1545"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      L(x,y,z / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(115(a,1),1545(a,1,3)),flip(a)].">
      <j1 rule="para" parents="115 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      L(x,y,(z * u) / z) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(235(a,1),1545(a,1,3)),flip(a)].">
      <j1 rule="para" parents="235 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),1545(a,1,3))].">
      <j1 rule="para" parents="114 1545"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      L(x \ 1,x,y \ z) = ((z / y) * x) \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(475,a,1551,a),flip(a)].">
      <j1 rule="hyper" parents="475 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      L(x,y,z / (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1489,a(flip),b,1551,a),flip(a)].">
      <j1 rule="hyper" parents="325 1489 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,731,a(flip),b,1551,a),flip(a)].">
      <j1 rule="hyper" parents="65 731 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,713,a(flip),b,1551,a),flip(a)].">
      <j1 rule="hyper" parents="65 713 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      L(x,y / x,x \ y) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,659,a(flip),b,1551,a),flip(a)].">
      <j1 rule="hyper" parents="65 659 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,472,a(flip),b,1551,a),flip(a)].">
      <j1 rule="hyper" parents="65 472 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(201,a,1551,a(flip),b,473,a(flip))].">
      <j1 rule="hyper" parents="201 1551 473"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,1551,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="137 1551 103"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,363,a(flip),b,1552,a)].">
      <j1 rule="hyper" parents="65 363 1552"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      L(x,y,T(z,u)) = L(x,y,(z \ w) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1545,a,b,1553,a)].">
      <j1 rule="hyper" parents="325 1545 1553"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1555(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11 1555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(570(a,1),1555(a,1,3))].">
      <j1 rule="para" parents="570 1555"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      L(x,y,z \ (u / (w * w))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(695(a,1),1555(a,1,3))].">
      <j1 rule="para" parents="695 1555"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      L(x,y,z \ (u * u)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(395(a,1),1565(a,1,3))].">
      <j1 rule="para" parents="395 1565"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,1 / T(y,z),(y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1535,a(flip),b,1563,a)].">
      <j1 rule="hyper" parents="65 1535 1563"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ z) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1257(a,1),1566(a,1,3))].">
      <j1 rule="para" parents="1257 1566"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      L(x,y,z \ (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a(flip),b,1568,a),flip(a)].">
      <j1 rule="hyper" parents="325 1499 1568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      L(x,y,(z * z) / u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1551,a,b,1571,a)].">
      <j1 rule="hyper" parents="65 1551 1571"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(846(a,1),1542(a,1,3))].">
      <j1 rule="para" parents="846 1542"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(1226(a,2),1542(a,1,3))].">
      <j1 rule="para" parents="1226 1542"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(22(a,1),1574(a,1,3))].">
      <j1 rule="para" parents="22 1574"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(114(a,1),1574(a,1,3))].">
      <j1 rule="para" parents="114 1574"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(x,y) \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(261(a,2),1574(a,1))].">
      <j1 rule="para" parents="261 1574"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      T(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(1546(a,1),1574(a,1))].">
      <j1 rule="para" parents="1546 1574"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),1560(a,1,2,1))].">
      <j1 rule="para" parents="9 1560"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,1561,a),flip(a)].">
      <j1 rule="hyper" parents="373 1561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,1166,a,b,1562,a),flip(a)].">
      <j1 rule="hyper" parents="40 1166 1562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(375,a,1581,a)].">
      <j1 rule="hyper" parents="375 1581"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(295,a,1581,a)].">
      <j1 rule="hyper" parents="295 1581"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      (x * K(y,x)) \ (y * x) = y
    ]]></literal>
    <justification jstring="[hyper(195,a,1581,a)].">
      <j1 rule="hyper" parents="195 1581"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[hyper(147,a,1581,a)].">
      <j1 rule="hyper" parents="147 1581"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,1581,a,b,9,a)].">
      <j1 rule="hyper" parents="137 1581 9"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(132,a,1581,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="132 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(10(a,1),1581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(1581(a,1),235(a,1,1))].">
      <j1 rule="para" parents="1581 235"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(1581(a,1),295(a,1))].">
      <j1 rule="para" parents="1581 295"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(1581(a,1),303(a,1,1))].">
      <j1 rule="para" parents="1581 303"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),274(a,1,1,1))].">
      <j1 rule="para" parents="1581 274"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),110(a,1,1))].">
      <j1 rule="para" parents="1581 110"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      R(x * K(y,x),y,y) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1581(a,1),572(a,1,1))].">
      <j1 rule="para" parents="1581 572"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),424(a,1,1,1))].">
      <j1 rule="para" parents="1581 424"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(1581(a,1),426(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1581 426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(1581(a,1),749(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1581 749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(1581(a,1),588(a,1,1,1))].">
      <j1 rule="para" parents="1581 588"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1581(a,1),593(a,1,1,1))].">
      <j1 rule="para" parents="1581 593"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(1581(a,2),92(a,1,2))].">
      <j1 rule="para" parents="1581 92"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),785(a,1,1))].">
      <j1 rule="para" parents="1581 785"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      ((x * K(y * z,x)) * y) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),789(a,1,1,1))].">
      <j1 rule="para" parents="1581 789"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),1552(a,1,3))].">
      <j1 rule="para" parents="1581 1552"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1589(a,1),295(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="1589 295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      (x * (y * K(z,y))) * T(y * K(z,y),z) = (x * y) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(1589(a,1),1131(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1589 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * (z * K(y,z))) * y) = a(x,z * K(y,z),y)
    ]]></literal>
    <justification jstring="[para(1585(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1585 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      ((x * y) * z) * a(z * K(x * y,z),x,y) = ((z * K(x * y,z)) * x) * y
    ]]></literal>
    <justification jstring="[para(1585(a,1),89(a,1,1))].">
      <j1 rule="para" parents="1585 89"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1095,a(flip),b,1587,a)].">
      <j1 rule="hyper" parents="325 1095 1587"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(132,a,1587,a,b,1095,a(flip))].">
      <j1 rule="hyper" parents="132 1587 1095"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1587(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * y) / z) = u
    ]]></literal>
    <justification jstring="[para(1587(a,2),331(a,1,2,2))].">
      <j1 rule="para" parents="1587 331"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(42,a,1589,a,b,1592,a)].">
      <j1 rule="hyper" parents="42 1589 1592"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(42,a,274,a,b,1592,a)].">
      <j1 rule="hyper" parents="42 274 1592"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(1612(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1612 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      (K(x,y) * T(z * K(u,z),w)) * u = K(x,y) * (u * T(z,w))
    ]]></literal>
    <justification jstring="[para(1595(a,1),287(a,2,2))].">
      <j1 rule="para" parents="1595 287"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,1596,a,b,1581,a(flip))].">
      <j1 rule="hyper" parents="132 1596 1581"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      L(T(x * K(y * z,x),u),z,y) = (y * (z * T(x,u))) / (y * z)
    ]]></literal>
    <justification jstring="[para(1596(a,2),785(a,1,1))].">
      <j1 rule="para" parents="1596 785"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      T(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(1596(a,2),1606(a,1))].">
      <j1 rule="para" parents="1596 1606"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,1 / x) = z
    ]]></literal>
    <justification jstring="[para(1611(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1611 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      L(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1499(a,1),1573(a,1))].">
      <j1 rule="para" parents="1499 1573"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      R((x * y) * (x \ 1),z,u) * (x * x) = (R(y * K(x,y),z,u) * x) * x
    ]]></literal>
    <justification jstring="[para(1594(a,1),406(a,1,1,1))].">
      <j1 rule="para" parents="1594 406"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      L(x,y,z \ (u \ 1)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(271(a,1),1567(a,1,3,2))].">
      <j1 rule="para" parents="271 1567"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,1585,a,b,1598,a)].">
      <j1 rule="hyper" parents="37 1585 1598"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      L(L(x,y,z) * K(u,L(x,y,z)),w,v5) * u = u * L(L(x,w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(30(a,1),1598(a,2,2))].">
      <j1 rule="para" parents="30 1598"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,1585,a,b,1599,a)].">
      <j1 rule="hyper" parents="37 1585 1599"/>
    </justification>
  </clause>

  <clause id="1631">
    <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(1615(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1615 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      R(x,y,(T(z,u) * w) \ L(T(z,u) * w,w,z)) = R(x,y,T(z,u) * (w * (T(z,u) * w)))
    ]]></literal>
    <justification jstring="[para(1549(a,1),1039(a,2,3))].">
      <j1 rule="para" parents="1549 1039"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      ((x / y) * z) \ (x / y) = ((y \ x) * z) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(475,a,1554,a),flip(a)].">
      <j1 rule="hyper" parents="475 1554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(195,a,1579,a),flip(a)].">
      <j1 rule="hyper" parents="195 1579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      x / L(y,y,x) = (x / (y * y)) * y
    ]]></literal>
    <justification jstring="[para(1489(a,1),1579(a,1,2))].">
      <j1 rule="para" parents="1489 1579"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      L(x,y,R(z * K(u,z),u,w)) = L(x,y,(u * w) \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(1593(a,2),1551(a,1,3))].">
      <j1 rule="para" parents="1593 1551"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (z * y)) * z = u
    ]]></literal>
    <justification jstring="[para(1634(a,2),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1634 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      L(x,y,z * L(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(824(a,1),1570(a,1,3)),flip(a)].">
      <j1 rule="para" parents="824 1570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      ((x \ y) * (y / x)) \ (x \ y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,273,a(flip),b,1633,a),flip(a)].">
      <j1 rule="hyper" parents="65 273 1633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      (x \ (x \ 1)) \ (x \ 1) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(665(a,1),1642(a,1,1))].">
      <j1 rule="para" parents="665 1642"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(341,a,1643,a)].">
      <j1 rule="hyper" parents="341 1643"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      (x * x) * ((y * x) \ y) = L(1 / (1 / x),x,y)
    ]]></literal>
    <justification jstring="[para(1644(a,1),1484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1644 1484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      L(T(x * K(y * z,x),u),z,y) = T((y * (z * x)) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(1602(a,1),25(a,2,1))].">
      <j1 rule="para" parents="1602 25"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      L(x,1 / T(y,z),(y \ u) \ u) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1574,a,1569,a),flip(a)].">
      <j1 rule="hyper" parents="1574 1569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * y) = T((x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1621,a(flip),b,1646,a)].">
      <j1 rule="hyper" parents="65 1621 1646"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      T((x * (y * z)) / (x * y),y) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(113(a,1),1651(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 1651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      (x * (y * T(T(z,y),u))) / (x * y) = T((x * (z * y)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(113(a,1),1651(a,2,1,1,2))].">
      <j1 rule="para" parents="113 1651"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      (x * (y * K(z,y))) * y = (x * y) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(1589(a,1),1607(a,1,2))].">
      <j1 rule="para" parents="1589 1607"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (x * (T(y,z) * u)) / (x * u) = T((x * (y * u)) / (x * u),z)
    ]]></literal>
    <justification jstring="[para(241(a,1),1653(a,1,1,2))].">
      <j1 rule="para" parents="241 1653"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      L(L(x * K(y,x),z,u),w,v5) * y = y * L(L(x,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(1628(a,1),1629(a,1,1,1))].">
      <j1 rule="para" parents="1628 1629"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      x * L(L(T(y,x),z,u),w,v5) = L(L(y,w,v5),z,u) * x
    ]]></literal>
    <justification jstring="[para(1583(a,1),1657(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1583 1657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (x \ 1) = x \ L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,953,a(flip),b,1658,a),flip(a)].">
      <j1 rule="hyper" parents="65 953 1658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      L(x,y,z \ L(L(z,u,w),v5,v6)) = L(x,y,L(L(z,v5,v6),u,w) * z)
    ]]></literal>
    <justification jstring="[para(1659(a,1),1566(a,1,3))].">
      <j1 rule="para" parents="1659 1566"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      L(x,y,z \ L(L(z,u,w),v5,v6)) = L(x,y,z * L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(876(a,1),1660(a,2,3))].">
      <j1 rule="para" parents="876 1660"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      L(x \ y,x,x * L(L(x,z,u),w,v5)) = L(L(x,z,u),w,v5) \ ((L(L(x,z,u),w,v5) / x) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1559,a(flip),b,1661,a),flip(a)].">
      <j1 rule="hyper" parents="65 1559 1661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      x \ (R((x * x) / x,y,z) * u) = R(1 / x,y,z) * ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(1056(a,1),973(a,1,2))].">
      <j1 rule="para" parents="1056 973"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      R(1 / x,y,z) * ((1 / x) \ u) = x \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1665(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      R(1 / x,y,z) * ((1 / x) \ u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,958,a(flip),b,1666,a),flip(a)].">
      <j1 rule="hyper" parents="325 958 1666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      R(x,y,z) * (1 / x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,177,a(flip),b,1666,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 177 1666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),980(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,803,a(flip),b,995,a)].">
      <j1 rule="hyper" parents="65 803 995"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,803,a(flip),b,996,a),flip(a)].">
      <j1 rule="hyper" parents="325 803 996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      (x * y) * K(z \ (z / K(y,x)),z) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16(a,2),1124(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      (x * y) * (K(y,x) * T(K(y,x) \ 1,z)) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(896(a,1),1673(a,1,2))].">
      <j1 rule="para" parents="896 1673"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,1674,a)].">
      <j1 rule="hyper" parents="140 1674"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[hyper(140,a,1235,a)].">
      <j1 rule="hyper" parents="140 1235"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ x,z,u)) = T(y,x) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1414(a,2,2,1))].">
      <j1 rule="para" parents="22 1414"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * x) * L((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,1310,a,b,1677,a)].">
      <j1 rule="hyper" parents="137 1310 1677"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1432(a,1),1436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1432 1436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1680">
    <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(944(a,1),1679(a,1,1)),flip(a)].">
      <j1 rule="para" parents="944 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1457(a,1),1480(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1457 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <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(966(a,1),1681(a,1,1)),flip(a)].">
      <j1 rule="para" parents="966 1681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(803(a,1),1671(a,2,1))].">
      <j1 rule="para" parents="803 1671"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(327,a,1672,a),flip(a)].">
      <j1 rule="hyper" parents="327 1672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(1672(a,1),327(a,1))].">
      <j1 rule="para" parents="1672 327"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[para(8(a,1),1676(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1676(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(1623,a,1686,a),flip(a)].">
      <j1 rule="hyper" parents="1623 1686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(137,a,1425,a,b,1686,a(flip))].">
      <j1 rule="hyper" parents="137 1425 1686"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1689(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(245,a,1432,a(flip),b,1678,a),flip(a)].">
      <j1 rule="hyper" parents="245 1432 1678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(327,a,1683,a),flip(a)].">
      <j1 rule="hyper" parents="327 1683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1683(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7 1683"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(245,a,1698,a(flip),b,1690,a(flip))].">
      <j1 rule="hyper" parents="245 1698 1690"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      ((x * x) * (y * (z * u))) \ (((x * x) * (y * z)) * u) = a((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),122(a,1,2,1))].">
      <j1 rule="para" parents="33 122"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (K(x,y) * (z * (u * w))) \ ((K(x,y) * (z * u)) * w) = a(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(287(a,1),627(a,1,2,1))].">
      <j1 rule="para" parents="287 627"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,408,a(flip),b,782,a),flip(a)].">
      <j1 rule="hyper" parents="65 408 782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1703(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(587(a,1),1703(a,2,1))].">
      <j1 rule="para" parents="587 1703"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(588(a,1),1704(a,1,1))].">
      <j1 rule="para" parents="588 1704"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(540,a,1706,a)].">
      <j1 rule="hyper" parents="540 1706"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(532,a,1706,a)].">
      <j1 rule="hyper" parents="532 1706"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,154,a(flip),b,1706,a),flip(a)].">
      <j1 rule="hyper" parents="325 154 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(211,a,1706,a),flip(a)].">
      <j1 rule="hyper" parents="211 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(140,a,1706,a)].">
      <j1 rule="hyper" parents="140 1706"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,154,a(flip),b,1706,a)].">
      <j1 rule="hyper" parents="135 154 1706"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x * (y * y)) / y = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,100,a(flip),b,1706,a)].">
      <j1 rule="hyper" parents="135 100 1706"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      ((x / L(y,z,u)) / y) * L(y,z,u) = x / y
    ]]></literal>
    <justification jstring="[hyper(135,a,88,a(flip),b,1706,a),flip(a)].">
      <j1 rule="hyper" parents="135 88 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(132,a,154,a(flip),b,1706,a)].">
      <j1 rule="hyper" parents="132 154 1706"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (x * L(y,z,u)) = y * K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(135,a,1706,a(flip),b,1585,a)].">
      <j1 rule="hyper" parents="135 1706 1585"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (L(y,z,u) * y) = R(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(135,a,1706,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="135 1706 109"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      ((x * y) * z) * L(z,y,x) = (x * (y * z)) * z
    ]]></literal>
    <justification jstring="[para(100(a,1),1706(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1719">
    <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(1706(a,1),316(a,1,1))].">
      <j1 rule="para" parents="1706 316"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      x * L(y,y,x) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,566,a(flip),b,1713,a),flip(a)].">
      <j1 rule="hyper" parents="65 566 1713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      L(x,x,y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(132,a,566,a(flip),b,1713,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 566 1713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      L(x,x,R(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(132,a,309,a(flip),b,1713,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 309 1713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      L(x * K(y,x),x,y) = (y / (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,1720,a(flip),b,1598,a),flip(a)].">
      <j1 rule="hyper" parents="135 1720 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),y) = (y / (x \ 1)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(1720(a,1),102(a,2,1))].">
      <j1 rule="para" parents="1720 102"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      R(x,y,(z * K(u,z)) * L(z * K(u,z),z,u)) = R(x,y,(z * K(u,z)) \ ((u / (z \ 1)) / u))
    ]]></literal>
    <justification jstring="[para(1723(a,1),1039(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1723 1039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      (x * K(y,x)) * L((x * K(y,x)) \ 1,x,y) = (x * K(y,x)) \ ((y / (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(1723(a,1),1310(a,2,2))].">
      <j1 rule="para" parents="1723 1310"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) * x) \ ((z * (y * x)) * x)
    ]]></literal>
    <justification jstring="[para(193(a,1),1708(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="193 1708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(135,a,100,a(flip),b,1709,a),flip(a)].">
      <j1 rule="hyper" parents="135 100 1709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1711(a,1),1150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1711 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(140,a,1728,a),flip(a)].">
      <j1 rule="hyper" parents="140 1728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      (x * (R(y / z,z,y) \ 1)) / (y \ 1) = ((x * z) / (y \ 1)) * L(y \ 1,z,x)
    ]]></literal>
    <justification jstring="[para(1011(a,2),1728(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1011 1728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,1729,a(flip),b,591,a)].">
      <j1 rule="hyper" parents="137 1729 591"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ ((x * y) / z) = L(z,y / z,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1730(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      R((x * y) / y,y,L(y,z,u)) = R(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,503,a(flip),b,1717,a)].">
      <j1 rule="hyper" parents="65 503 1717"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      R(x,L(y,z,u),y) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),1734(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(((x / y) * y) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(327,a,1705,a),flip(a)].">
      <j1 rule="hyper" parents="327 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,908,a(flip),b,1705,a)].">
      <j1 rule="hyper" parents="65 908 1705"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,907,a(flip),b,1705,a),flip(a)].">
      <j1 rule="hyper" parents="65 907 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(245,a,1705,a(flip),b,908,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 1705 908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),1705(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) != y * v5
    ]]></literal>
    <literal><![CDATA[
      T(x * L(x \ z,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(1705(a,2),246(a,2)),flip(a)].">
      <j1 rule="para" parents="1705 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1742">
    <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),1739(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,1742,a,b,xx)].">
      <j1 rule="hyper" parents="132 1742"/>
    </justification>
  </clause>

  <clause id="1744">
    <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),1743(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1112(a,1),1744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1112 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1116,a(flip),b,1745,a),flip(a)].">
      <j1 rule="hyper" parents="65 1116 1745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      x * (T(y,z) * L(T(y,z) \ (x \ (y * z)),u,w)) = (x * L(x \ z,u,w)) * T(y,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1737(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="113 1737"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      x * L(x \ (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,1307,a(flip),b,1740,a),flip(a)].">
      <j1 rule="hyper" parents="135 1307 1740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      x \ L(x * (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1322,a,b,1748,a)].">
      <j1 rule="hyper" parents="65 1322 1748"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(137,a,1748,a(flip),b,1322,a),flip(a)].">
      <j1 rule="hyper" parents="137 1748 1322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,1322,a,b,1748,a(flip))].">
      <j1 rule="hyper" parents="136 1322 1748"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(179(a,1),1749(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="179 1749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      L(R(x,y,z),u,w) / x = x \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1468(a,1),1749(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1468 1749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(195,a,1752,a)].">
      <j1 rule="hyper" parents="195 1752"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(147,a,1752,a)].">
      <j1 rule="hyper" parents="147 1752"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      x * (L(x,y,z) / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,1752,a,b,xx)].">
      <j1 rule="hyper" parents="137 1752"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1238,a,b,1752,a)].">
      <j1 rule="hyper" parents="65 1238 1752"/>
    </justification>
  </clause>

  <clause id="1758">
    <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(1754(a,1),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1754 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      K(x \ L(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,1755,a(flip),b,313,a),flip(a)].">
      <j1 rule="hyper" parents="131 1755 313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1760">
    <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(1755(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1755 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x * u)) \ (L(x,y,z) * u) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(1755(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1755 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <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(1755(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1755 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) * ((y \ L(y,z,u)) * y) = (y \ L(y,z,u)) * (y * T(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1755(a,1),584(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1755 584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      L(x \ 1,y,z) \ L(x,y,z) = x * x
    ]]></literal>
    <justification jstring="[para(1755(a,1),1334(a,1,2))].">
      <j1 rule="para" parents="1755 1334"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1755(a,1),1335(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1755 1335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      L(L(x,y,z),u,w) / x = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1756(a,1),1749(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1756 1749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1757(a,1),1505(a,1,3))].">
      <j1 rule="para" parents="1757 1505"/>
    </justification>
  </clause>

  <clause id="1768">
    <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="[para(1757(a,1),1513(a,1,3,1))].">
      <j1 rule="para" parents="1757 1513"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      L(x * (((y \ z) \ u) / x),y \ z,y) = x * ((z \ (y * u)) / x)
    ]]></literal>
    <justification jstring="[para(469(a,1),1750(a,2,2,1))].">
      <j1 rule="para" parents="469 1750"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1751(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 1751"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(81(a,1),1751(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 1751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(389(a,1),1770(a,1,1))].">
      <j1 rule="para" parents="389 1770"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      L((x * y) * x,z,u) = (x * L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1324(a,1),1770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1324 1770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,176,a(flip),b,1771,a),flip(a)].">
      <j1 rule="hyper" parents="43 176 1771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x
    ]]></literal>
    <justification jstring="[para(308(a,1),1771(a,2,1,2))].">
      <j1 rule="para" parents="308 1771"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(468(a,1),1771(a,2,1,2))].">
      <j1 rule="para" parents="468 1771"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(340,a,1774,a)].">
      <j1 rule="hyper" parents="340 1774"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,1774,a)].">
      <j1 rule="hyper" parents="145 1774"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,1774,a)].">
      <j1 rule="hyper" parents="140 1774"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(37,a,1710,a,b,1774,a)].">
      <j1 rule="hyper" parents="37 1710 1774"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      a(x,x \ 1,y) \ y = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(719(a,1),1779(a,1,1))].">
      <j1 rule="para" parents="719 1779"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      a(x,x,y) \ y = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(824(a,1),1779(a,1,1))].">
      <j1 rule="para" parents="824 1779"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      a(x,x,y) / y = 1 / L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,824,a(flip),b,1780,a)].">
      <j1 rule="hyper" parents="135 824 1780"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      a(x,x,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,849,a(flip),b,1783,a),flip(a)].">
      <j1 rule="hyper" parents="325 849 1783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      K(x \ 1,x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,343,a,b,1784,a)].">
      <j1 rule="hyper" parents="39 343 1784"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(245,a,1772,a,b,261,a)].">
      <j1 rule="hyper" parents="245 1772 261"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(313(a,1),1786(a,1,1,2))].">
      <j1 rule="para" parents="313 1786"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((u * z) \ u)) = L(x,y,z * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1507,a(flip),b,1767,a)].">
      <j1 rule="hyper" parents="65 1507 1767"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,u,x * L(x,y,z)) = (x \ L(x,y,z)) / (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,1767,a(flip),b,1721,a(flip))].">
      <j1 rule="hyper" parents="137 1767 1721"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      L(x,y,(T(z,u) * w) \ L(T(z,u) * w,w,z)) = L(x,y,T(z,u) * (w * (T(z,u) * w)))
    ]]></literal>
    <justification jstring="[para(1549(a,1),1767(a,2,3))].">
      <j1 rule="para" parents="1549 1767"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[hyper(137,a,1775,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 1775 18"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,1776,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 1776 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      (x \ 1) * (y * (((x \ 1) \ z) / y)) = x \ (y * ((1 \ (x * z)) / y))
    ]]></literal>
    <justification jstring="[hyper(132,a,1769,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 1769 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * (x * u)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1767,a(flip),b,1762,a),flip(a)].">
      <j1 rule="hyper" parents="325 1767 1762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      (x \ 1) * (y * (((x \ 1) \ z) / y)) = x \ (y * ((x * z) / y))
    ]]></literal>
    <justification jstring="[para(67(a,1),1793(a,2,2,2,1))].">
      <j1 rule="para" parents="67 1793"/>
    </justification>
  </clause>

  <clause id="1796">
    <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(10(a,1),1794(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(1716(a,1),749(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1716 749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1798">
    <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(1622,a,1797,a)].">
      <j1 rule="hyper" parents="1622 1797"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(907(a,1),1738(a,1,1))].">
      <j1 rule="para" parents="907 1738"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(135,a,154,a(flip),b,1799,a)].">
      <j1 rule="hyper" parents="135 154 1799"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      (x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y
    ]]></literal>
    <justification jstring="[para(358(a,1),1799(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="358 1799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      (x * (y * (1 / y))) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(358(a,1),1801(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="358 1801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(1366(a,2),1802(a,1,1,2))].">
      <j1 rule="para" parents="1366 1802"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1366(a,2),1803(a,2,2))].">
      <j1 rule="para" parents="1366 1803"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(135,a,154,a(flip),b,1804,a)].">
      <j1 rule="hyper" parents="135 154 1804"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1450,a(flip),b,1806,a),flip(a)].">
      <j1 rule="hyper" parents="65 1450 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(135,a,1807,a(flip),b,1387,a)].">
      <j1 rule="hyper" parents="135 1807 1387"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      (x / (1 / (1 / y))) * K(y \ 1,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(39,a,1200,a,b,1808,a(flip))].">
      <j1 rule="hyper" parents="39 1200 1808"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(765,a,787,a),flip(a)].">
      <j1 rule="hyper" parents="765 787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(592(a,1),1810(a,2,1))].">
      <j1 rule="para" parents="592 1810"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,910,a(flip),b,1811,a)].">
      <j1 rule="hyper" parents="65 910 1811"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(245,a,1811,a(flip),b,983,a),flip(a)].">
      <j1 rule="hyper" parents="245 1811 983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,1811,a(flip),b,983,a),flip(a)].">
      <j1 rule="hyper" parents="132 1811 983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1811(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1815(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1815"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(140,a,1816,a)].">
      <j1 rule="hyper" parents="140 1816"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,83,a(flip),b,1816,a),flip(a)].">
      <j1 rule="hyper" parents="135 83 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1464,a(flip),b,1819,a),flip(a)].">
      <j1 rule="hyper" parents="325 1464 1819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      L(x,y,z \ R(z,u,w)) = L(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1820(a,1),1505(a,1,3))].">
      <j1 rule="para" parents="1820 1505"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      L(x,y,(y * x) \ 1) \ R(L(x,y,(y * x) \ 1),z,u) = ((1 / (y * x)) * y) * R(L(x,y,(y * x) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(1579(a,1),1820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1579 1820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1818(a,1),1150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1818 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,1824,a(flip),b,591,a)].">
      <j1 rule="hyper" parents="137 1824 591"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * (y * R(x,z,u)) = (y * R(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1824(a,1),243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1824 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <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(37,a,1585,a,b,1826,a)].">
      <j1 rule="hyper" parents="37 1585 1826"/>
    </justification>
  </clause>

  <clause id="1828">
    <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),1813(a,1,1))].">
      <j1 rule="para" parents="22 1813"/>
    </justification>
  </clause>

  <clause id="1829">
    <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),1828(a,1,2,1,1))].">
      <j1 rule="para" parents="22 1828"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      R(x \ y,(x \ y) \ 1,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,11,a(flip),b,1421,a),flip(a)].">
      <j1 rule="hyper" parents="325 11 1421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      R(x,y,(z \ u) * L(z \ u,z \ u,z)) = R(x,y,(u \ z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1036,a(flip),b,1533,a),flip(a)].">
      <j1 rule="hyper" parents="325 1036 1533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      R(x,y,(z \ u) \ (u \ z)) = R(x,y,(u \ z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1035,a(flip),b,1832,a),flip(a)].">
      <j1 rule="hyper" parents="65 1035 1832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      ((x * y) * z) * a(z * K(x * y,z),x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1603,a(flip),b,1609,a),flip(a)].">
      <j1 rule="hyper" parents="325 1603 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      ((x * x) * (y * (z * u))) \ ((x * x) * ((y * z) * u)) = a((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),1701(a,1,2))].">
      <j1 rule="para" parents="33 1701"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(287(a,1),1702(a,1,2))].">
      <j1 rule="para" parents="287 1702"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),u * u) = a((u * u) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,474,a(flip),b,1835,a)].">
      <j1 rule="hyper" parents="65 474 1835"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      a((x * x) * y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(461,a,1837,a),flip(a)].">
      <j1 rule="hyper" parents="461 1837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      a((x * x) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1837(a,1),461(a,1))].">
      <j1 rule="para" parents="1837 461"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(227(a,1),1838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="227 1838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(100(a,1),1838(a,1,1))].">
      <j1 rule="para" parents="100 1838"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      a(T(x,y * y) * z,u,w) = a((x * (y * y)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(244(a,1),1838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="244 1838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      a(((x * (x * y)) * z) * u,w,v5) = a((L(y,x,x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(823(a,1),1838(a,1,1))].">
      <j1 rule="para" parents="823 1838"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      a(L((x * x) * y,z,u),w,v5) = a(L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1311(a,2),1838(a,1,1))].">
      <j1 rule="para" parents="1311 1838"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      a(x \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),1842(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 1842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      a(L(x \ y,x,x),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(102(a,2),1841(a,1,1))].">
      <j1 rule="para" parents="102 1841"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      a((1 / x) * y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(647(a,1),1841(a,1,1))].">
      <j1 rule="para" parents="647 1841"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      a((x \ 1) * y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),1849(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 1849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) = a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1757(a,1),1849(a,1,1))].">
      <j1 rule="para" parents="1757 1849"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      a(L((x * x) * y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(L(y,z,u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(1311(a,2),1839(a,1,1))].">
      <j1 rule="para" parents="1311 1839"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      a(L(L(x,x,y),y,y),z,u) = a(y * (y / (x \ 1)),z,u)
    ]]></literal>
    <justification jstring="[para(1720(a,1),1843(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1720 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      a(L((x * x) * L(y,z,u),w,v5),v6,v7) = a(L(L(y,w,v5),z,u),v6,v7)
    ]]></literal>
    <justification jstring="[para(30(a,1),1846(a,2,1))].">
      <j1 rule="para" parents="30 1846"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      a(L(((x * x) \ y) * z,u,w),v5,v6) = a(L(y * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(119(a,1),1846(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="119 1846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      a(L((1 / x) * y,z,u),w,v5) = a(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(273(a,1),1855(a,1,1,1,1))].">
      <j1 rule="para" parents="273 1855"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      a(L((x \ 1) * y,z,u),w,v5) = a(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),1856(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 1856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      a(L(((x * x) \ y) * z,u,w),v5,v6) = a(L((y \ (x * x)) * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(435(a,1),1856(a,1,1,1,1))].">
      <j1 rule="para" parents="435 1856"/>
    </justification>
  </clause>

  <clause id="1859">
    <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(1852,a,1854,a)].">
      <j1 rule="hyper" parents="1852 1854"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(L(L(x,u,w),y,z),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(1854(a,1),1852(a,1))].">
      <j1 rule="para" parents="1854 1852"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      a(L((x \ (y * y)) * z,u,w),v5,v6) = a(L(x * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,1855,a(flip),b,1858,a),flip(a)].">
      <j1 rule="hyper" parents="65 1855 1858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      a(L(((x * y) \ (x * (x \ 1))) * z,u,w),v5,v6) = a(L(((x \ 1) * y) * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(1516(a,1),1861(a,1,1,1,1))].">
      <j1 rule="para" parents="1516 1861"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u,w)) = a(K(u,w) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,474,a(flip),b,1836,a)].">
      <j1 rule="hyper" parents="65 474 1836"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(216,a,1864,a),flip(a)].">
      <j1 rule="hyper" parents="216 1864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(1864(a,1),216(a,1))].">
      <j1 rule="para" parents="1864 216"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(1226(a,2),1865(a,1,1))].">
      <j1 rule="para" parents="1226 1865"/>
    </justification>
  </clause>

  <clause id="1869">
    <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),1868(a,1,1))].">
      <j1 rule="para" parents="25 1868"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      a(x / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),1868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 1868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(114(a,1),1868(a,1,1))].">
      <j1 rule="para" parents="114 1868"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      a(L(x / y,z,u),w,v5) = a(L(y \ x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(252(a,1),1868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="252 1868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      a(x * K(y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(1589(a,1),1868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1589 1868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      a(R(x * K(y,x),y,z),u,w) = a((y * z) \ ((y * x) * z),u,w)
    ]]></literal>
    <justification jstring="[para(1593(a,2),1870(a,1,1))].">
      <j1 rule="para" parents="1593 1870"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[para(1873(a,1),1834(a,1,2))].">
      <j1 rule="para" parents="1873 1834"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      a(T(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(1226(a,2),1866(a,1,1))].">
      <j1 rule="para" parents="1226 1866"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      a(x \ (y * x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(22(a,1),1876(a,1,1))].">
      <j1 rule="para" parents="22 1876"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      a(L(T(x,y),z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(L(x,z,u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(25(a,2),1876(a,1,1))].">
      <j1 rule="para" parents="25 1876"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(114(a,1),1876(a,1,1))].">
      <j1 rule="para" parents="114 1876"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1877,a,1841,a),flip(a)].">
      <j1 rule="hyper" parents="1877 1841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      a(x * (y * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(1841(a,1),1877(a,1))].">
      <j1 rule="para" parents="1841 1877"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      a(x * (y * (z * z)),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(34(a,1),1880(a,1,1))].">
      <j1 rule="para" parents="34 1880"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      a(x \ (y / (z * z)),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(559(a,1),1880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="559 1880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      a(L(x * (y * y),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1069(a,2),1880(a,1,1))].">
      <j1 rule="para" parents="1069 1880"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      a(L(L(x,x,y),y * x,z),u,w) = a((z * (y * x)) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(1064(a,1),1880(a,1,1))].">
      <j1 rule="para" parents="1064 1880"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      a(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1847(a,1),1879(a,1))].">
      <j1 rule="para" parents="1847 1879"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      a(L(x \ y,x \ y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(561(a,1),1881(a,1,1))].">
      <j1 rule="para" parents="561 1881"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      a(L(R(x / y,y,z),u,w),v5,v6) = a(L((y * z) \ (x * z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(499(a,1),1869(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="499 1869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      a(x * (y / (z * z)),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),1882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      a(x * (y \ 1),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(221(a,1),1882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="221 1882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      a(x * (y \ (z * z)),u,w) = a(x * (y \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(395(a,1),1882(a,1,1,2))].">
      <j1 rule="para" parents="395 1882"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      a(x * L(y * (z * z),u,w),v5,v6) = a(x * L(y,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(1069(a,2),1882(a,1,1,2))].">
      <j1 rule="para" parents="1069 1882"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ ((y * z) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(140,a,1875,a),flip(a)].">
      <j1 rule="hyper" parents="140 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      x * a(x,y,y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,33,a(flip),b,1875,a(flip))].">
      <j1 rule="hyper" parents="36 33 1875"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      x \ R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,1894,a)].">
      <j1 rule="hyper" parents="140 1894"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      R(x,y,y) / x = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1468,a,b,1894,a)].">
      <j1 rule="hyper" parents="36 1468 1894"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      x \ R(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(1894(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1894 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),x) = R(x,y,y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(1894(a,1),102(a,2,1))].">
      <j1 rule="para" parents="1894 102"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      a(x,y,y) * x = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,1896,a(flip),b,1464,a)].">
      <j1 rule="hyper" parents="136 1896 1464"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      L(x,y,z * R(z,u,u)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(1896(a,1),1822(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1896 1822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,u),y,z) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,z),u,u) = w
    ]]></literal>
    <justification jstring="[para(29(a,1),1898(a,1,2))].">
      <j1 rule="para" parents="29 1898"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(221(a,1),1884(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="221 1884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      a(L(x \ (y \ (z * z)),u,w),v5,v6) = a(L(x \ (y \ 1),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(557(a,1),1884(a,1,1,1))].">
      <j1 rule="para" parents="557 1884"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      a(x * (y \ (z * z)),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1890,a(flip),b,1891,a),flip(a)].">
      <j1 rule="hyper" parents="325 1890 1891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1906">
    <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),1905(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14 1905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,102,a,b,1893,a),flip(a)].">
      <j1 rule="hyper" parents="325 102 1893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      L(x,y,z * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(1907(a,2),52(a,1)),flip(a)].">
      <j1 rule="para" parents="1907 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      a(x * L(y \ 1,z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(221(a,1),1892(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="221 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      a(L(L(x,y * x,z),x,y),u,w) = a((z * (y * x)) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(1860,a,1885,a)].">
      <j1 rule="hyper" parents="1860 1885"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      a(L(((x * x) \ y) * x,z,u),w,v5) = a(L(R(y / x,x,x),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(391(a,1),1888(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="391 1888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      a(L(R(x / y,y,y),z,u),w,v5) = a(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,1855,a(flip),b,1911,a),flip(a)].">
      <j1 rule="hyper" parents="65 1855 1911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      a(L(x * (y \ 1),z,u),w,v5) = a(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(572(a,1),1912(a,1,1,1))].">
      <j1 rule="para" parents="572 1912"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      a(L(L(x,y,z) \ x,u,w),v5,v6) = a(L(x * L(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(1257(a,1),1914(a,1,1,1))].">
      <j1 rule="para" parents="1257 1914"/>
    </justification>
  </clause>

  <clause id="1916">
    <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(113(a,1),1072(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(245,a,1457,a(flip),b,1916,a),flip(a)].">
      <j1 rule="hyper" parents="245 1457 1916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      x \ ((y * x) * T((y * x) \ z,u)) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1167(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(821(a,1),1918(a,1,2))].">
      <j1 rule="para" parents="821 1918"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ (y \ z),u) = T(x * T(x \ (z / y),u),y)
    ]]></literal>
    <justification jstring="[hyper(1190,a,1919,a),flip(a)].">
      <j1 rule="hyper" parents="1190 1919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1920(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1921(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 1921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(236(a,1),1921(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="236 1921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(205(a,1),1923(a,1,2,1,2))].">
      <j1 rule="para" parents="205 1923"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(898,a,1924,a),flip(a)].">
      <j1 rule="hyper" parents="898 1924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(929(a,2),1925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="929 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(1523(a,1),1526(a,1,2))].">
      <j1 rule="para" parents="1523 1526"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1263,a(flip),b,1928,a),flip(a)].">
      <j1 rule="hyper" parents="325 1263 1928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      K(x \ 1,x) * L(L(x,y,z) \ u,x,x \ 1) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,458,a,b,1929,a)].">
      <j1 rule="hyper" parents="65 458 1929"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,y) = L(x,((y \ z) \ z) \ 1,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1649,a(flip),b,1537,a)].">
      <j1 rule="hyper" parents="325 1649 1537"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),1736(a,2,2,1,1))].">
      <j1 rule="para" parents="12 1736"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,1935,a)].">
      <j1 rule="hyper" parents="145 1935"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1936(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1936(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <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),1937(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 1937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1142(a,2),1938(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1142 1938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(586(a,1),1940(a,1,1)),flip(a)].">
      <j1 rule="para" parents="586 1940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(1942(a,1),115(a,1,1))].">
      <j1 rule="para" parents="1942 115"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1251,a(flip),b,1943,a),flip(a)].">
      <j1 rule="hyper" parents="325 1251 1943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      K(x \ 1,x) * L(L(x,y,z) \ u,x,x) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1499(a,1),1930(a,1,2))].">
      <j1 rule="para" parents="1499 1930"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),x) = ((x * y) * y) \ ((x * (y * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1565,a(flip),b,711,a)].">
      <j1 rule="hyper" parents="65 1565 711"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      ((x * y) * y) \ ((x * (y * y)) * z) = R(x,y,y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1899,a(flip),b,1946,a),flip(a)].">
      <j1 rule="hyper" parents="65 1899 1946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      R(x,y,y) \ (x * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1727,a,b,1947,a),flip(a)].">
      <j1 rule="hyper" parents="65 1727 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      R(x,y,y) * L(y,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,1727,a,b,1947,a(flip))].">
      <j1 rule="hyper" parents="137 1727 1947"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      L(x,x,R(y,x,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1722,a,b,1948,a)].">
      <j1 rule="hyper" parents="65 1722 1948"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      L(x,x,y * (x \ 1)) = L(x,x,y / x)
    ]]></literal>
    <justification jstring="[para(572(a,1),1950(a,1,3))].">
      <j1 rule="para" parents="572 1950"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ u))) / z)) = w
    ]]></literal>
    <justification jstring="[para(10(a,1),992(a,1,2,1,2,2))].">
      <j1 rule="para" parents="10 992"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      R(T(x,K(y,z) * u),K(y,z),u) = T(L(T(x,u),u,K(y,z)),K(y,z))
    ]]></literal>
    <justification jstring="[para(240(a,1),1151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="240 1151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      R(T(x,K(y,z) * u),K(y,z),u) = T(T(x,u),K(y,z))
    ]]></literal>
    <justification jstring="[para(153(a,1),1953(a,2,1))].">
      <j1 rule="para" parents="153 1953"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(1952,a,1684,a)].">
      <j1 rule="hyper" parents="1952 1684"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ (u * y)))) / z)) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(1952,a,1683,a)].">
      <j1 rule="hyper" parents="1952 1683"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[hyper(1952,a,xx),flip(a)].">
      <j1 rule="hyper" parents="1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1959">
    <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(347(a,2),1956(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="347 1956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1698(a,1),1956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1698 1956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) * y = x * (y * ((x \ (z * y)) / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),1957(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[para(69(a,1),1957(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="69 1957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * z = (x * y) * (z * (L(y \ z,y,x) / z))
    ]]></literal>
    <justification jstring="[para(102(a,2),1961(a,2,2,2,1))].">
      <j1 rule="para" parents="102 1961"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[para(69(a,1),1958(a,2,2,2,1,2,2))].">
      <j1 rule="para" parents="69 1958"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,1698,a(flip),b,1964,a)].">
      <j1 rule="hyper" parents="65 1698 1964"/>
    </justification>
  </clause>

  <clause id="1966">
    <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),1964(a,1,1))].">
      <j1 rule="para" parents="100 1964"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1188(a,1),1965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1188 1965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1188(a,1),1967(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1188 1967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,1968,a)].">
      <j1 rule="hyper" parents="145 1968"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1969(a,1),813(a,1,1))].">
      <j1 rule="para" parents="1969 813"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(541,a,1971,a),flip(a)].">
      <j1 rule="hyper" parents="541 1971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1972(a,1),670(a,1,1))].">
      <j1 rule="para" parents="1972 670"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(376,a,1973,a),flip(a)].">
      <j1 rule="hyper" parents="376 1973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(325,a,16,a,b,1974,a)].">
      <j1 rule="hyper" parents="325 16 1974"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),1975(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(38,a,194,a,b,1976,a)].">
      <j1 rule="hyper" parents="38 194 1976"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,1976,a(flip),b,1581,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 1976 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(82(a,1),1978(a,1,1))].">
      <j1 rule="para" parents="82 1978"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,1979,a)].">
      <j1 rule="hyper" parents="58 1979"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1980(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1980 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(1977(a,1),251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1977 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,115,a(flip),b,1982,a),flip(a)].">
      <j1 rule="hyper" parents="325 115 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      K(x * y,(x * y) \ 1) * ((((x * y) \ 1) * x) * y) = a((x * y) \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(887,a,515,a),flip(a)].">
      <j1 rule="hyper" parents="887 515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      a((x * y) \ 1,x,y) / y = (1 / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(135,a,1988,a(flip),b,804,a(flip))].">
      <j1 rule="hyper" parents="135 1988 804"/>
    </justification>
  </clause>

  <clause id="1990">
    <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(262(a,2),913(a,1,2,1,1))].">
      <j1 rule="para" parents="262 913"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      L(R(x,x \ 1,x \ L(x,y,z)),y,z) \ 1 = (x \ 1) * ((L(x,y,z) * (x \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(29(a,1),1033(a,1,1))].">
      <j1 rule="para" parents="29 1033"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(78(a,1),1229(a,1,1)),flip(a)].">
      <j1 rule="para" parents="78 1229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(529,a,1992,a)].">
      <j1 rule="hyper" parents="529 1992"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1993(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(1993(a,1),46(a,1))].">
      <j1 rule="para" parents="1993 46"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1755(a,1),1993(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1755 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(1995(a,2),46(a,1))].">
      <j1 rule="para" parents="1995 46"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1391,a(flip),b,1997,a)].">
      <j1 rule="hyper" parents="65 1391 1997"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      x * ((y \ 1) * L((y \ 1) \ (x \ (y * y)),z,u)) = (x * (y \ 1)) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(924,a,1325,a)].">
      <j1 rule="hyper" parents="924 1325"/>
    </justification>
  </clause>

  <clause id="2001">
    <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(1366(a,2),1371(a,1,2,1,1))].">
      <j1 rule="para" parents="1366 1371"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(944(a,1),1680(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="944 1680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(132,a,75,a(flip),b,2002,a),flip(a)].">
      <j1 rule="hyper" parents="132 75 2002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(966(a,1),1682(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="966 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(132,a,75,a(flip),b,2004,a),flip(a)].">
      <j1 rule="hyper" parents="132 75 2004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1696(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 1696"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2006,a)].">
      <j1 rule="hyper" parents="145 2006"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2007(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      a(L(((x * y) \ 1) * z,u,w),v5,v6) = a(L(((x \ 1) * y) * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),1863(a,1,1,1,1,2))].">
      <j1 rule="para" parents="10 1863"/>
    </justification>
  </clause>

  <clause id="2010">
    <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(65,a,1857,a(flip),b,2009,a),flip(a)].">
      <j1 rule="hyper" parents="65 1857 2009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,z) * (x \ 1)) \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1346(a,1),1991(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1346 1991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(946(a,1),2012(a,1,2,1))].">
      <j1 rule="para" parents="946 2012"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2003,a(flip),b,2013,a)].">
      <j1 rule="hyper" parents="65 2003 2013"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,1528,a,b,2013,a),flip(a)].">
      <j1 rule="hyper" parents="36 1528 2013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(202,a,2015,a)].">
      <j1 rule="hyper" parents="202 2015"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(136,a,2015,a,b,1778,a)].">
      <j1 rule="hyper" parents="136 2015 1778"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x \ L(x,y,z)) = (x \ L(x,y,z)) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2015(a,1),272(a,1,1))].">
      <j1 rule="para" parents="2015 272"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ u = ((x \ L(x,y,z)) \ (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(2015(a,1),581(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2015 581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      L(x,y,z) \ (x * ((x \ L(x,y,z)) \ 1)) = (x \ L(x,y,z)) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2015(a,1),780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2015 780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      L(x * (((y \ L(y,z,u)) \ 1) / (y \ L(y,z,u))),w,v5) = L(x,w,v5) * ((L(y,z,u) \ y) / (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(2015(a,1),1118(a,2,2,1))].">
      <j1 rule="para" parents="2015 1118"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      L(L(x,y,z) * (L(x,y,z) \ x),u,w) / ((x \ L(x,y,z)) \ 1) = L(x,u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2015(a,1),830(a,1,1,1,2))].">
      <j1 rule="para" parents="2015 830"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) \ 1 = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(1410(a,1),2015(a,1,1))].">
      <j1 rule="para" parents="1410 2015"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(2016(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2016 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2025">
    <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(2016(a,1),648(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2016 648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(946(a,2),2014(a,1,1))].">
      <j1 rule="para" parents="946 2014"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (y * y)),z,u)) = (x * (y \ 1)) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(1338(a,1),2000(a,1,2))].">
      <j1 rule="para" parents="1338 2000"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1222(a,1),2001(a,2,2))].">
      <j1 rule="para" parents="1222 2001"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(176(a,1),2028(a,2,2,1,1))].">
      <j1 rule="para" parents="176 2028"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(136,a,2029,a(flip),b,889,a)].">
      <j1 rule="hyper" parents="136 2029 889"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(433(a,1),2030(a,1,2))].">
      <j1 rule="para" parents="433 2030"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(433(a,1),2031(a,2,1,2))].">
      <j1 rule="para" parents="433 2031"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1208(a,1),2032(a,2,1))].">
      <j1 rule="para" parents="1208 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(940,a,1125,a),flip(a)].">
      <j1 rule="hyper" parents="940 1125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(724(a,1),2034(a,2,2))].">
      <j1 rule="para" parents="724 2034"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(455,a,2035,a)].">
      <j1 rule="hyper" parents="455 2035"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1130(a,1),1174(a,2,1))].">
      <j1 rule="para" parents="1130 1174"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1156(a,1),2037(a,2,1,1))].">
      <j1 rule="para" parents="1156 2037"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,20,a,b,2038,a)].">
      <j1 rule="hyper" parents="325 20 2038"/>
    </justification>
  </clause>

  <clause id="2041">
    <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(325,a,896,a(flip),b,2039,a)].">
      <j1 rule="hyper" parents="325 896 2039"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      R(x * T(x \ 1,R(x,y,z)),y,z) != u * R(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(2041(a,1),247(a,1)),flip(b)].">
      <j1 rule="para" parents="2041 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(262(a,2),923(a,1,2,1,1))].">
      <j1 rule="para" parents="262 923"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * R((x \ 1) \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,1812,a(flip),b,2045,a),flip(a)].">
      <j1 rule="hyper" parents="325 1812 2045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1094(a,1),2046(a,2,1))].">
      <j1 rule="para" parents="1094 2046"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x,x \ 1) * (y * x),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(515(a,1),2047(a,1,2,1))].">
      <j1 rule="para" parents="515 2047"/>
    </justification>
  </clause>

  <clause id="2049">
    <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(325,a,406,a(flip),b,788,a),flip(a)].">
      <j1 rule="hyper" parents="325 406 788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2050">
    <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(1066,a,2049,a)].">
      <j1 rule="hyper" parents="1066 2049"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,y \ 1,y)) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1013(a,1),2050(a,2,1,1))].">
      <j1 rule="para" parents="1013 2050"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1063(a,1),2051(a,1,2,2))].">
      <j1 rule="para" parents="1063 2051"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(548,a,2052,a),flip(a)].">
      <j1 rule="hyper" parents="548 2052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(641,a,2053,a(flip))].">
      <j1 rule="hyper" parents="641 2053"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(85(a,1),2054(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 2054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1688,a,b,2055,a)].">
      <j1 rule="hyper" parents="65 1688 2055"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1610,a,b,2055,a)].">
      <j1 rule="hyper" parents="65 1610 2055"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2055,a(flip),b,1688,a)].">
      <j1 rule="hyper" parents="137 2055 1688"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      x \ K(y,x \ 1) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(132,a,2055,a(flip),b,1610,a)].">
      <j1 rule="hyper" parents="132 2055 1610"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2008,a(flip),b,2057,a)].">
      <j1 rule="hyper" parents="65 2008 2057"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2057,a(flip),b,950,a)].">
      <j1 rule="hyper" parents="136 2057 950"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(2057(a,1),1964(a,2,2))].">
      <j1 rule="para" parents="2057 1964"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(2057(a,1),1962(a,2,2))].">
      <j1 rule="para" parents="2057 1962"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2059(a,2),235(a,1,1))].">
      <j1 rule="para" parents="2059 235"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1958(a,1),2060(a,1,1))].">
      <j1 rule="para" parents="1958 2060"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),2063(a,1,2,1))].">
      <j1 rule="para" parents="10 2063"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ z,y,x) / z)) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2063(a,1),1963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2063 1963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ z) / z),y,x) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1750(a,2),2069(a,1,2))].">
      <j1 rule="para" parents="1750 2069"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      x * (y * (z * ((y \ z) / z))) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(298,a,2071,a)].">
      <j1 rule="hyper" parents="298 2071"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(245,a,1585,a(flip),b,2072,a),flip(a)].">
      <j1 rule="hyper" parents="245 1585 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(140,a,2073,a)].">
      <j1 rule="hyper" parents="140 2073"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * y = x * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(2073(a,1),2072(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2073 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(135,a,2074,a,b,2061,a)].">
      <j1 rule="hyper" parents="135 2074 2061"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(85(a,1),2074(a,2,2,1))].">
      <j1 rule="para" parents="85 2074"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(366(a,2),2074(a,2,2)),flip(a)].">
      <j1 rule="para" parents="366 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,(z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2054(a,1),2075(a,1,1,2))].">
      <j1 rule="para" parents="2054 2075"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,1585,a(flip),b,2079,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 1585 2079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(85(a,1),2080(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 2080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(2080(a,1),2079(a,2,2))].">
      <j1 rule="para" parents="2080 2079"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      ((1 / x) \ y) * (x \ (1 / x)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,900,a,b,2081,a)].">
      <j1 rule="hyper" parents="65 900 2081"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,754,a(flip),b,2081,a),flip(a)].">
      <j1 rule="hyper" parents="65 754 2081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(284,a,2082,a)].">
      <j1 rule="hyper" parents="284 2082"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2082,a)].">
      <j1 rule="hyper" parents="145 2082"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(140,a,2082,a)].">
      <j1 rule="hyper" parents="140 2082"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(135,a,12,a(flip),b,2082,a),flip(a)].">
      <j1 rule="hyper" parents="135 12 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      ((x * y) * K(L(z,y,x),u)) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,416,a(flip),b,2082,a)].">
      <j1 rule="hyper" parents="132 416 2082"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(37,a,1143,a,b,2082,a),flip(a)].">
      <j1 rule="hyper" parents="37 1143 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,1135,a,b,2082,a)].">
      <j1 rule="hyper" parents="37 1135 2082"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,1131,a,b,2082,a),flip(a)].">
      <j1 rule="hyper" parents="37 1131 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,248,a,b,2082,a)].">
      <j1 rule="hyper" parents="37 248 2082"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(36,a,465,a(flip),b,2082,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 465 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(2082(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2082 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2097">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(2082(a,1),225(a,2,1))].">
      <j1 rule="para" parents="2082 225"/>
    </justification>
  </clause>

  <clause id="2098">
    <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(2082(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="2082 456"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      (x \ y) \ y = x * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(381,a,2094,a)].">
      <j1 rule="hyper" parents="381 2094"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(201,a,2094,a,b,192,a)].">
      <j1 rule="hyper" parents="201 2094 192"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,2094,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="132 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(132,a,25,a,b,2094,a(flip))].">
      <j1 rule="hyper" parents="132 25 2094"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = L(K(y,z),y,x)
    ]]></literal>
    <justification jstring="[para(2094(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2094 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2094(a,2),45(a,1))].">
      <j1 rule="para" parents="2094 45"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2094(a,2),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2094 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      L(K(x,y) \ z,K(x,y),x) = T(x,y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(2094(a,2),102(a,2,1))].">
      <j1 rule="para" parents="2094 102"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(1578,a,2095,a),flip(a)].">
      <j1 rule="hyper" parents="1578 2095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      (x \ y) \ y = K(x,x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(381,a,2095,a)].">
      <j1 rule="hyper" parents="381 2095"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2095,a,b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2095 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,2095,a,b,377,a),flip(a)].">
      <j1 rule="hyper" parents="136 2095 377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(135,a,2095,a,b,471,a)].">
      <j1 rule="hyper" parents="135 2095 471"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,2095,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="135 2095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      K(x,y) * x = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2094,a(flip),b,2095,a),flip(a)].">
      <j1 rule="hyper" parents="65 2094 2095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(245,a,2094,a(flip),b,2095,a(flip))].">
      <j1 rule="hyper" parents="245 2094 2095"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(137,a,2095,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 2095 22"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      T(x,y) != z * x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2095(a,2),46(a,1))].">
      <j1 rule="para" parents="2095 46"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      T(x,y) \ K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2095(a,2),360(a,1,1))].">
      <j1 rule="para" parents="2095 360"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2095(a,2),471(a,1,1))].">
      <j1 rule="para" parents="2095 471"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(2095(a,2),522(a,1,2,1))].">
      <j1 rule="para" parents="2095 522"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[para(2095(a,2),666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2095 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,K(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(2095(a,2),456(a,1,2,2))].">
      <j1 rule="para" parents="2095 456"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      K(x,y) * R(x,z,u) = R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2095(a,2),1057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2095 1057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(2095(a,2),1058(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2095 1058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(T(x,y),a(K(x,y),z,z \ x)) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(2095(a,2),858(a,1,2,1))].">
      <j1 rule="para" parents="2095 858"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      T(x,K(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,23,a,b,2119,a(flip))].">
      <j1 rule="hyper" parents="42 23 2119"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2119(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2119 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2119(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2119 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,890,a(flip),b,2104,a)].">
      <j1 rule="hyper" parents="325 890 2104"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2057,a,b,2104,a)].">
      <j1 rule="hyper" parents="65 2057 2104"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2104(a,2),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2104 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      x * L(x \ K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ L(T(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(2104(a,2),1336(a,1,2,1,2))].">
      <j1 rule="para" parents="2104 1336"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[para(2104(a,1),2119(a,1,2))].">
      <j1 rule="para" parents="2104 2119"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1138,a,b,2117,a),flip(a)].">
      <j1 rule="hyper" parents="325 1138 2117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1140,a,2117,a(flip))].">
      <j1 rule="hyper" parents="1140 2117"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2117,a(flip),b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 2117 2104"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2117(a,2),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2117 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2117(a,2),1140(a,1))].">
      <j1 rule="para" parents="2117 1140"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      T(x / y,K(y \ x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(115(a,1),2133(a,1,2,1))].">
      <j1 rule="para" parents="115 2133"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,2115,a,b,113,a),flip(a)].">
      <j1 rule="hyper" parents="132 2115 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2153">
    <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(2115(a,2),456(a,1,2,2))].">
      <j1 rule="para" parents="2115 456"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,2134,a)].">
      <j1 rule="hyper" parents="56 2134"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(245,a,2144,a(flip),b,2115,a(flip))].">
      <j1 rule="hyper" parents="245 2144 2115"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2146(a,1),2033(a,1,1))].">
      <j1 rule="para" parents="2146 2033"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2154(a,1),292(a,1,2))].">
      <j1 rule="para" parents="2154 292"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      T(x,T(x \ 1,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),2157(a,1,1))].">
      <j1 rule="para" parents="82 2157"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),2109(a,1,2))].">
      <j1 rule="para" parents="25 2109"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(599(a,2),2109(a,1,2))].">
      <j1 rule="para" parents="599 2109"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      (x / (y \ z)) * K(z / y,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(115(a,1),2089(a,1,1,2))].">
      <j1 rule="para" parents="115 2089"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,2092,a)].">
      <j1 rule="hyper" parents="334 2092"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(145,a,2092,a)].">
      <j1 rule="hyper" parents="145 2092"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,2092,a)].">
      <j1 rule="hyper" parents="140 2092"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,191,a(flip),b,2092,a(flip))].">
      <j1 rule="hyper" parents="132 191 2092"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(132,a,2092,a(flip),b,2082,a)].">
      <j1 rule="hyper" parents="132 2092 2082"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(2117(a,2),2092(a,1,1))].">
      <j1 rule="para" parents="2117 2092"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(284,a,2093,a),flip(a)].">
      <j1 rule="hyper" parents="284 2093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,2093,a)].">
      <j1 rule="hyper" parents="140 2093"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2093(a,1),210(a,1))].">
      <j1 rule="para" parents="2093 210"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(2093(a,1),327(a,1))].">
      <j1 rule="para" parents="2093 327"/>
    </justification>
  </clause>

  <clause id="2178">
    <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(2093(a,1),488(a,1,1))].">
      <j1 rule="para" parents="2093 488"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(140,a,2114,a)].">
      <j1 rule="hyper" parents="140 2114"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,2114,a)].">
      <j1 rule="hyper" parents="65 233 2114"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      K(x,y) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,2114,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2114 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      K(L(x,y,z),u) * (L(x,y,z) * w) = L(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),2114(a,2,1))].">
      <j1 rule="para" parents="25 2114"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),2114(a,1,2))].">
      <j1 rule="para" parents="100 2114"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(242(a,1),2114(a,1,2))].">
      <j1 rule="para" parents="242 2114"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      (T(x,y) * z) \ (K(x,y) * u) = (x * z) \ u
    ]]></literal>
    <justification jstring="[para(2114(a,1),470(a,1,1))].">
      <j1 rule="para" parents="2114 470"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      (x \ (y * K(z,u))) * (z * z) = x \ (y * (T(z,u) * z))
    ]]></literal>
    <justification jstring="[para(2114(a,1),558(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2114 558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      L(x,y,T(z,u) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(2114(a,1),1541(a,1,3))].">
      <j1 rule="para" parents="2114 1541"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      a(T(x,y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(2114(a,1),1865(a,1,1))].">
      <j1 rule="para" parents="2114 1865"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(857,a,2125,a)].">
      <j1 rule="hyper" parents="857 2125"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(2125(a,1),520(a,1))].">
      <j1 rule="para" parents="2125 520"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      K(x,y) * ((x / z) * u) = (T(x,y) / z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,2127,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2127 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      K(x,y) * ((x / z) / u) = (T(x,y) / z) / u
    ]]></literal>
    <justification jstring="[para(2127(a,1),666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2127 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K((x * y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1157,a,2145,a)].">
      <j1 rule="hyper" parents="1157 2145"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(827,a,2145,a)].">
      <j1 rule="hyper" parents="827 2145"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,423,a,b,2145,a)].">
      <j1 rule="hyper" parents="65 423 2145"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2138,a(flip),b,2145,a)].">
      <j1 rule="hyper" parents="65 2138 2145"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2145,a(flip),b,1119,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 2145 1119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,2145,a(flip),b,1172,a(flip))].">
      <j1 rule="hyper" parents="136 2145 1172"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(132,a,2145,a(flip),b,821,a(flip))].">
      <j1 rule="hyper" parents="132 2145 821"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(2145(a,1),724(a,2,2))].">
      <j1 rule="para" parents="2145 724"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(2145(a,1),1158(a,2,1))].">
      <j1 rule="para" parents="2145 1158"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(2145(a,1),1925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2145 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      K(x \ (x / L(y,z,u)),x) = L(K(y \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(2145(a,1),2036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2145 2036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),2202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 2202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      T(x,T(x \ 1,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,114,a,b,2160,a),flip(a)].">
      <j1 rule="hyper" parents="325 114 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      ((x / y) \ T(x * K(y,z),(x / y) \ 1)) / T(y,z) = K(x * K(y,z),(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(2166(a,1),2076(a,1,2))].">
      <j1 rule="para" parents="2166 2076"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(2174(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2174 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2157(a,1),2201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2157 2201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,262,a,b,2217,a),flip(a)].">
      <j1 rule="hyper" parents="325 262 2217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(245,a,2114,a,b,2091,a)].">
      <j1 rule="hyper" parents="245 2114 2091"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2220(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(114(a,1),2221(a,1,1))].">
      <j1 rule="para" parents="114 2221"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(596(a,1),2221(a,1,1)),flip(a)].">
      <j1 rule="para" parents="596 2221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2222(a,2),207(a,1)),flip(b)].">
      <j1 rule="para" parents="2222 207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2223,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 2223 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      x * K(y \ x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(2223(a,1),247(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2223 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      T(x,y) * (x \ R(x,z,u)) = R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2125,a,b,2130,a)].">
      <j1 rule="hyper" parents="65 2125 2130"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,2130,a(flip),b,2125,a)].">
      <j1 rule="hyper" parents="132 2130 2125"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      x * K((y * z) \ x,u) = y * (z * T(z \ (y \ x),u))
    ]]></literal>
    <justification jstring="[hyper(827,a,2164,a),flip(a)].">
      <j1 rule="hyper" parents="827 2164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,1170,a(flip),b,2164,a(flip))].">
      <j1 rule="hyper" parents="132 1170 2164"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(2164(a,2),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2164 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(2164(a,1),1922(a,2,1))].">
      <j1 rule="para" parents="2164 1922"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      (x * K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(2169(a,1),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2169 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      x \ (K(y,z) * ((T(y,z) \ x) * y)) = K(T(y,z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,2185,a,b,2164,a(flip))].">
      <j1 rule="hyper" parents="132 2185 2164"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,287,a,b,2185,a)].">
      <j1 rule="hyper" parents="65 287 2185"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      L(x,y,z * T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(461,a,2193,a),flip(a)].">
      <j1 rule="hyper" parents="461 2193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5) * v6) = L(x,y,L(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(25(a,2),2193(a,1,3,1))].">
      <j1 rule="para" parents="25 2193"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      L(x,y,(z / u) * w) = L(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(115(a,1),2193(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="115 2193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      ((x * T(x,y)) * z) * u = (x * T(x,y)) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(989,a,2237,a),flip(a)].">
      <j1 rule="hyper" parents="989 2237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      (x * T(x,y)) * (1 / z) = (x * T(x,y)) / z
    ]]></literal>
    <justification jstring="[hyper(201,a,2237,a(flip),b,229,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 2237 229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      ((x * T(x,y)) * z) / u = (x * T(x,y)) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(201,a,2237,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="201 2237 104"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      a((x * (y * y)) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1844,a(flip),b,2194,a)].">
      <j1 rule="hyper" parents="65 1844 2194"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2164,a,b,2225,a),flip(a)].">
      <j1 rule="hyper" parents="325 2164 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(135,a,820,a(flip),b,2244,a)].">
      <j1 rule="hyper" parents="135 820 2244"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2174,a(flip),b,2107,a),flip(a)].">
      <j1 rule="hyper" parents="65 2174 2107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      (x * y) * T(K(y,z),u) = x * (y * T(K(y,z),u))
    ]]></literal>
    <justification jstring="[para(2248(a,1),416(a,1,2,1))].">
      <j1 rule="para" parents="2248 416"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      (1 / x) \ L(K(x,y),z,u) = x * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2248(a,1),518(a,1,2,1))].">
      <j1 rule="para" parents="2248 518"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      K(x \ (x / y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(896(a,2),2175(a,1))].">
      <j1 rule="para" parents="896 2175"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1119(a,1),2175(a,1))].">
      <j1 rule="para" parents="1119 2175"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2138(a,1),2175(a,1))].">
      <j1 rule="para" parents="2138 2175"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),2196(a,1,2))].">
      <j1 rule="para" parents="10 2196"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1426,a,2139,a)].">
      <j1 rule="hyper" parents="1426 2139"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(2139(a,1),1699(a,1,1))].">
      <j1 rule="para" parents="2139 1699"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(2139(a,1),1960(a,2,2,1))].">
      <j1 rule="para" parents="2139 1960"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) * z) * u) = x \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,2186,a(flip),b,2125,a)].">
      <j1 rule="hyper" parents="132 2186 2125"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      (T(x,y) * z) \ R(K(x,y) * u,w,v5) = (x * z) \ R(u,w,v5)
    ]]></literal>
    <justification jstring="[para(1057(a,2),2190(a,1,2))].">
      <j1 rule="para" parents="1057 2190"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      (T(x,y) * z) \ T(x,y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[para(2095(a,2),2190(a,1,2))].">
      <j1 rule="para" parents="2095 2190"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      (T(x,y) * z) \ (T(x,y) * u) = (x * z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(2114(a,1),2190(a,1,2))].">
      <j1 rule="para" parents="2114 2190"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      (T(x,y) * z) \ ((T(x,y) * u) * w) = (x * z) \ ((x * u) * w)
    ]]></literal>
    <justification jstring="[para(2186(a,1),2190(a,1,2))].">
      <j1 rule="para" parents="2186 2190"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1754(a,1),2195(a,1,2,1))].">
      <j1 rule="para" parents="1754 2195"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      (((x * y) \ 1) * x) / ((x * y) \ 1) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2199,a,b,1587,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 2199 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      x * K((x \ (y \ x)) \ 1,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,2195,a(flip),b,2204,a),flip(a)].">
      <j1 rule="hyper" parents="65 2195 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(245,a,2244,a,b,2204,a(flip))].">
      <j1 rule="hyper" parents="245 2244 2204"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      K((x \ (y \ x)) \ 1,z) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(245,a,2195,a(flip),b,2204,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 2195 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,2204,a(flip),b,423,a)].">
      <j1 rule="hyper" parents="135 2204 423"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,u),y) = K((T(x,y) \ T(z,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,1923,a(flip),b,2204,a(flip))].">
      <j1 rule="hyper" parents="132 1923 2204"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,1170,a(flip),b,2204,a(flip))].">
      <j1 rule="hyper" parents="132 1170 2204"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2164,a(flip),b,2204,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 2164 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ z) \ 1,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(2204(a,2),1631(a,1,2,1))].">
      <j1 rule="para" parents="2204 1631"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T((x \ 1) \ (x \ L(x,y,z)),u)
    ]]></literal>
    <justification jstring="[para(2014(a,1),2204(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2014 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2275(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2279,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="137 2279 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,2244,a,b,2205,a),flip(a)].">
      <j1 rule="hyper" parents="37 2244 2205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2205(a,2,2,1))].">
      <j1 rule="para" parents="9 2205"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(82(a,1),2205(a,1,1,1,1))].">
      <j1 rule="para" parents="82 2205"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2202,a,b,2281,a)].">
      <j1 rule="hyper" parents="65 2202 2281"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),2281(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 2281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),2281(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 2281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2284(a,1),2256(a,1))].">
      <j1 rule="para" parents="2284 2256"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(2254,a,2209,a)].">
      <j1 rule="hyper" parents="2254 2209"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      T(K(x \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(2209(a,1),2254(a,1))].">
      <j1 rule="para" parents="2209 2254"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(2211(a,1),2288(a,2,1))].">
      <j1 rule="para" parents="2211 2288"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      L(x,y,(z / (u * u)) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1492,a(flip),b,2239,a),flip(a)].">
      <j1 rule="hyper" parents="325 1492 2239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      L(x,y,((z * u) * u) * w) = L(x,y,R(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(20(a,2),2291(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="20 2291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(85(a,1),2078(a,2,2,2))].">
      <j1 rule="para" parents="85 2078"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2159,a,2170,a(flip))].">
      <j1 rule="hyper" parents="2159 2170"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2170(a,2),2159(a,1))].">
      <j1 rule="para" parents="2170 2159"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(863(a,1),2232(a,1,2))].">
      <j1 rule="para" parents="863 2232"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1189,a(flip),b,2200,a)].">
      <j1 rule="hyper" parents="65 1189 2200"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,2200,a)].">
      <j1 rule="hyper" parents="65 233 2200"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(85(a,1),2200(a,1,2,2,1,2))].">
      <j1 rule="para" parents="85 2200"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2254,a,2210,a),flip(a)].">
      <j1 rule="hyper" parents="2254 2210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <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(2210(a,1),2254(a,1))].">
      <j1 rule="para" parents="2210 2254"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(1435(a,1),2307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1435 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2211(a,1),2307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2211 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(2275(a,1),2307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2275 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      T(x * K(L(y \ 1,z,u) \ 1,x),w) = T(x,w) * L(K(y,T(x,w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,2310,a(flip),b,1620,a),flip(a)].">
      <j1 rule="hyper" parents="137 2310 1620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      (x * T(x,y)) * ((1 / z) * u) = ((x * T(x,y)) / z) * u
    ]]></literal>
    <justification jstring="[para(2241(a,1),2240(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2241 2240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      (x * T(x,x \ (x \ 1))) * (y / z) = ((x * (1 / (1 / x))) * y) / z
    ]]></literal>
    <justification jstring="[para(1644(a,1),2242(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1644 2242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2258,a(flip),b,2259,a),flip(a)].">
      <j1 rule="hyper" parents="325 2258 2259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2125,a,b,2267,a)].">
      <j1 rule="hyper" parents="325 2125 2267"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      L(x,y,z * T(u,w)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2282(a,1),1541(a,1,3))].">
      <j1 rule="para" parents="2282 1541"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      a(x * T(y,z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(2282(a,1),1865(a,1,1))].">
      <j1 rule="para" parents="2282 1865"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      a(x * T(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * y,u,w) = v5
    ]]></literal>
    <justification jstring="[para(2282(a,1),1866(a,1,1))].">
      <j1 rule="para" parents="2282 1866"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      L(x,y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(113(a,1),2318(a,1,3))].">
      <j1 rule="para" parents="113 2318"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      L(x,y,z * (u / w)) = L(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(115(a,1),2318(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="115 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      L(x,y,z * (u / z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(230(a,1),2318(a,1,3)),flip(a)].">
      <j1 rule="para" parents="230 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1542,a,2321,a),flip(a)].">
      <j1 rule="hyper" parents="1542 2321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      L(x,y,(z / u) * w) = L(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2239,a,b,2321,a)].">
      <j1 rule="hyper" parents="325 2239 2321"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1907,a,b,2321,a)].">
      <j1 rule="hyper" parents="325 1907 2321"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1506,a,b,2321,a)].">
      <j1 rule="hyper" parents="325 1506 2321"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      L(x,y,(1 / z) * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1505,a,b,2321,a)].">
      <j1 rule="hyper" parents="325 1505 2321"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      L(x,y,((z * z) \ u) * w) = L(x,y,w * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1492,a,b,2321,a)].">
      <j1 rule="hyper" parents="325 1492 2321"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      L(x,y,z * (1 / u)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1505,a(flip),b,2321,a),flip(a)].">
      <j1 rule="hyper" parents="325 1505 2321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      L(x,y,z * (u * (u * w))) = L(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1493,a(flip),b,2321,a),flip(a)].">
      <j1 rule="hyper" parents="325 1493 2321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      L(x,y,(z * u) * z) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1491,a(flip),b,2321,a),flip(a)].">
      <j1 rule="hyper" parents="325 1491 2321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(2321(a,1),1542(a,1))].">
      <j1 rule="para" parents="2321 1542"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      L(x,y,z * u) != a(y,u,z)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,u,z) = x
    ]]></literal>
    <justification jstring="[para(2321(a,1),1908(a,1))].">
      <j1 rule="para" parents="2321 1908"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      L((x * (y / x)) \ z,x * (y / x),y) = (1 / (x * (y / x))) * z
    ]]></literal>
    <justification jstring="[hyper(660,a,2323,a),flip(a)].">
      <j1 rule="hyper" parents="660 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      a(x * y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),2319(a,1,1))].">
      <j1 rule="para" parents="113 2319"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      a(x * (y / z),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(115(a,1),2319(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="115 2319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      a(x * (((y * z) * u) / (y * u)),w,v5) = a(x * R(z,y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(749(a,2),2319(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="749 2319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(1866,a,2337,a),flip(a)].">
      <j1 rule="hyper" parents="1866 2337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      a((x * y) * x,z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1843,a(flip),b,2337,a),flip(a)].">
      <j1 rule="hyper" parents="325 1843 2337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      a(x * R(y,y,x),z,u) = a((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(1289(a,1),2337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1289 2337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      L(x,y,((z * u) \ z) * u) = L(x,y,u * L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1788,a(flip),b,2327,a),flip(a)].">
      <j1 rule="hyper" parents="65 1788 2327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      ((x * y) * z) * a(z,y,x) = (x * y) * R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,2326,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="137 2326 102"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,z * y) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2326(a,2),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2326 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      L((1 / x) * R(x,y,z),x,z * y) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(2326(a,2),658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2326 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ L(x \ R(x,y,z),x,z * y) = a(x,y,z) * ((x \ R(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(2326(a,2),946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2326 946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      L(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(93(a,1),2334(a,1,3))].">
      <j1 rule="para" parents="93 2334"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(313(a,1),2334(a,1,3))].">
      <j1 rule="para" parents="313 2334"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      L(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(1588(a,1),2334(a,1,3))].">
      <j1 rule="para" parents="1588 2334"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(1566(a,2),2349(a,1))].">
      <j1 rule="para" parents="1566 2349"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      L(x,y,L(z * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u * z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(1770(a,1),2350(a,1,3))].">
      <j1 rule="para" parents="1770 2350"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      L(x,y,z * (((u * u) * w) / u)) = L(x,y,z * ((1 / u) \ w))
    ]]></literal>
    <justification jstring="[para(652(a,1),2322(a,2,3,2))].">
      <j1 rule="para" parents="652 2322"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      L(x,y,z * ((u * u) \ w)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(2349,a,2329,a)].">
      <j1 rule="hyper" parents="2349 2329"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * w)) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2329(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      L(x,y,z * ((u * u) / w)) = L(x,y,(1 / w) * z)
    ]]></literal>
    <justification jstring="[para(438(a,1),2329(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="438 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      a(L(L(x,x,y),y,y),z,u) = a(y * ((x \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1853,a,b,2338,a)].">
      <j1 rule="hyper" parents="65 1853 2338"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      a(x * ((y * y) \ z),u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1889,a(flip),b,2338,a),flip(a)].">
      <j1 rule="hyper" parents="65 1889 2338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      a(x * (((y * y) * z) / y),u,w) = a(x * ((1 / y) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(652(a,1),2338(a,2,1,2))].">
      <j1 rule="para" parents="652 2338"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      L(x,y,z \ L(u,z,z)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(874(a,1),2355(a,1,3))].">
      <j1 rule="para" parents="874 2355"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) * (u \ w))) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(663(a,1),2356(a,1,3,2))].">
      <j1 rule="para" parents="663 2356"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      a(x * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(113(a,1),2320(a,1,1))].">
      <j1 rule="para" parents="113 2320"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      a(L(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((y * x) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1843(a,1),2363(a,1))].">
      <j1 rule="para" parents="1843 2363"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      L(x,x,y / x) = L(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(2352,a,1951,a),flip(a)].">
      <j1 rule="hyper" parents="2352 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(946(a,1),2352(a,1,3))].">
      <j1 rule="para" parents="946 2352"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      L(x,y,z \ R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(959(a,1),2352(a,1,3))].">
      <j1 rule="para" parents="959 2352"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      L(x,x,x \ y) = L(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(2351,a,2365,a)].">
      <j1 rule="hyper" parents="2351 2365"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      (x \ y) * L(x,x,x * y) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,2368,a(flip),b,1721,a(flip))].">
      <j1 rule="hyper" parents="137 2368 1721"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(2218(a,1),2283(a,1,1))].">
      <j1 rule="para" parents="2218 2283"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(2283(a,2),2208(a,1,2))].">
      <j1 rule="para" parents="2283 2208"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a,b,2316,a),flip(a)].">
      <j1 rule="hyper" parents="325 2104 2316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2104(a,2),2372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2104 2372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,2373,a(flip),b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 2373 2104"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2054(a,1),2373(a,2,1))].">
      <j1 rule="para" parents="2054 2373"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      L(x,y,z * ((u * u) / w)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2328,a(flip),b,2357,a),flip(a)].">
      <j1 rule="hyper" parents="325 2328 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) * w)) = L(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2362(a,1,3,2,2))].">
      <j1 rule="para" parents="9 2362"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(85(a,1),2371(a,1,2,1,1))].">
      <j1 rule="para" parents="85 2371"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(2211(a,1),2371(a,1,2,1))].">
      <j1 rule="para" parents="2211 2371"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * w) = L(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(2349,a,2377,a)].">
      <j1 rule="hyper" parents="2349 2377"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      L(x,y,((z \ L(z,u,w)) * L(z,u,w)) * v5) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(2017(a,1),2380(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2017 2380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(1100(a,1),2255(a,1,2))].">
      <j1 rule="para" parents="1100 2255"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2168(a,1),2255(a,1))].">
      <j1 rule="para" parents="2168 2255"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      L(x,y,z * (R(z,u,w) * (z * v5))) = L(x,y,L(v5,z,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(956(a,1),2332(a,1,3))].">
      <j1 rule="para" parents="956 2332"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) * (z * v5))) = L(x,y,L(v5,z,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1249(a,1),2332(a,1,3))].">
      <j1 rule="para" parents="1249 2332"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(2128,a,2088,a)].">
      <j1 rule="hyper" parents="2128 2088"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2388(a,1),25(a,2,1))].">
      <j1 rule="para" parents="2388 25"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(2388(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="2388 412"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2389(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2389 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(2391(a,1),298(a,1,2))].">
      <j1 rule="para" parents="2391 298"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      (x \ (y * K(z,u))) * (z * z) = x \ (y * (z * T(z,u)))
    ]]></literal>
    <justification jstring="[para(248(a,1),2192(a,2,2,2))].">
      <j1 rule="para" parents="248 2192"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,233,a(flip),b,2229,a),flip(a)].">
      <j1 rule="hyper" parents="325 233 2229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(2164(a,1),2229(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2164 2229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,2233,a(flip),b,2164,a(flip))].">
      <j1 rule="hyper" parents="132 2233 2164"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(85(a,1),2397(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      L(x,y,(z * (u * z)) * w) = L(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1508,a(flip),b,2238,a)].">
      <j1 rule="hyper" parents="65 1508 2238"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      L(x,y,z * (u * (w * u))) = L(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(2349,a,2399,a)].">
      <j1 rule="hyper" parents="2349 2399"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,z * y) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(1820(a,1),2347(a,1,1))].">
      <j1 rule="para" parents="1820 2347"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      L(a(x,y,z),x,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2326,a,b,2402,a),flip(a)].">
      <j1 rule="hyper" parents="65 2326 2402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      (x * y) \ R(x * y,y,x) = a(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(52,a,2402,a)].">
      <j1 rule="hyper" parents="52 2402"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      (1 / x) \ a(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,2403,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="132 2403 650"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      (x * y) \ a(x * y,y,x) = R((x * y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2404,a(flip),b,1077,a)].">
      <j1 rule="hyper" parents="132 2404 1077"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,1454,a(flip),b,2370,a),flip(a)].">
      <j1 rule="hyper" parents="65 1454 2370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (K(x * y,z) * ((x * y) * u)) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(2188(a,1),474(a,1,1))].">
      <j1 rule="para" parents="2188 474"/>
    </justification>
  </clause>

  <clause id="2409">
    <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(2097(a,2),2153(a,1))].">
      <j1 rule="para" parents="2097 2153"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(2409,a,2324,a)].">
      <j1 rule="hyper" parents="2409 2324"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(2195(a,1),2246(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2195 2246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      (T(x,y) * z) \ R(T(x,y) * u,w,v5) = (x * z) \ R(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(2114(a,1),2263(a,1,2,1))].">
      <j1 rule="para" parents="2114 2263"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      (T(x,y) * z) \ ((T(x,y) * x) * u) = (((x * x) \ x) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(325,a,691,a,b,2266,a),flip(a)].">
      <j1 rule="hyper" parents="325 691 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      (x * y) \ ((x * T(x,z)) * u) = ((1 / T(x,z)) * y) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,692,a(flip),b,2266,a),flip(a)].">
      <j1 rule="hyper" parents="65 692 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w / u))) = L(x,y,z * ((1 / u) \ w))
    ]]></literal>
    <justification jstring="[para(556(a,1),2354(a,1,3,2))].">
      <j1 rule="para" parents="556 2354"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      a(x * ((y * y) * (z / y)),u,w) = a(x * ((1 / y) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(556(a,1),2360(a,1,1,2))].">
      <j1 rule="para" parents="556 2360"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(85(a,1),2378(a,2,1,1))].">
      <j1 rule="para" parents="85 2378"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      ((x \ 1) * (K(x,y) * ((x \ 1) \ z))) * (z \ u) = K((x \ 1) \ 1,y) * u
    ]]></literal>
    <justification jstring="[para(2379(a,2),471(a,1,1))].">
      <j1 rule="para" parents="2379 471"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(729,a,2396,a)].">
      <j1 rule="hyper" parents="729 2396"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      (T(x,y) * z) \ ((x * T(x,y)) * u) = (((x * x) \ x) * z) \ u
    ]]></literal>
    <justification jstring="[para(248(a,1),2416(a,1,2,1))].">
      <j1 rule="para" parents="248 2416"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      L(x,y,z * ((1 / u) \ w)) = L(x,y,(w / u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2356,a(flip),b,2419,a),flip(a)].">
      <j1 rule="hyper" parents="65 2356 2419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      L(x,y,z * ((1 / u) \ w)) = L(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2239,a(flip),b,2426,a),flip(a)].">
      <j1 rule="hyper" parents="325 2239 2426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      (T(x,y) * z) \ ((x * T(x,y)) * u) = ((1 / x) * z) \ u
    ]]></literal>
    <justification jstring="[para(273(a,1),2425(a,2,1,1))].">
      <j1 rule="para" parents="273 2425"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      (T(x,y) * z) \ ((x * T(x,y)) * R((1 / x) * z,u,w)) = (1 / ((1 / x) * z)) * R((1 / x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1820,a,b,2429,a),flip(a)].">
      <j1 rule="hyper" parents="325 1820 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      (x * T(x,y)) * (((1 / x) * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(137,a,9,a(flip),b,2429,a),flip(a)].">
      <j1 rule="hyper" parents="137 9 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,353,a(flip),b,2309,a),flip(a)].">
      <j1 rule="hyper" parents="325 353 2309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(944(a,1),2432(a,1,2))].">
      <j1 rule="para" parents="944 2432"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2434,a)].">
      <j1 rule="hyper" parents="58 2434"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(56,a,2435,a)].">
      <j1 rule="hyper" parents="56 2435"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(946(a,2),2436(a,1,1))].">
      <j1 rule="para" parents="946 2436"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      (x * (y * (x / y))) \ (x * z) = (1 / (y * (x / y))) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,102,a(flip),b,2336,a)].">
      <j1 rule="hyper" parents="65 102 2336"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      a(x * ((y * z) \ ((y * u) * z)),w,v5) = a(x * R(u,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,2338,a(flip),b,2339,a)].">
      <j1 rule="hyper" parents="65 2338 2339"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      a(x * ((y * z) * y),u,w) = a(x * R(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1889,a(flip),b,2339,a)].">
      <j1 rule="hyper" parents="65 1889 2339"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * z = (x * z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(2063(a,1),2064(a,1,1))].">
      <j1 rule="para" parents="2063 2064"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,83,a(flip),b,2442,a),flip(a)].">
      <j1 rule="hyper" parents="135 83 2442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2054(a,1),2442(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2054 2442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2054(a,1),2445(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2054 2445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,73,a(flip),b,2448,a),flip(a)].">
      <j1 rule="hyper" parents="325 73 2448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      (x * K(y,x)) \ K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,73,a(flip),b,2448,a)].">
      <j1 rule="hyper" parents="132 73 2448"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(2164(a,2),2449(a,1,1))].">
      <j1 rule="para" parents="2164 2449"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,360,a,b,2450,a)].">
      <j1 rule="hyper" parents="41 360 2450"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      (x / y) \ K(y,y \ x) = (y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(1588(a,1),2450(a,1,1))].">
      <j1 rule="para" parents="1588 2450"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,1581,a,b,2452,a)].">
      <j1 rule="hyper" parents="325 1581 2452"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(325,a,1588,a(flip),b,2452,a),flip(a)].">
      <j1 rule="hyper" parents="325 1588 2452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(246,a,2452,a)].">
      <j1 rule="hyper" parents="246 2452"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,2452,a,b,xx)].">
      <j1 rule="hyper" parents="245 2452"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(135,a,1628,a(flip),b,2452,a)].">
      <j1 rule="hyper" parents="135 1628 2452"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      (x / y) / (y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(135,a,1588,a(flip),b,2452,a)].">
      <j1 rule="hyper" parents="135 1588 2452"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,2225,a,b,2452,a)].">
      <j1 rule="hyper" parents="37 2225 2452"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,2452,a(flip),b,419,a)].">
      <j1 rule="hyper" parents="136 2452 419"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = K(y,x) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2452(a,1),1057(a,1,1))].">
      <j1 rule="para" parents="2452 1057"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2452(a,2),1589(a,1,1))].">
      <j1 rule="para" parents="2452 1589"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,25,a,b,2456,a(flip))].">
      <j1 rule="hyper" parents="43 25 2456"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2456(a,1),372(a,1,2,1))].">
      <j1 rule="para" parents="2456 372"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(2456(a,1),2091(a,1,2,1))].">
      <j1 rule="para" parents="2456 2091"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[para(2310(a,1),2456(a,1,2))].">
      <j1 rule="para" parents="2310 2456"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2222,a,b,2457,a)].">
      <j1 rule="hyper" parents="65 2222 2457"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,2464,a(flip),b,623,a),flip(a)].">
      <j1 rule="hyper" parents="137 2464 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(2127(a,1),2464(a,1,1))].">
      <j1 rule="para" parents="2127 2464"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(325,a,2125,a,b,2454,a)].">
      <j1 rule="hyper" parents="325 2125 2454"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(325,a,2116,a,b,2454,a)].">
      <j1 rule="hyper" parents="325 2116 2454"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2454,a,b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2454 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[hyper(135,a,892,a,b,2454,a(flip))].">
      <j1 rule="hyper" parents="135 892 2454"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2454(a,2),471(a,1,1))].">
      <j1 rule="para" parents="2454 471"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      ((x * y) / x) \ z = y \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(2454(a,2),521(a,1,1))].">
      <j1 rule="para" parents="2454 521"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[para(2104(a,1),2454(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2104 2454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(331,a,2472,a)].">
      <j1 rule="hyper" parents="331 2472"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,2472,a),flip(a)].">
      <j1 rule="hyper" parents="145 2472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(140,a,2472,a)].">
      <j1 rule="hyper" parents="140 2472"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      T(x,L(y,z,u)) * L(T(y,x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2189,a(flip),b,2472,a)].">
      <j1 rule="hyper" parents="65 2189 2472"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(65,a,2185,a(flip),b,2472,a)].">
      <j1 rule="hyper" parents="65 2185 2472"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2472,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2472 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,2472,a(flip),b,377,a),flip(a)].">
      <j1 rule="hyper" parents="136 2472 377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2472,a(flip),b,2185,a(flip))].">
      <j1 rule="hyper" parents="132 2472 2185"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[para(2472(a,1),360(a,1,1))].">
      <j1 rule="para" parents="2472 360"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[para(100(a,1),2472(a,1,2))].">
      <j1 rule="para" parents="100 2472"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(2472(a,1),470(a,1,1))].">
      <j1 rule="para" parents="2472 470"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2472(a,1),471(a,1,1))].">
      <j1 rule="para" parents="2472 471"/>
    </justification>
  </clause>

  <clause id="2495">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(2472(a,1),666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2472 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * (y * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(2472(a,1),451(a,1,1))].">
      <j1 rule="para" parents="2472 451"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(2472(a,1),2093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2472 2093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      (x * (y / x)) / y = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2484(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[para(2485(a,1),624(a,2,1))].">
      <j1 rule="para" parents="2485 624"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(369,a,2487,a)].">
      <j1 rule="hyper" parents="369 2487"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,1133,a,b,2487,a)].">
      <j1 rule="hyper" parents="37 1133 2487"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,2082,a,b,2487,a(flip))].">
      <j1 rule="hyper" parents="37 2082 2487"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      T(x,T(y,x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a(flip),b,2500,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 2500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      T(x * K(y,x),T(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,1592,a,b,2500,a(flip))].">
      <j1 rule="hyper" parents="42 1592 2500"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(2500(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2500 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(23(a,1),2500(a,1,2))].">
      <j1 rule="para" parents="23 2500"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),2500(a,1,2))].">
      <j1 rule="para" parents="25 2500"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),2500(a,1,2)),flip(a)].">
      <j1 rule="para" parents="115 2500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2500(a,1),241(a,1,2,1))].">
      <j1 rule="para" parents="2500 241"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1589(a,1),2500(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1589 2500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,2504,a),flip(a)].">
      <j1 rule="hyper" parents="145 2504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(140,a,2504,a),flip(a)].">
      <j1 rule="hyper" parents="140 2504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,319,a(flip),b,2504,a)].">
      <j1 rule="hyper" parents="65 319 2504"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1583,a,b,2504,a)].">
      <j1 rule="hyper" parents="36 1583 2504"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      x / (x * K(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,2504,a(flip),b,2114,a)].">
      <j1 rule="hyper" parents="135 2504 2114"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,2504,a(flip),b,2092,a),flip(a)].">
      <j1 rule="hyper" parents="135 2504 2092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2504,a(flip),b,2114,a)].">
      <j1 rule="hyper" parents="132 2504 2114"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2504,a(flip),b,2092,a)].">
      <j1 rule="hyper" parents="132 2504 2092"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2504(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2504 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      K(x * x,(x * x) \ y) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,687,a,b,2515,a)].">
      <j1 rule="hyper" parents="325 687 2515"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      T(1 / x,y) \ (1 / x) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2055,a(flip),b,2515,a),flip(a)].">
      <j1 rule="hyper" parents="65 2055 2515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2527">
    <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),2515(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 2515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      L(x \ K(y,z),x,z) = (T(z,y) * x) \ z
    ]]></literal>
    <justification jstring="[para(2515(a,2),1548(a,1,1,2))].">
      <j1 rule="para" parents="2515 1548"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      K(x,T(T(y,x),z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(23(a,1),2517(a,1,2))].">
      <j1 rule="para" parents="23 2517"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),2517(a,1,2))].">
      <j1 rule="para" parents="25 2517"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),2517(a,1,2)),flip(a)].">
      <j1 rule="para" parents="115 2517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      (x * R(y,z,u)) / R(T(y,x),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(201,a,27,a,b,2490,a)].">
      <j1 rule="hyper" parents="201 27 2490"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(22(a,1),2490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 2490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(135,a,2500,a(flip),b,2503,a)].">
      <j1 rule="hyper" parents="135 2500 2503"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2505(a,2),2140(a,1))].">
      <j1 rule="para" parents="2505 2140"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2506(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2506 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,114,a(flip),b,2510,a),flip(a)].">
      <j1 rule="hyper" parents="325 114 2510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,758,a,b,2510,a)].">
      <j1 rule="hyper" parents="65 758 2510"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(2510(a,1),860(a,1,2,2))].">
      <j1 rule="para" parents="2510 860"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      K(T(x,y / x),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(2510(a,2),2221(a,1,1))].">
      <j1 rule="para" parents="2510 2221"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(1581(a,2),2518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1581 2518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1628(a,1),2518(a,1,2))].">
      <j1 rule="para" parents="1628 2518"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2127,a,b,2519,a)].">
      <j1 rule="hyper" parents="65 2127 2519"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,2519,a(flip),b,1112,a),flip(a)].">
      <j1 rule="hyper" parents="137 2519 1112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      (T(x,y) / y) * K(y,x) = x / y
    ]]></literal>
    <justification jstring="[para(2519(a,2),2089(a,1,1))].">
      <j1 rule="para" parents="2519 2089"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,1581,a,b,2520,a)].">
      <j1 rule="hyper" parents="137 1581 2520"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(137,a,1588,a(flip),b,2520,a)].">
      <j1 rule="hyper" parents="137 1588 2520"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(2520(a,1),432(a,1,1))].">
      <j1 rule="para" parents="2520 432"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      L(x * K(y,x),K(x,y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(2520(a,1),102(a,1,1))].">
      <j1 rule="para" parents="2520 102"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,96,a,b,2532,a)].">
      <j1 rule="hyper" parents="65 96 2532"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2532,a(flip),b,96,a)].">
      <j1 rule="hyper" parents="137 2532 96"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(82(a,1),2539(a,1,2))].">
      <j1 rule="para" parents="82 2539"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(2539(a,1),838(a,2,2))].">
      <j1 rule="para" parents="2539 838"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(135,a,2545,a,b,1185,a)].">
      <j1 rule="hyper" parents="135 2545 1185"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[para(2553(a,1),360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2553 360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(2553(a,1),471(a,1,1))].">
      <j1 rule="para" parents="2553 471"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(89(a,1),2553(a,1,2,1))].">
      <j1 rule="para" parents="89 2553"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2455,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2455 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(132,a,2455,a(flip),b,2125,a)].">
      <j1 rule="hyper" parents="132 2455 2125"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(2455(a,1),471(a,1,1))].">
      <j1 rule="para" parents="2455 471"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[para(2455(a,1),666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2455 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      a(x / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(2455(a,1),1866(a,1,1))].">
      <j1 rule="para" parents="2455 1866"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(2532(a,2),2455(a,1,1))].">
      <j1 rule="para" parents="2532 2455"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(2473(a,1),251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2473 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(245,a,1141,a,b,2474,a)].">
      <j1 rule="hyper" parents="245 1141 2474"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      T(x,(y \ x) * y) * K(y \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(94(a,1),2474(a,1,2))].">
      <j1 rule="para" parents="94 2474"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,T(x,y)) = ((x * y) / x) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(2474(a,1),102(a,2,1))].">
      <j1 rule="para" parents="2474 102"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2475(a,1),115(a,1,1))].">
      <j1 rule="para" parents="2475 115"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((1 / (x * y)) \ T(1 / (x * y),x)) * x
    ]]></literal>
    <justification jstring="[para(1989(a,2),2480(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1989 2480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2483,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2483 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(2483(a,1),471(a,1,1))].">
      <j1 rule="para" parents="2483 471"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(2483(a,1),1787(a,2,2))].">
      <j1 rule="para" parents="2483 1787"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      a((x \ y) * x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2483(a,1),1866(a,1,1))].">
      <j1 rule="para" parents="2483 1866"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2532,a(flip),b,2498,a)].">
      <j1 rule="hyper" parents="136 2532 2498"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(2500(a,1),2508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2500 2508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(2535(a,2),2222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2535 2222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2554,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2554 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,x) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[para(2554(a,1),360(a,1,1))].">
      <j1 rule="para" parents="2554 360"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(2554(a,1),471(a,1,1))].">
      <j1 rule="para" parents="2554 471"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      (x * K(y,x)) * L(x \ K(x,y),x,y) = (x * K(y,x)) \ ((y / (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(2555(a,1),1726(a,1,2,1))].">
      <j1 rule="para" parents="2555 1726"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(2558(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2558 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(2559(a,1),733(a,1,1))].">
      <j1 rule="para" parents="2559 733"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      K(R(x,y,y \ 1),y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(810(a,1),2561(a,2,2))].">
      <j1 rule="para" parents="810 2561"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(1581(a,1),2561(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1581 2561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      (x * x) \ K(x * x,x \ 1) = (x / (x \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(221(a,1),2562(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="221 2562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(2257,a,2587,a)].">
      <j1 rule="hyper" parents="2257 2587"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[hyper(245,a,2558,a,b,2587,a)].">
      <j1 rule="hyper" parents="245 2558 2587"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2587(a,1),2174(a,1,1))].">
      <j1 rule="para" parents="2587 2174"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(195,a,2600,a)].">
      <j1 rule="hyper" parents="195 2600"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,2114,a(flip),b,2478,a)].">
      <j1 rule="hyper" parents="132 2114 2478"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,2562,a(flip),b,2479,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 2562 2479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      x \ (y * (T(y,x) \ z)) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[para(2126(a,2),2479(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2126 2479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2517,a(flip),b,2608,a),flip(a)].">
      <j1 rule="hyper" parents="325 2517 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(202,a,2608,a)].">
      <j1 rule="hyper" parents="202 2608"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(201,a,2290,a(flip),b,2608,a),flip(a)].">
      <j1 rule="hyper" parents="201 2290 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(148,a,2608,a)].">
      <j1 rule="hyper" parents="148 2608"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2608,a(flip),b,2124,a)].">
      <j1 rule="hyper" parents="137 2608 2124"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2608,a(flip),b,2126,a),flip(a)].">
      <j1 rule="hyper" parents="132 2608 2126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2608,a(flip),b,522,a),flip(a)].">
      <j1 rule="hyper" parents="132 2608 522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2608(a,1),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2608 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(2608(a,1),510(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2608 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[para(2608(a,1),512(a,1,1))].">
      <j1 rule="para" parents="2608 512"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(2608(a,1),699(a,1,1))].">
      <j1 rule="para" parents="2608 699"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      (x * y) \ ((y * x) * T(K(x,y),z)) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2608(a,1),1675(a,2,2,1))].">
      <j1 rule="para" parents="2608 1675"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(z \ y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2275(a,1),2608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2275 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(z / y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2281(a,1),2608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2281 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[para(2608(a,1),2307(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2608 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2611(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2611 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(135,a,2613,a(flip),b,2125,a),flip(a)].">
      <j1 rule="hyper" parents="135 2613 2125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(135,a,2613,a(flip),b,471,a)].">
      <j1 rule="hyper" parents="135 2613 471"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2613(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="2613 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,2608,a,b,2610,a),flip(a)].">
      <j1 rule="hyper" parents="41 2608 2610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(115(a,1),2629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 2629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1589(a,1),2629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1589 2629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,432,a,b,2615,a),flip(a)].">
      <j1 rule="hyper" parents="41 432 2615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(41,a,360,a,b,2615,a(flip))].">
      <j1 rule="hyper" parents="41 360 2615"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2615(a,1),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2615 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(2615(a,1),1691(a,1,2,1))].">
      <j1 rule="para" parents="2615 1691"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2126,a,b,2634,a)].">
      <j1 rule="hyper" parents="325 2126 2634"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,2634,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="201 2634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(135,a,2634,a,b,2126,a)].">
      <j1 rule="hyper" parents="135 2634 2126"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2634,a,b,2126,a),flip(a)].">
      <j1 rule="hyper" parents="132 2634 2126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2634(a,2),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2634 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(2634(a,2),624(a,2,1))].">
      <j1 rule="para" parents="2634 624"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[para(2634(a,2),674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2634 674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(2275(a,1),2634(a,2,1))].">
      <j1 rule="para" parents="2275 2634"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2635,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2635 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(2635(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2635 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(2635(a,1),471(a,1,1))].">
      <j1 rule="para" parents="2635 471"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      T(x,y) \ (K(y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(2635(a,1),521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2635 521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[para(2635(a,1),666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2635 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2244,a(flip),b,2618,a),flip(a)].">
      <j1 rule="hyper" parents="325 2244 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2657">
    <literal><![CDATA[
      K(x,y) \ R(y,z,u) = R(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2130,a(flip),b,2618,a),flip(a)].">
      <j1 rule="hyper" parents="325 2130 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(301,a,2618,a),flip(a)].">
      <j1 rule="hyper" parents="301 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(202,a,2618,a)].">
      <j1 rule="hyper" parents="202 2618"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,2114,a(flip),b,2618,a)].">
      <j1 rule="hyper" parents="201 2114 2618"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,10,a(flip),b,2618,a)].">
      <j1 rule="hyper" parents="201 10 2618"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      K(x,y) * R(K(y,x) * z,u,w) = R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,1057,a,b,2618,a)].">
      <j1 rule="hyper" parents="137 1057 2618"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = a(K(v5,v6),v7,v8) * w
    ]]></literal>
    <justification jstring="[hyper(137,a,800,a,b,2618,a)].">
      <j1 rule="hyper" parents="137 800 2618"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(w,v5) * R(K(v5,w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(137,a,634,a,b,2618,a),flip(a)].">
      <j1 rule="hyper" parents="137 634 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(137,a,287,a,b,2618,a)].">
      <j1 rule="hyper" parents="137 287 2618"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) * z) * u) = (y * z) * u
    ]]></literal>
    <justification jstring="[hyper(137,a,2186,a(flip),b,2618,a)].">
      <j1 rule="hyper" parents="137 2186 2618"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      (K(x,y) \ z) * u = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(136,a,2618,a,b,419,a)].">
      <j1 rule="hyper" parents="136 2618 419"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(132,a,2618,a,b,113,a)].">
      <j1 rule="hyper" parents="132 2618 113"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ u) = K(z,y) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,522,a,b,2618,a)].">
      <j1 rule="hyper" parents="65 522 2618"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      L(K(x,y) \ z,u,K(w,v5)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,153,a,b,2618,a)].">
      <j1 rule="hyper" parents="65 153 2618"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,2173,a(flip),b,2618,a),flip(a)].">
      <j1 rule="hyper" parents="65 2173 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(245,a,2618,a(flip),b,522,a),flip(a)].">
      <j1 rule="hyper" parents="245 2618 522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,w) * z) = K(x,y) * K(w,u)
    ]]></literal>
    <justification jstring="[hyper(201,a,2618,a(flip),b,470,a)].">
      <j1 rule="hyper" parents="201 2618 470"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      (K(x,y) * z) \ u = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,2618,a(flip),b,522,a),flip(a)].">
      <j1 rule="hyper" parents="132 2618 522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(2618(a,1),143(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2618 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(2618(a,1),148(a,1))].">
      <j1 rule="para" parents="2618 148"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(2618(a,1),260(a,1,2))].">
      <j1 rule="para" parents="2618 260"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(2618(a,1),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2618 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(2618(a,1),308(a,1,1))].">
      <j1 rule="para" parents="2618 308"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      R(K(x,y),z,u) = w / (K(y,x) * w)
    ]]></literal>
    <justification jstring="[para(2618(a,1),635(a,2,2))].">
      <j1 rule="para" parents="2618 635"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      T((K(x,y) * z) \ u,w) = T(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[para(2618(a,1),826(a,2,1,2))].">
      <j1 rule="para" parents="2618 826"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      x \ (K(y,z) * L(K(z,y) * (x * u),w,v5)) = (x \ K(y,z)) * L((x \ K(y,z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(2618(a,1),1242(a,1,2,2,1))].">
      <j1 rule="para" parents="2618 1242"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      K(x,y) \ L(z,u,K(w,v5)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(132,a,153,a,b,2619,a)].">
      <j1 rule="hyper" parents="132 153 2619"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(2619(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2619 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(2619(a,1),668(a,1,1))].">
      <j1 rule="para" parents="2619 668"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      T(x,(y * z) \ y) = 1 / (x \ K(z \ 1,x))
    ]]></literal>
    <justification jstring="[para(2279(a,1),2626(a,2,2,2))].">
      <j1 rule="para" parents="2279 2626"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(2287,a,2630,a)].">
      <j1 rule="hyper" parents="2287 2630"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,2630,a,b,94,a)].">
      <j1 rule="hyper" parents="137 2630 94"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2286,a(flip),b,2630,a),flip(a)].">
      <j1 rule="hyper" parents="65 2286 2630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(2630(a,1),1582(a,2,2))].">
      <j1 rule="para" parents="2630 1582"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(2630(a,1),2163(a,1,2))].">
      <j1 rule="para" parents="2630 2163"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(245,a,2503,a,b,2641,a)].">
      <j1 rule="hyper" parents="245 2503 2641"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      x \ (R(x,y,z) * T(u,x)) = R(x,y,z) * (T(x,u) \ u)
    ]]></literal>
    <justification jstring="[para(2644(a,2),958(a,2,2))].">
      <j1 rule="para" parents="2644 958"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(38,a,2414,a(flip),b,2659,a),flip(a)].">
      <j1 rule="hyper" parents="38 2414 2659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2661(a,1),182(a,1)),flip(b)].">
      <j1 rule="para" parents="2661 182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2629(a,2),2625(a,1,1))].">
      <j1 rule="para" parents="2629 2625"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ 1 = K(u,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2618,a(flip),b,2616,a),flip(a)].">
      <j1 rule="hyper" parents="325 2618 2616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(430(a,1),2616(a,1,1))].">
      <j1 rule="para" parents="430 2616"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(2616(a,1),2288(a,2,1,1))].">
      <j1 rule="para" parents="2616 2288"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = y * T(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,113,a(flip),b,2647,a)].">
      <j1 rule="hyper" parents="137 113 2647"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(245,a,2647,a(flip),b,2126,a),flip(a)].">
      <j1 rule="hyper" parents="245 2647 2126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(631,a,2648,a)].">
      <j1 rule="hyper" parents="631 2648"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) * z) / u) = (y * z) / u
    ]]></literal>
    <justification jstring="[para(2650(a,1),666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2650 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2244,a(flip),b,2652,a)].">
      <j1 rule="hyper" parents="325 2244 2652"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) = K(w,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),2660(a,1,2,1))].">
      <j1 rule="para" parents="27 2660"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(2285(a,1),2689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2285 2689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y \ x) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(2286(a,1),2689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2286 2689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      (x * K(x \ y,x)) * (y / x) = y
    ]]></literal>
    <justification jstring="[hyper(147,a,2691,a)].">
      <j1 rule="hyper" parents="147 2691"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(2691(a,2),1589(a,1,1))].">
      <j1 rule="para" parents="2691 1589"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      T(T(x / (x / y),z),y \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(2691(a,2),1592(a,1,1,1))].">
      <j1 rule="para" parents="2691 1592"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      T(x,y) \ T(z / (z / x),y) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[para(2691(a,2),1620(a,1,2,1))].">
      <j1 rule="para" parents="2691 1620"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      T(x / T(y,x),z) * y = y * T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(2693(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2693 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      K(x,y) * R(K(y,x) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(1057(a,2),2677(a,1,2))].">
      <j1 rule="para" parents="1057 2677"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      R(K(x,y),z,u) = w / (R(K(y,x),v5,v6) * w)
    ]]></literal>
    <justification jstring="[para(625(a,2),2680(a,2,2,1))].">
      <j1 rule="para" parents="625 2680"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),2684(a,1))].">
      <j1 rule="para" parents="22 2684"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      K(x,y) * (((y * x) * z) * u) = ((x * y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,2488,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2488 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      (x * (y / x)) * (y \ z) = K(x,y / x) * z
    ]]></literal>
    <justification jstring="[para(311(a,1),2488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="311 2488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      L(x,y,(z * u) * w) = L(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(2488(a,1),1541(a,1,3))].">
      <j1 rule="para" parents="2488 1541"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1816(a,2),2488(a,1,2))].">
      <j1 rule="para" parents="1816 2488"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      (T(x,y) * z) \ ((x * y) * u) = (x * z) \ ((y * x) * u)
    ]]></literal>
    <justification jstring="[para(2488(a,1),2190(a,1,2))].">
      <j1 rule="para" parents="2488 2190"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      x * (((y \ x) * y) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,2493,a(flip),b,159,a(flip))].">
      <j1 rule="hyper" parents="137 2493 159"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      (x * y) \ R(K(x,y) * z,u,w) = (y * x) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[para(1057(a,2),2493(a,1,2))].">
      <j1 rule="para" parents="1057 2493"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      (((K(x,y) * z) / (x * y)) * x) \ (K(x,y) * z) = L(y,x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(2493(a,1),1634(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2493 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (((x \ 1) * L(x,y,z)) \ u) = K(L(x,y,z),x \ 1) * u
    ]]></literal>
    <justification jstring="[para(946(a,1),2494(a,1,1))].">
      <j1 rule="para" parents="946 2494"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      K(x * x,(x * x) \ x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,97,a(flip),b,2525,a),flip(a)].">
      <j1 rule="hyper" parents="325 97 2525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(284,a,2560,a)].">
      <j1 rule="hyper" parents="284 2560"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2125,a,b,2563,a),flip(a)].">
      <j1 rule="hyper" parents="325 2125 2563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      x * (x * T(T(x,x \ (y * x)) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(2567(a,2),1175(a,1,2,2,1))].">
      <j1 rule="para" parents="2567 1175"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,115,a(flip),b,2576,a),flip(a)].">
      <j1 rule="hyper" parents="325 115 2576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(82(a,1),2741(a,1,1,2,2))].">
      <j1 rule="para" parents="82 2741"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(2602(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2602 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2608,a(flip),b,2622,a),flip(a)].">
      <j1 rule="hyper" parents="325 2608 2622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(2622(a,2),2625(a,1))].">
      <j1 rule="para" parents="2622 2625"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2744,a(flip),b,2056,a)].">
      <j1 rule="hyper" parents="137 2744 2056"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),2744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2744(a,2,2))].">
      <j1 rule="para" parents="9 2744"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(14(a,2),2744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(85(a,1),2744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y))
    ]]></literal>
    <justification jstring="[para(102(a,2),2744(a,1,2,1))].">
      <j1 rule="para" parents="102 2744"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(2618(a,1),2744(a,1,2,1))].">
      <j1 rule="para" parents="2618 2744"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      K(x * x,x \ 1) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2736,a(flip),b,2747,a),flip(a)].">
      <j1 rule="hyper" parents="65 2736 2747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2608,a(flip),b,2623,a),flip(a)].">
      <j1 rule="hyper" parents="325 2608 2623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(2623(a,2),2625(a,1))].">
      <j1 rule="para" parents="2623 2625"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),2755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 2755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),2755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 2755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,u / (z * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2750,a,b,2758,a)].">
      <j1 rule="hyper" parents="325 2750 2758"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      x \ T(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2104,a(flip),b,2758,a)].">
      <j1 rule="hyper" parents="65 2104 2758"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      R(K(x,y / (z * y)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = v5
    ]]></literal>
    <justification jstring="[para(2758(a,2),638(a,1,1))].">
      <j1 rule="para" parents="2758 638"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2634,a,b,2649,a),flip(a)].">
      <j1 rule="hyper" parents="325 2634 2649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(2649(a,2),2651(a,1))].">
      <j1 rule="para" parents="2649 2651"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),2763(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ (y * z)) = T(x,L(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(18(a,2),2763(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18 2763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(22(a,2),2763(a,1,2,1))].">
      <j1 rule="para" parents="22 2763"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(381,a,2767,a),flip(a)].">
      <j1 rule="hyper" parents="381 2767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      K(x * y,y) * T(y,x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,756,a(flip),b,2657,a)].">
      <j1 rule="hyper" parents="137 756 2657"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = u * T(z,K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,2665,a)].">
      <j1 rule="hyper" parents="65 233 2665"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      K(x,y) * ((z * T(y,x)) * u) = T(z * y,K(y,x)) * u
    ]]></literal>
    <justification jstring="[para(2173(a,1),2667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2173 2667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      x * ((y * (x / y)) \ z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(2587(a,1),2669(a,1,2,1))].">
      <j1 rule="para" parents="2587 2669"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) \ v5 = R(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(1057(a,2),2674(a,1,1))].">
      <j1 rule="para" parents="1057 2674"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,114,a,b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="325 114 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,2104,a(flip),b,2761,a),flip(a)].">
      <j1 rule="hyper" parents="40 2104 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,2539,a(flip),b,2782,a),flip(a)].">
      <j1 rule="hyper" parents="65 2539 2782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2510,a(flip),b,2782,a)].">
      <j1 rule="hyper" parents="65 2510 2782"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      T((x * y) \ y,x \ 1) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,280,a(flip),b,2782,a),flip(a)].">
      <j1 rule="hyper" parents="65 280 2782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),2782(a,1,2,2))].">
      <j1 rule="para" parents="10 2782"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),2782(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      T(x,(y * z) / ((u * y) * z)) = T(x,R(u,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),2782(a,1,2,2))].">
      <j1 rule="para" parents="109 2782"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(137,a,2786,a(flip),b,2539,a(flip))].">
      <j1 rule="hyper" parents="137 2786 2539"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2510,a(flip),b,2787,a),flip(a)].">
      <j1 rule="hyper" parents="325 2510 2787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(2562(a,1),2787(a,1,2))].">
      <j1 rule="para" parents="2562 2787"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2790(a,1),2077(a,1,2))].">
      <j1 rule="para" parents="2790 2077"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      T(1 * x,x \ 1) \ ((1 * x) \ 1) = ((1 * x) \ 1) * ((1 * x) \ 1)
    ]]></literal>
    <justification jstring="[para(2772(a,2),272(a,1,1))].">
      <j1 rule="para" parents="2772 272"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(201,a,2437,a(flip),b,2783,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 2437 2783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(85(a,1),2789(a,1,2,2))].">
      <j1 rule="para" parents="85 2789"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),2792(a,2,2))].">
      <j1 rule="para" parents="11 2792"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      L(T(K(x,y) \ z,u),w,K(v5,v6)) = T(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(2670(a,1),25(a,2,1))].">
      <j1 rule="para" parents="2670 25"/>
    </justification>
  </clause>

  <clause id="2799">
    <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),2745(a,1,2,1))].">
      <j1 rule="para" parents="102 2745"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(2055(a,2),2745(a,1))].">
      <j1 rule="para" parents="2055 2745"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(2618(a,1),2745(a,1,2,1))].">
      <j1 rule="para" parents="2618 2745"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(67(a,1),2800(a,1,2,2))].">
      <j1 rule="para" parents="67 2800"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2303,a(flip),b,2451,a)].">
      <j1 rule="hyper" parents="65 2303 2451"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1630,a,b,2463,a)].">
      <j1 rule="hyper" parents="65 1630 2463"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      (x * K(y,x)) \ x = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,2504,a(flip),b,2468,a)].">
      <j1 rule="hyper" parents="132 2504 2468"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ L(x,z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(1628(a,1),2806(a,1,1))].">
      <j1 rule="para" parents="1628 2806"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(23(a,1),2511(a,1,2))].">
      <j1 rule="para" parents="23 2511"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) * z) * u) = ((y / x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,2566,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 2566 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      (x / y) * (y \ (x * R(x \ y,z,u))) = K(y,y \ x) * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(1404(a,1),2566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1404 2566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      a((x / y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ x) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(2566(a,1),1866(a,1,1))].">
      <j1 rule="para" parents="2566 1866"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      ((x \ y) * z) \ (K(x \ y,x) * u) = ((y / x) * z) \ u
    ]]></literal>
    <justification jstring="[para(2566(a,1),2674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2566 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,2421,a,b,2570,a)].">
      <j1 rule="hyper" parents="36 2421 2570"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(2570(a,1),520(a,1))].">
      <j1 rule="para" parents="2570 520"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(2580(a,1),856(a,1,1))].">
      <j1 rule="para" parents="2580 856"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      K(x \ y,x) * (z * y) = ((x \ y) * x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,2582,a)].">
      <j1 rule="hyper" parents="65 233 2582"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(2582(a,1),213(a,1)),flip(b)].">
      <j1 rule="para" parents="2582 213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2508,a(flip),b,2588,a),flip(a)].">
      <j1 rule="hyper" parents="325 2508 2588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      (x / y) * K(y \ x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,2118,a,b,2591,a),flip(a)].">
      <j1 rule="hyper" parents="36 2118 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(245,a,287,a,b,2593,a)].">
      <j1 rule="hyper" parents="245 287 2593"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,2582,a(flip),b,2593,a)].">
      <j1 rule="hyper" parents="132 2582 2593"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ z,u) = z * K(y \ (x * (T(x,y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(2609(a,2),2164(a,2,2,1))].">
      <j1 rule="para" parents="2609 2164"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2375,a(flip),b,2612,a),flip(a)].">
      <j1 rule="hyper" parents="65 2375 2612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(195,a,2824,a)].">
      <j1 rule="hyper" parents="195 2824"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,2825,a(flip),b,2615,a(flip))].">
      <j1 rule="hyper" parents="137 2825 2615"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2676,a,2826,a)].">
      <j1 rule="hyper" parents="2676 2826"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,2094,a(flip),b,2827,a)].">
      <j1 rule="hyper" parents="36 2094 2827"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(2697,a,2828,a)].">
      <j1 rule="hyper" parents="2697 2828"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      x \ T(x,K(y,z)) = K(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a(flip),b,2828,a)].">
      <j1 rule="hyper" parents="325 2104 2828"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,2828,a,b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 2828 2104"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      K(K(x,y),z) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(136,a,2828,a,b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 2828 2117"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,2828,a,b,2619,a),flip(a)].">
      <j1 rule="hyper" parents="131 2828 2619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2828,a(flip),b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 2828 2117"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(2828(a,1),2654(a,1,1))].">
      <j1 rule="para" parents="2828 2654"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(2829(a,1),2625(a,1))].">
      <j1 rule="para" parents="2829 2625"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(2830(a,1),2109(a,1))].">
      <j1 rule="para" parents="2830 2109"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1590,a,2831,a)].">
      <j1 rule="hyper" parents="1590 2831"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,2831,a(flip),b,1581,a)].">
      <j1 rule="hyper" parents="136 2831 1581"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(2831(a,1),1591(a,1,1))].">
      <j1 rule="para" parents="2831 1591"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(42,a,479,a,b,2838,a),flip(a)].">
      <j1 rule="hyper" parents="42 479 2838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      K(x,y) * z != u * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(2838(a,1),247(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2838 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(2614(a,2),2837(a,1))].">
      <j1 rule="para" parents="2614 2837"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(479(a,1),2840(a,1,1)),flip(b)].">
      <j1 rule="para" parents="479 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1983(a,1),2839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1983 2839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,2658,a(flip),b,2842,a),flip(a)].">
      <j1 rule="hyper" parents="42 2658 2842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,2847,a),flip(a)].">
      <j1 rule="hyper" parents="327 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,2847,a)].">
      <j1 rule="hyper" parents="140 2847"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(37,a,2550,a,b,2847,a),flip(a)].">
      <j1 rule="hyper" parents="37 2550 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(37,a,2093,a,b,2847,a),flip(a)].">
      <j1 rule="hyper" parents="37 2093 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,2089,a,b,2847,a),flip(a)].">
      <j1 rule="hyper" parents="37 2089 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2847,a(flip),b,2087,a),flip(a)].">
      <j1 rule="hyper" parents="136 2847 2087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,2847,a(flip),b,2092,a),flip(a)].">
      <j1 rule="hyper" parents="135 2847 2092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(2847(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2847 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(2847(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2847 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(2847(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2847 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2860">
    <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(2847(a,1),709(a,1,1,2))].">
      <j1 rule="para" parents="2847 709"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(325,a,2089,a(flip),b,2848,a),flip(a)].">
      <j1 rule="hyper" parents="325 2089 2848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(2848(a,1),256(a,1,1))].">
      <j1 rule="para" parents="2848 256"/>
    </justification>
  </clause>

  <clause id="2863">
    <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(2848(a,1),541(a,1,1))].">
      <j1 rule="para" parents="2848 541"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      L(x,y,z / K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(2848(a,2),2334(a,1,3))].">
      <j1 rule="para" parents="2848 2334"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      ((x * K(y,z)) * R((x * K(y,z)) \ u,w,v5)) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(2849(a,1),1400(a,1,2))].">
      <j1 rule="para" parents="2849 1400"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(2093(a,1),2849(a,1,1))].">
      <j1 rule="para" parents="2093 2849"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(2164(a,2),2849(a,1,1))].">
      <j1 rule="para" parents="2164 2849"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(2229(a,1),2849(a,1,1))].">
      <j1 rule="para" parents="2229 2849"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(2849(a,2),2618(a,1,1))].">
      <j1 rule="para" parents="2849 2618"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,2851,a),flip(a)].">
      <j1 rule="hyper" parents="327 2851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2851,a(flip),b,2087,a),flip(a)].">
      <j1 rule="hyper" parents="136 2851 2087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * y = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(411(a,1),2851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="411 2851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2852,a),flip(a)].">
      <j1 rule="hyper" parents="334 2852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 2852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      (x * y) / T(x * (L(x,z,u) \ y),w) = L(x,z,u) * K(w,x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(1255(a,1),2852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1255 2852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      T(x,y) * T(x,y) = x * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1583(a,1),2854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1583 2854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(2855(a,1),115(a,1,1))].">
      <j1 rule="para" parents="2855 115"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * K(z,y)) * K(y,u) = w
    ]]></literal>
    <justification jstring="[para(2855(a,1),2176(a,1,1))].">
      <j1 rule="para" parents="2855 2176"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(2861(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2861 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      (x / y) * K(z,y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(2861(a,1),328(a,1,1))].">
      <j1 rule="para" parents="2861 328"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      x / T(z,y) = u
    ]]></literal>
    <justification jstring="[para(2870(a,1),46(a,1))].">
      <j1 rule="para" parents="2870 46"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      x * K(y,z) != z * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(z,y),z) = u
    ]]></literal>
    <justification jstring="[para(2870(a,1),246(a,2)),flip(a)].">
      <j1 rule="para" parents="2870 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2514(a,2),2858(a,1))].">
      <j1 rule="para" parents="2514 2858"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(1628(a,1),2859(a,1,1))].">
      <j1 rule="para" parents="1628 2859"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(2229(a,1),2859(a,1,1))].">
      <j1 rule="para" parents="2229 2859"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(1100(a,1),2867(a,1,1))].">
      <j1 rule="para" parents="1100 2867"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1130(a,1),2867(a,1,1))].">
      <j1 rule="para" parents="1130 2867"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      (x * (y * T(T(y,z),z))) / u = x / (u / (T(y,z) * T(y,z)))
    ]]></literal>
    <justification jstring="[para(2880(a,1),696(a,1,1,2))].">
      <j1 rule="para" parents="2880 696"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      R((T(x,y) * T(x,y)) * z,u,w) = (x * T(T(x,y),y)) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(2880(a,1),1049(a,2,1))].">
      <j1 rule="para" parents="2880 1049"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(2820(a,1),2884(a,1))].">
      <j1 rule="para" parents="2820 2884"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      R(x * y,z,u) / y = y \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,2662,a(flip),b,2048,a(flip))].">
      <j1 rule="hyper" parents="135 2662 2048"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      L(x,y,L((T(z,u) * w) * v5,K(u,z),K(u,z)) * v6) = L(x,y,v6 * (K(u,z) * ((z * w) * v5)))
    ]]></literal>
    <justification jstring="[para(2666(a,1),2332(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="2666 2332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      K(x,y) * ((y * T(T(y,x),x)) * z) = (y * T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(2880(a,1),2666(a,1,2,1))].">
      <j1 rule="para" parents="2880 2666"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      T(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(2687(a,2),2636(a,1))].">
      <j1 rule="para" parents="2687 2636"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),2899(a,1,2,1))].">
      <j1 rule="para" parents="12 2899"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      K(x,x \ K(y,z)) * K(z,y) = ((x \ K(y,z)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(313(a,1),2699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="313 2699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2671,a(flip),b,2703,a)].">
      <j1 rule="hyper" parents="65 2671 2703"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T((y * x) / y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(135,a,2904,a,b,424,a)].">
      <j1 rule="hyper" parents="135 2904 424"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,1227,a(flip),b,2708,a),flip(a)].">
      <j1 rule="hyper" parents="65 1227 2708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      ((x \ y) \ z) * K(y \ x,z) = (z \ ((x \ y) \ z)) * z
    ]]></literal>
    <justification jstring="[para(2275(a,1),2711(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2275 2711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      R(K(x,y),z,u) = R(K(y,x),w,v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,271,a(flip),b,2724,a),flip(a)].">
      <j1 rule="hyper" parents="325 271 2724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),v5,v6) * w
    ]]></literal>
    <justification jstring="[hyper(195,a,2724,a(flip))].">
      <j1 rule="hyper" parents="195 2724"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      (x * (y / x)) \ (y / x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(132,a,2575,a(flip),b,2728,a)].">
      <j1 rule="hyper" parents="132 2575 2728"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      L(x,y,(z * u) * w) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(2349,a,2729,a),flip(a)].">
      <j1 rule="hyper" parents="2349 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (z \ L(z,u,w))) * v5) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,2381,a(flip),b,2729,a),flip(a)].">
      <j1 rule="hyper" parents="325 2381 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) * w) = L(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(12(a,1),2729(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * (((x \ y) \ 1) \ z)) = y * ((((x \ y) \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(1511(a,1),2732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1511 2732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2549,a(flip),b,2738,a),flip(a)].">
      <j1 rule="hyper" parents="65 2549 2738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1684,a(flip),b,2746,a)].">
      <j1 rule="hyper" parents="325 1684 2746"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ z) = y * ((x * (y / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2583,a,b,2778,a)].">
      <j1 rule="hyper" parents="325 2583 2778"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),2797(a,1,2,2))].">
      <j1 rule="para" parents="22 2797"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(2500(a,1),2920(a,1,2))].">
      <j1 rule="para" parents="2500 2920"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(226(a,2),2921(a,1,1))].">
      <j1 rule="para" parents="226 2921"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(202,a,2922,a)].">
      <j1 rule="hyper" parents="202 2922"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R(1 / y,y,x) * R((T(x,y) / (x * y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2923(a,1),1280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2923 1280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      R(1 / T(x,y),T(x,y),y) = T(y,x) / (y * T(x,y))
    ]]></literal>
    <justification jstring="[para(2500(a,1),2923(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2500 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2926">
    <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(137,a,2809,a(flip),b,732,a),flip(a)].">
      <j1 rule="hyper" parents="137 2809 732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(2676,a,2814,a)].">
      <j1 rule="hyper" parents="2676 2814"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      R(x * y,z,u) / y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1076,a(flip),b,2896,a),flip(a)].">
      <j1 rule="hyper" parents="325 1076 2896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      R(x * (y * y),z,u) = R(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,1052,a(flip),b,2896,a),flip(a)].">
      <j1 rule="hyper" parents="136 1052 2896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      L(x,y,z * (u * z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2333,a(flip),b,2913,a),flip(a)].">
      <j1 rule="hyper" parents="65 2333 2913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      L(x,y,z * ((u * w) * u)) = L(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1493,a(flip),b,2913,a),flip(a)].">
      <j1 rule="hyper" parents="65 1493 2913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(520,a,2927,a),flip(a)].">
      <j1 rule="hyper" parents="520 2927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      K(x \ 1,x) * (x * x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[para(272(a,1),2927(a,1,2))].">
      <j1 rule="para" parents="272 2927"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,1074,a(flip),b,2928,a),flip(a)].">
      <j1 rule="hyper" parents="136 1074 2928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      x * R(x \ (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),2928(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      R(((x * y) * (x \ 1)) * (x * x),z,u) = (R(y * K(x,y),z,u) * x) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,1626,a(flip),b,2929,a),flip(a)].">
      <j1 rule="hyper" parents="325 1626 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      R(x * (y * y),y,y) = (x * y) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,109,a(flip),b,2929,a),flip(a)].">
      <j1 rule="hyper" parents="325 109 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      x \ ((K(x \ 1,x) * y) / ((x \ 1) * y)) = (((x \ 1) * y) / L(y,x \ 1,x)) * x
    ]]></literal>
    <justification jstring="[para(2932(a,1),1294(a,1,2,1))].">
      <j1 rule="para" parents="2932 1294"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(495(a,1),2934(a,2,1,2))].">
      <j1 rule="para" parents="495 2934"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(1218(a,1),2934(a,2,1,2))].">
      <j1 rule="para" parents="1218 2934"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,x) * (y * x) = x * ((y * x) * T((y * x) \ 1,x))
    ]]></literal>
    <justification jstring="[para(2934(a,2),1106(a,1,1))].">
      <j1 rule="para" parents="2934 1106"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(137,a,2935,a(flip),b,1076,a),flip(a)].">
      <j1 rule="hyper" parents="137 2935 1076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      (x * x) \ a(x,x,x) = (x / (x \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(2753(a,1),2601(a,1,2))].">
      <j1 rule="para" parents="2753 2601"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(485(a,1),2762(a,1))].">
      <j1 rule="para" parents="485 2762"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),2948(a,1,2,2))].">
      <j1 rule="para" parents="10 2948"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(2760(a,2),2948(a,1))].">
      <j1 rule="para" parents="2760 2948"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = w
    ]]></literal>
    <justification jstring="[para(2848(a,1),2949(a,1,2))].">
      <j1 rule="para" parents="2848 2949"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(400(a,1),2950(a,1,2,2))].">
      <j1 rule="para" parents="400 2950"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ ((y / x) \ (y * z)) = w
    ]]></literal>
    <justification jstring="[para(2822(a,2),533(a,1))].">
      <j1 rule="para" parents="2822 533"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      L(x * K(y,x),K(x * K(y,x),y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(2633(a,2),2556(a,1,2))].">
      <j1 rule="para" parents="2633 2556"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      K(x,y) \ T(K(z,u) * w,v5) = K(y,x) * T(K(u,z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(2798(a,1),2683(a,1,2))].">
      <j1 rule="para" parents="2798 2683"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(2125(a,2),2801(a,1,2,1))].">
      <j1 rule="para" parents="2125 2801"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,2452,a,b,2805,a(flip))].">
      <j1 rule="hyper" parents="37 2452 2805"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,625,a,b,2957,a)].">
      <j1 rule="hyper" parents="325 625 2957"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      T(x,R(y,z,u)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2957,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 2957 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      K(x,T(R(y,z,u),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(27(a,1),2957(a,1,2))].">
      <j1 rule="para" parents="27 2957"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      K(x,(y / z) / u) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(310(a,1),2957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="310 2957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(495(a,1),2957(a,1,2))].">
      <j1 rule="para" parents="495 2957"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,v5,v6)) = w
    ]]></literal>
    <justification jstring="[para(2957(a,1),638(a,1,1))].">
      <j1 rule="para" parents="2957 638"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(497(a,1),2957(a,1,2))].">
      <j1 rule="para" parents="497 2957"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(756(a,1),2957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="756 2957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1153(a,1),2957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1153 2957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      K(x,T(y / (1 / z),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(1219(a,1),2957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1219 2957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      K(x,T(y,z * L(y,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1729(a,1),2957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1729 2957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2540(a,1),2957(a,1,2))].">
      <j1 rule="para" parents="2540 2957"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(u,x) \ 1
    ]]></literal>
    <justification jstring="[para(2957(a,1),2608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2957 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,2959,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 2959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      T(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(2959(a,2),2140(a,1))].">
      <j1 rule="para" parents="2959 2140"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      T(x / R(y,z,u),y) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,2973,a),flip(a)].">
      <j1 rule="hyper" parents="376 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      T(x / y,R(y,z,u)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,115,a(flip),b,2973,a),flip(a)].">
      <j1 rule="hyper" parents="325 115 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      R(x,y,z) * T(u,x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2973,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 2973 22"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,2973,a(flip),b,2534,a)].">
      <j1 rule="hyper" parents="136 2973 2534"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      T(x,(y * z) / (u * z)) = T(x,y / u)
    ]]></literal>
    <justification jstring="[para(110(a,1),2973(a,1,2))].">
      <j1 rule="para" parents="110 2973"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      T(x,(y / z) / u) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(310(a,1),2973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="310 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(495(a,1),2973(a,1,2))].">
      <j1 rule="para" parents="495 2973"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(576(a,1),2973(a,1,2))].">
      <j1 rule="para" parents="576 2973"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      T(x,y \ (z * (u \ y))) = T(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[para(866(a,1),2973(a,1,2))].">
      <j1 rule="para" parents="866 2973"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      T(x,T(y,y * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1153(a,1),2973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1153 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(1218(a,1),2973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1218 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      T(x,(y * (z * u)) / ((w * z) * u)) = T(x,y / R(w,z,u))
    ]]></literal>
    <justification jstring="[para(505(a,1),2973(a,1,2))].">
      <j1 rule="para" parents="505 2973"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2540(a,1),2973(a,1,2))].">
      <j1 rule="para" parents="2540 2973"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(R(x,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2972,a,b,2972,a)].">
      <j1 rule="hyper" parents="325 2972 2972"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2608,a(flip),b,2972,a),flip(a)].">
      <j1 rule="hyper" parents="325 2608 2972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(2972(a,2),2625(a,1))].">
      <j1 rule="para" parents="2972 2625"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,625,a,b,2993,a)].">
      <j1 rule="hyper" parents="325 625 2993"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x,y,z)) = u * K(x,R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(137,a,2993,a(flip),b,2557,a),flip(a)].">
      <j1 rule="hyper" parents="137 2993 2557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      K((x / y) / z,u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(310(a,1),2993(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 2993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(495(a,1),2993(a,1,1))].">
      <j1 rule="para" parents="495 2993"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      K((x * y) / z,u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(497(a,1),2993(a,1,1))].">
      <j1 rule="para" parents="497 2993"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * w) = (R(x,z,u) * y) * w
    ]]></literal>
    <justification jstring="[para(2993(a,1),2488(a,1,1))].">
      <j1 rule="para" parents="2993 2488"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = (u / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2979,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 2979 22"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(2958(a,1),494(a,1)),flip(b)].">
      <j1 rule="para" parents="2958 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      R(K(x,y / z),u,w) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(495(a,1),2958(a,2,2))].">
      <j1 rule="para" parents="495 2958"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),w,v5) = K(x,((y * z) * u) / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(1471(a,1),2958(a,2,2))].">
      <j1 rule="para" parents="1471 2958"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(2958(a,1),2957(a,1,2))].">
      <j1 rule="para" parents="2958 2957"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      R(K(x,R(y,z,u)),w,v5) = K(x,R(y,v6,v7))
    ]]></literal>
    <justification jstring="[para(2957(a,2),2958(a,1,1))].">
      <j1 rule="para" parents="2957 2958"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2517,a(flip),b,2966,a),flip(a)].">
      <j1 rule="hyper" parents="325 2517 2966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      K(x,T(x \ y,y)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3010(a,1,2,2))].">
      <j1 rule="para" parents="10 3010"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      K(x * y,T(x,y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2517,a(flip),b,2968,a),flip(a)].">
      <j1 rule="hyper" parents="65 2517 2968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(596(a,1),2971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="596 2971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1010(a,1),2975(a,1,2))].">
      <j1 rule="para" parents="1010 2975"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1013(a,1),2975(a,1,2))].">
      <j1 rule="para" parents="1013 2975"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2500,a(flip),b,2988,a),flip(a)].">
      <j1 rule="hyper" parents="325 2500 2988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(3016(a,1),373(a,1,2,1))].">
      <j1 rule="para" parents="3016 373"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2500,a(flip),b,2991,a),flip(a)].">
      <j1 rule="hyper" parents="325 2500 2991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(596(a,1),2991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="596 2991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(596(a,1),3018(a,1,2)),flip(a)].">
      <j1 rule="para" parents="596 3018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2767,a(flip),b,3021,a),flip(a)].">
      <j1 rule="hyper" parents="325 2767 3021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      x * K(x,y \ x) = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a(flip),b,3021,a)].">
      <j1 rule="hyper" parents="325 2094 3021"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2984,a,b,3021,a)].">
      <j1 rule="hyper" parents="65 2984 3021"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      T(T(x,y \ x) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(3021(a,1),2473(a,1,1,1))].">
      <j1 rule="para" parents="3021 2473"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      R(K(R(x,y,z),u),w,v5) = K(R(x,v6,v7),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,625,a,b,2992,a)].">
      <j1 rule="hyper" parents="325 625 2992"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(493(a,1),2994(a,1,1))].">
      <j1 rule="para" parents="493 2994"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      K(T(x,x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(2540(a,1),2994(a,1,1))].">
      <j1 rule="para" parents="2540 2994"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      R(R(K(x,y),z,u),w,v5) = K(R(x,v6,v7),y)
    ]]></literal>
    <justification jstring="[para(2995(a,2),625(a,1,1))].">
      <j1 rule="para" parents="2995 625"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2630,a(flip),b,2998,a),flip(a)].">
      <j1 rule="hyper" parents="325 2630 2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2461,a(flip),b,2998,a),flip(a)].">
      <j1 rule="hyper" parents="325 2461 2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      K(x,L(R(y,z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(29(a,1),3002(a,1,2))].">
      <j1 rule="para" parents="29 3002"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      K(x,(y * z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(497(a,1),3002(a,1,2))].">
      <j1 rule="para" parents="497 3002"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1010(a,1),3002(a,1,2))].">
      <j1 rule="para" parents="1010 3002"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2540(a,1),3002(a,1,2))].">
      <j1 rule="para" parents="2540 3002"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2517,a(flip),b,3013,a)].">
      <j1 rule="hyper" parents="65 2517 3013"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      K(x,R(T(y / z,y * u),z,u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(498(a,1),3013(a,1,2))].">
      <j1 rule="para" parents="498 3013"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      T(x,(1 / y) * K(z,u)) = T(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(679(a,1),3019(a,1,2))].">
      <j1 rule="para" parents="679 3019"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2746,a(flip),b,3024,a)].">
      <j1 rule="hyper" parents="65 2746 3024"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3025(a,1),2968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3025 2968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(495(a,1),3008(a,1,2,2))].">
      <j1 rule="para" parents="495 3008"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      K(x,K(y,T((z * u) / w,w / u))) = K(x,K(y,(w / u) \ z))
    ]]></literal>
    <justification jstring="[para(745(a,1),3008(a,1,2,2))].">
      <j1 rule="para" parents="745 3008"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(2275(a,2),3031(a,1))].">
      <j1 rule="para" parents="2275 3031"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2532,a(flip),b,2962,a),flip(a)].">
      <j1 rule="hyper" parents="65 2532 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      R(K(x,(y / z) / u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * z)) = v6
    ]]></literal>
    <justification jstring="[para(2962(a,2),638(a,1,1))].">
      <j1 rule="para" parents="2962 638"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,3040,a(flip),b,2965,a),flip(a)].">
      <j1 rule="hyper" parents="325 3040 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      (x / R(y,z,u)) * y = y * (R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(137,a,2976,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 2976 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,u) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(235(a,1),2980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="235 2980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ u) = (u / T(x,u)) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2693(a,1),2980(a,1,2))].">
      <j1 rule="para" parents="2693 2980"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      T(x,R(y,z,u) \ 1) = T(x,z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2788,a(flip),b,2982,a)].">
      <j1 rule="hyper" parents="65 2788 2982"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2630,a(flip),b,2997,a),flip(a)].">
      <j1 rule="hyper" parents="65 2630 2997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(3044(a,1),1685(a,1))].">
      <j1 rule="para" parents="3044 1685"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(2763(a,1),3046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2763 3046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),u,w) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(325,a,625,a,b,3052,a)].">
      <j1 rule="hyper" parents="325 625 3052"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1707(a,1),3052(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1707 3052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,v5,v6)) = w
    ]]></literal>
    <justification jstring="[para(2958(a,1),2964(a,1))].">
      <j1 rule="para" parents="2958 2964"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2517,a(flip),b,2970,a),flip(a)].">
      <j1 rule="hyper" parents="65 2517 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(100(a,1),2970(a,1,2,2))].">
      <j1 rule="para" parents="100 2970"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(3005(a,1),2973(a,1,2))].">
      <j1 rule="para" parents="3005 2973"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (w * v5) = (K(x,R(y,v6,v7)) * w) * v5
    ]]></literal>
    <justification jstring="[hyper(136,a,3009,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="136 3009 20"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,v5,v6),u) = w
    ]]></literal>
    <justification jstring="[para(3030(a,1),494(a,1)),flip(b)].">
      <j1 rule="para" parents="3030 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(3032,a,2221,a)].">
      <j1 rule="hyper" parents="3032 2221"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(2221(a,1),3032(a,1))].">
      <j1 rule="para" parents="2221 3032"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2222,a,b,3069,a)].">
      <j1 rule="hyper" parents="325 2222 3069"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      x \ (K(y,z) * x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,22,a(flip),b,3069,a)].">
      <j1 rule="hyper" parents="325 22 3069"/>
    </justification>
  </clause>

  <clause id="3073">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(137,a,3069,a,b,2672,a)].">
      <j1 rule="hyper" parents="137 3069 2672"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(137,a,3069,a,b,2668,a)].">
      <j1 rule="hyper" parents="137 3069 2668"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(137,a,3069,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="137 3069 22"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      T(K(x,y),z * x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2589,a,b,3069,a)].">
      <j1 rule="hyper" parents="65 2589 3069"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      T(K(x,y),x \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2221,a(flip),b,3069,a),flip(a)].">
      <j1 rule="hyper" parents="65 2221 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      1 / T(K(x,y),z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(201,a,3069,a(flip),b,2608,a)].">
      <j1 rule="hyper" parents="201 3069 2608"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2119(a,1),3069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2119 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2456(a,1),3069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2456 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      K(T(x,y),z) \ 1 = T(K(z,x),y)
    ]]></literal>
    <justification jstring="[para(3069(a,2),2825(a,1,1))].">
      <j1 rule="para" parents="3069 2825"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,3080,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 3080 22"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3080(a,1),2839(a,1,1))].">
      <j1 rule="para" parents="3080 2839"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2725,a,3081,a)].">
      <j1 rule="hyper" parents="2725 3081"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,3081,a)].">
      <j1 rule="hyper" parents="56 3081"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3081(a,1),292(a,1,2))].">
      <j1 rule="para" parents="3081 292"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(w,x) = K(w,x) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3081(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3081 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      K(x,y) * L(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(y,z),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(3081(a,1),373(a,1,2,1))].">
      <j1 rule="para" parents="3081 373"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,x)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(2725,a,3088,a)].">
      <j1 rule="hyper" parents="2725 3088"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3069,a,b,3088,a)].">
      <j1 rule="hyper" parents="65 3069 3088"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3088(a,1),292(a,1,2))].">
      <j1 rule="para" parents="3088 292"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,u) = K(y,u) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3088(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3088 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3088(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3088 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(T(x,K(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(136,a,3093,a(flip),b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 3093 2117"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[para(479(a,1),3093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="479 3093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(2869(a,1),3071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2869 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(41,a,2849,a,b,3072,a)].">
      <j1 rule="hyper" parents="41 2849 3072"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(2857,a,3073,a)].">
      <j1 rule="hyper" parents="2857 3073"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,1981,a,b,3075,a),flip(a)].">
      <j1 rule="hyper" parents="36 1981 3075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),3075(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 3075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(235(a,1),3075(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="235 3075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2824,a(flip),b,3078,a),flip(a)].">
      <j1 rule="hyper" parents="65 2824 3078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3076,a,b,3111,a)].">
      <j1 rule="hyper" parents="325 3076 3111"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3069,a,b,3111,a)].">
      <j1 rule="hyper" parents="325 3069 3111"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,2834,a,b,3111,a)].">
      <j1 rule="hyper" parents="325 2834 3111"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2827,a,b,3111,a)].">
      <j1 rule="hyper" parents="325 2827 3111"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2373,a,b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="325 2373 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2222,a,b,3111,a)].">
      <j1 rule="hyper" parents="325 2222 3111"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2221,a,b,3111,a)].">
      <j1 rule="hyper" parents="325 2221 3111"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,637,a,b,3111,a)].">
      <j1 rule="hyper" parents="325 637 3111"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3077,a(flip),b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="325 3077 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2223,a(flip),b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="325 2223 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2154,a(flip),b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="325 2154 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3013,a(flip),b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="65 3013 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2968,a(flip),b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="65 2968 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2966,a(flip),b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="65 2966 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2218,a(flip),b,3111,a),flip(a)].">
      <j1 rule="hyper" parents="65 2218 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,3111,a(flip),b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 3111 2104"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      T(T(K(x,y),z),u) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(3111(a,2),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3111 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),3111(a,1,2))].">
      <j1 rule="para" parents="23 3111"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      T(K(x,y / z),z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),3111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="115 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      K(x \ 1,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(3111(a,2),2289(a,1))].">
      <j1 rule="para" parents="3111 2289"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3111(a,2),2826(a,1,2))].">
      <j1 rule="para" parents="3111 2826"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(u / (u / K(x,y)),z) = K(K(x,y) \ u,T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(3111(a,2),2718(a,1,1))].">
      <j1 rule="para" parents="3111 2718"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = T(K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[para(3111(a,2),3111(a,1,2))].">
      <j1 rule="para" parents="3111 3111"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,3013,a(flip),b,3113,a),flip(a)].">
      <j1 rule="hyper" parents="325 3013 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2220,a,b,3113,a)].">
      <j1 rule="hyper" parents="65 2220 3113"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      K(x,T(y,z / x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2544,a(flip),b,3113,a),flip(a)].">
      <j1 rule="hyper" parents="65 2544 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(201,a,3113,a(flip),b,2849,a)].">
      <j1 rule="hyper" parents="201 3113 2849"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,3113,a(flip),b,2661,a),flip(a)].">
      <j1 rule="hyper" parents="136 3113 2661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(136,a,3113,a(flip),b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 3113 2117"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      K(T(x,y),T(z,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),3113(a,2,2))].">
      <j1 rule="para" parents="23 3113"/>
    </justification>
  </clause>

  <clause id="3143">
    <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),3113(a,1,1))].">
      <j1 rule="para" parents="25 3113"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      K(R(T(x,y),z,u),w) = K(R(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(27(a,2),3113(a,1,1))].">
      <j1 rule="para" parents="27 3113"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),3113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(115(a,1),3113(a,2,2))].">
      <j1 rule="para" parents="115 3113"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(235(a,1),3113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="235 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      K(x,T(y,K(z,L(x,u,w)))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2465(a,1),3113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2465 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2603(a,1),3113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2603 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(3113(a,1),2620(a,1,1))].">
      <j1 rule="para" parents="3113 2620"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      1 / (x \ K(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3113(a,1),2636(a,1,2,2))].">
      <j1 rule="para" parents="3113 2636"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(3113(a,1),2857(a,1,2))].">
      <j1 rule="para" parents="3113 2857"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,3122,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 3122 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3083(a,1),2625(a,1))].">
      <j1 rule="para" parents="3083 2625"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2218(a,1),3105(a,1,2))].">
      <j1 rule="para" parents="2218 3105"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3106(a,1),45(a,1))].">
      <j1 rule="para" parents="3106 45"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),3106(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2150(a,1),3106(a,1,2,2))].">
      <j1 rule="para" parents="2150 3106"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2218(a,1),3106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2218 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(2968(a,1),3106(a,1,2))].">
      <j1 rule="para" parents="2968 3106"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = K(z,x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2971(a,1),3106(a,1,2))].">
      <j1 rule="para" parents="2971 3106"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      K(x * y,x) * y = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(3012(a,1),3106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3012 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      K(x,y / z) * y = y * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3013(a,1),3106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3013 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3111,a,b,3112,a)].">
      <j1 rule="hyper" parents="65 3111 3112"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      (x * y) * K(y,T(z,x)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,3112,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 3112 22"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3113,a(flip),b,3118,a)].">
      <j1 rule="hyper" parents="65 3113 3118"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(3118(a,1),3032(a,1))].">
      <j1 rule="para" parents="3118 3032"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(184(a,1),3121(a,1,2))].">
      <j1 rule="para" parents="184 3121"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3125(a,1),2826(a,1,2))].">
      <j1 rule="para" parents="3125 2826"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3125,a,b,3126,a),flip(a)].">
      <j1 rule="hyper" parents="325 3125 3126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,3127,a)].">
      <j1 rule="hyper" parents="56 3127"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(262(a,1),3127(a,1,1))].">
      <j1 rule="para" parents="262 3127"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(3127(a,1),233(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3127 233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2845,a,3172,a)].">
      <j1 rule="hyper" parents="2845 3172"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(2840,a,3172,a)].">
      <j1 rule="hyper" parents="2840 3172"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(262(a,1),3172(a,1,2))].">
      <j1 rule="para" parents="262 3172"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(3172(a,1),292(a,1,2))].">
      <j1 rule="para" parents="3172 292"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2725,a,3177,a)].">
      <j1 rule="hyper" parents="2725 3177"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(2686,a,3177,a)].">
      <j1 rule="hyper" parents="2686 3177"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3177(a,1),292(a,1,2))].">
      <j1 rule="para" parents="3177 292"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3178(a,1),2970(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3178 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2374,a(flip),b,3128,a),flip(a)].">
      <j1 rule="hyper" parents="65 2374 3128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      K(x,y \ z) * T(x,z) = T(T(x,z),z / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,3136,a(flip),b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 3136 2117"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      K(x,L(L(x,y,z),u,w) / v5) = K(x,v5 \ L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(219(a,1),3136(a,1,1))].">
      <j1 rule="para" parents="219 3136"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3131,a(flip),b,3137,a),flip(a)].">
      <j1 rule="hyper" parents="65 3131 3137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3111,a,b,3138,a),flip(a)].">
      <j1 rule="hyper" parents="325 3111 3138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,2286,a(flip),b,3145,a),flip(a)].">
      <j1 rule="hyper" parents="65 2286 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(136,a,3145,a(flip),b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 3145 2117"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(3145(a,1),2147(a,1,1))].">
      <j1 rule="para" parents="3145 2147"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(3145(a,2),3031(a,1))].">
      <j1 rule="para" parents="3145 3031"/>
    </justification>
  </clause>

  <clause id="3195">
    <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(3146(a,1),2884(a,1,2))].">
      <j1 rule="para" parents="3146 2884"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3153(a,2),2140(a,1))].">
      <j1 rule="para" parents="3153 2140"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      T(x,y * K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3153(a,1),2819(a,1,2))].">
      <j1 rule="para" parents="3153 2819"/>
    </justification>
  </clause>

  <clause id="3198">
    <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(89(a,1),3164(a,1,2,2))].">
      <j1 rule="para" parents="89 3164"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,3166,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 3166 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,3173,a(flip),b,2173,a)].">
      <j1 rule="hyper" parents="137 3173 2173"/>
    </justification>
  </clause>

  <clause id="3201">
    <literal><![CDATA[
      K(x * y,T(z,x \ 1)) = K(x * y,T(z,y))
    ]]></literal>
    <justification jstring="[para(2782(a,1),3190(a,1,2))].">
      <j1 rule="para" parents="2782 3190"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = u
    ]]></literal>
    <justification jstring="[para(2373(a,2),3154(a,1))].">
      <j1 rule="para" parents="2373 3154"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(3069(a,2),3154(a,1))].">
      <j1 rule="para" parents="3069 3154"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3120(a,2),3154(a,1))].">
      <j1 rule="para" parents="3120 3154"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(3019(a,1),3196(a,1))].">
      <j1 rule="para" parents="3019 3196"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2257,a,3085,a)].">
      <j1 rule="hyper" parents="2257 3085"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(136,a,3086,a,b,419,a)].">
      <j1 rule="hyper" parents="136 3086 419"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2673,a,b,3086,a)].">
      <j1 rule="hyper" parents="65 2673 3086"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,3114,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 3114 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(115(a,1),3116(a,2,2,1))].">
      <j1 rule="para" parents="115 3116"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      T(T(K(x,y),z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(3129(a,2),3154(a,1))].">
      <j1 rule="para" parents="3129 3154"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2299,a,3141,a)].">
      <j1 rule="hyper" parents="2299 3141"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,3141,a(flip),b,2298,a)].">
      <j1 rule="hyper" parents="132 3141 2298"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,2692,a,b,3155,a),flip(a)].">
      <j1 rule="hyper" parents="37 2692 3155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(37,a,1199,a,b,3155,a),flip(a)].">
      <j1 rule="hyper" parents="37 1199 3155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2814(a,1),3155(a,1,1))].">
      <j1 rule="para" parents="2814 3155"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * y = y * K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2755(a,2),3157(a,1,1))].">
      <j1 rule="para" parents="2755 3157"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2692,a(flip),b,3159,a),flip(a)].">
      <j1 rule="hyper" parents="325 2692 3159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(325,a,1209,a(flip),b,3159,a),flip(a)].">
      <j1 rule="hyper" parents="325 1209 3159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1028,a(flip),b,3159,a),flip(a)].">
      <j1 rule="hyper" parents="325 1028 3159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,1027,a(flip),b,3159,a),flip(a)].">
      <j1 rule="hyper" parents="325 1027 3159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[hyper(136,a,3159,a,b,1213,a)].">
      <j1 rule="hyper" parents="136 3159 1213"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,3159,a(flip),b,419,a)].">
      <j1 rule="hyper" parents="136 3159 419"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(132,a,3159,a(flip),b,2669,a),flip(a)].">
      <j1 rule="hyper" parents="132 3159 2669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[para(3159(a,2),1027(a,2,2))].">
      <j1 rule="para" parents="3159 1027"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(3159(a,2),2862(a,1))].">
      <j1 rule="para" parents="3159 2862"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      K(x,y * (z \ 1)) * y = y * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(2963(a,2),3163(a,1,1))].">
      <j1 rule="para" parents="2963 3163"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(3171(a,2),2614(a,1,1))].">
      <j1 rule="para" parents="3171 2614"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,2814,a(flip),b,3176,a),flip(a)].">
      <j1 rule="hyper" parents="65 2814 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      ((x \ 1) / y) * K(x,x \ 1) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,2571,a(flip),b,3176,a),flip(a)].">
      <j1 rule="hyper" parents="65 2571 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,2566,a(flip),b,3176,a),flip(a)].">
      <j1 rule="hyper" parents="65 2566 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,3176,a(flip),b,419,a)].">
      <j1 rule="hyper" parents="136 3176 419"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3176(a,2),1032(a,1,2))].">
      <j1 rule="para" parents="3176 1032"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ 1 = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3176(a,1),2616(a,1,1))].">
      <j1 rule="para" parents="3176 2616"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2770,a(flip),b,3186,a),flip(a)].">
      <j1 rule="hyper" parents="325 2770 3186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(947(a,1),3191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="947 3191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3199(a,2),2140(a,1))].">
      <j1 rule="para" parents="3199 2140"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,T(u,y))) = T(T(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(3111(a,2),3219(a,1,2,2))].">
      <j1 rule="para" parents="3111 3219"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,u),v5,v6) = w
    ]]></literal>
    <justification jstring="[para(3033(a,1),494(a,1)),flip(b)].">
      <j1 rule="para" parents="3033 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,z)) = u
    ]]></literal>
    <justification jstring="[para(2784(a,1),3039(a,1,2))].">
      <j1 rule="para" parents="2784 3039"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),3049(a,1,1,1,1))].">
      <j1 rule="para" parents="10 3049"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      T(x,R(y,z,u) \ 1) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2782,a(flip),b,3056,a),flip(a)].">
      <j1 rule="hyper" parents="325 2782 3056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      T(R(x,y,z) \ 1,x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,112,a(flip),b,3250,a),flip(a)].">
      <j1 rule="hyper" parents="65 112 3250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,w),y) = z
    ]]></literal>
    <justification jstring="[para(485(a,1),3068(a,1,1))].">
      <j1 rule="para" parents="485 3068"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),3194(a,1,1,1))].">
      <j1 rule="para" parents="10 3194"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(2767(a,1),3244(a,1,2))].">
      <j1 rule="para" parents="2767 3244"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),u,w) = z
    ]]></literal>
    <justification jstring="[para(485(a,1),3246(a,1,1))].">
      <j1 rule="para" parents="485 3246"/>
    </justification>
  </clause>

  <clause id="3261">
    <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),3248(a,1,1,1))].">
      <j1 rule="para" parents="22 3248"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      K(L(x \ y,x,z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * y) \ (z * x),u) = w
    ]]></literal>
    <justification jstring="[para(102(a,2),3248(a,1,1,1))].">
      <j1 rule="para" parents="102 3248"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(2270(a,2),3248(a,1))].">
      <j1 rule="para" parents="2270 3248"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(3111(a,2),3263(a,1))].">
      <j1 rule="para" parents="3111 3263"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      T(x,T(y * L(z \ u,z,u),w)) = T(x,T(y / ((1 / u) * z),w))
    ]]></literal>
    <justification jstring="[para(700(a,2),2986(a,1,2,1,2))].">
      <j1 rule="para" parents="700 2986"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3001(a,1),971(a,1))].">
      <j1 rule="para" parents="3001 971"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(2444(a,1),3043(a,1,2))].">
      <j1 rule="para" parents="2444 3043"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      (x / R(y,z,u)) * y != y * w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(3053(a,2),45(a,1))].">
      <j1 rule="para" parents="3053 45"/>
    </justification>
  </clause>

  <clause id="3271">
    <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(1824(a,1),3144(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1824 3144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(325,a,2566,a(flip),b,3160,a),flip(a)].">
      <j1 rule="hyper" parents="325 2566 3160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2215,a,3165,a),flip(a)].">
      <j1 rule="hyper" parents="2215 3165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      T((K(x,y) * (z * x)) \ T(x,T(y,z)),z \ 1) = (z * T(x,T(y,z))) \ T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3273(a,2),2785(a,1,1,1))].">
      <j1 rule="para" parents="3273 2785"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2999,a,b,3168,a)].">
      <j1 rule="hyper" parents="65 2999 3168"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3133,a(flip),b,3170,a),flip(a)].">
      <j1 rule="hyper" parents="65 3133 3170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),3277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      K(x * y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(3278(a,1),3031(a,1))].">
      <j1 rule="para" parents="3278 3031"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z \ x) * (x / y) = T(T(T(x,y \ x) / y,x),x / z)
    ]]></literal>
    <justification jstring="[para(3026(a,1),3187(a,1,2))].">
      <j1 rule="para" parents="3026 3187"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3185,a(flip),b,3201,a),flip(a)].">
      <j1 rule="hyper" parents="65 3185 3201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(3217(a,1),3106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3217 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      (x / (1 / y)) \ K(y \ 1,y) = (x / (y \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(3221(a,1),2616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3221 2616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,3223,a(flip),b,1206,a)].">
      <j1 rule="hyper" parents="136 3223 1206"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(3156,a,3224,a)].">
      <j1 rule="hyper" parents="3156 3224"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(82(a,1),3285(a,1,2,1,1))].">
      <j1 rule="para" parents="82 3285"/>
    </justification>
  </clause>

  <clause id="3287">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(137,a,3225,a(flip),b,2932,a)].">
      <j1 rule="hyper" parents="137 3225 2932"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      x * (1 / (1 / x)) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,2933,a(flip),b,3226,a),flip(a)].">
      <j1 rule="hyper" parents="65 2933 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(1454(a,1),3229(a,1,1))].">
      <j1 rule="para" parents="1454 3229"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      (1 / x) / (y \ (x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3237,a),flip(a)].">
      <j1 rule="hyper" parents="334 3237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      ((1 / x) * y) / (1 / x) = ((x \ 1) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(135,a,3238,a(flip),b,1387,a)].">
      <j1 rule="hyper" parents="135 3238 1387"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      T(R(x \ 1,y,z) \ 1,x) = R(x \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3014,a,3252,a)].">
      <j1 rule="hyper" parents="3014 3252"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(195,a,3290,a)].">
      <j1 rule="hyper" parents="195 3290"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),u,w) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2755,a,b,3061,a),flip(a)].">
      <j1 rule="hyper" parents="325 2755 3061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(y \ (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(3132,a,3191,a(flip))].">
      <j1 rule="hyper" parents="3132 3191"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      K((x * y) \ y,z) = K(y \ (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(3261,a,3297,a)].">
      <j1 rule="hyper" parents="3261 3297"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      1 / (x \ K(y \ (z \ y),x)) = T(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[para(3299(a,1),2626(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3299 2626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(3064(a,1),1798(a,1,2))].">
      <j1 rule="para" parents="3064 1798"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      (x * (y * (z * K(u \ 1,u)))) \ ((x * y) * (K(u \ 1,u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = w
    ]]></literal>
    <justification jstring="[para(3175(a,2),709(a,1,2))].">
      <j1 rule="para" parents="3175 709"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(667,a,3210,a)].">
      <j1 rule="hyper" parents="667 3210"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[hyper(39,a,419,a,b,3211,a)].">
      <j1 rule="hyper" parents="39 419 3211"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3175,a,b,3228,a),flip(a)].">
      <j1 rule="hyper" parents="325 3175 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(3228(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3228 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u != w * v5
    ]]></literal>
    <literal><![CDATA[
      (K(z \ 1,z) * ((x * y) * u)) / v5 = w
    ]]></literal>
    <justification jstring="[para(3228(a,1),669(a,1,1))].">
      <j1 rule="para" parents="3228 669"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      (x * ((y * z) * K(u \ 1,u))) \ (K(u \ 1,u) * ((x * y) * z)) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[para(3228(a,1),474(a,1,1))].">
      <j1 rule="para" parents="3228 474"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3228(a,1),2674(a,1,1))].">
      <j1 rule="para" parents="3228 2674"/>
    </justification>
  </clause>

  <clause id="3310">
    <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(3230(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="3230 456"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1029,a(flip),b,3231,a),flip(a)].">
      <j1 rule="hyper" parents="325 1029 3231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(37,a,3155,a,b,3232,a)].">
      <j1 rule="hyper" parents="37 3155 3232"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3232(a,1),1029(a,1,2))].">
      <j1 rule="para" parents="3232 1029"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2844,a,3235,a),flip(a)].">
      <j1 rule="hyper" parents="2844 3235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2837,a,3314,a),flip(a)].">
      <j1 rule="hyper" parents="2837 3314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      K(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3315(a,2),3279(a,1))].">
      <j1 rule="para" parents="3315 3279"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1047(a,1),3239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1047 3239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = K(y,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3176,a,b,3240,a),flip(a)].">
      <j1 rule="hyper" parents="325 3176 3240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2674,a,b,3240,a)].">
      <j1 rule="hyper" parents="65 2674 3240"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(3167,a,3281,a)].">
      <j1 rule="hyper" parents="3167 3281"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(2562(a,1),3282(a,1,1,2))].">
      <j1 rule="para" parents="2562 3282"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      (x * (R(x \ 1,y,z) \ 1)) / x = R(x \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(275,a,3292,a)].">
      <j1 rule="hyper" parents="275 3292"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(2636,a,3300,a),flip(a)].">
      <j1 rule="hyper" parents="2636 3300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      T(x,(y * z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(3300(a,1),2636(a,1))].">
      <j1 rule="para" parents="3300 2636"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      x * K(x,y \ (z \ y)) = T(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a(flip),b,3325,a)].">
      <j1 rule="hyper" parents="325 2094 3325"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3242,a,b,3325,a)].">
      <j1 rule="hyper" parents="65 3242 3325"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2770,a,b,3325,a)].">
      <j1 rule="hyper" parents="65 2770 3325"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(85(a,1),3328(a,2,2,2))].">
      <j1 rule="para" parents="85 3328"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(36,a,2094,a(flip),b,3327,a)].">
      <j1 rule="hyper" parents="36 2094 3327"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(3242(a,2),3326(a,1))].">
      <j1 rule="para" parents="3242 3326"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(548,a,3305,a)].">
      <j1 rule="hyper" parents="548 3305"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3230,a,b,3305,a)].">
      <j1 rule="hyper" parents="65 3230 3305"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3159,a,b,3311,a),flip(a)].">
      <j1 rule="hyper" parents="325 3159 3311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(517(a,1),3312(a,1,2,2))].">
      <j1 rule="para" parents="517 3312"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(3225(a,1),3312(a,1,2,2))].">
      <j1 rule="para" parents="3225 3312"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(3319(a,2),3184(a,1))].">
      <j1 rule="para" parents="3319 3184"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(3334(a,2),3179(a,1))].">
      <j1 rule="para" parents="3334 3179"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z
    ]]></literal>
    <justification jstring="[para(2158(a,1),3335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2158 3335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(201,a,199,a(flip),b,3337,a)].">
      <j1 rule="hyper" parents="201 199 3337"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(850(a,1),3337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="850 3337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3350">
    <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(3338(a,2),626(a,1,2,1))].">
      <j1 rule="para" parents="3338 626"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3338(a,1),3311(a,1,1))].">
      <j1 rule="para" parents="3338 3311"/>
    </justification>
  </clause>

  <clause id="3353">
    <literal><![CDATA[
      R(1 / T(x,y),T(x,y),y) = T(y,x) / (x * y)
    ]]></literal>
    <justification jstring="[para(113(a,1),2925(a,2,2))].">
      <j1 rule="para" parents="113 2925"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3058,a,3023,a)].">
      <j1 rule="hyper" parents="3058 3023"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(3258,a,xx),flip(a)].">
      <j1 rule="hyper" parents="3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      T(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(3355(a,1),3015(a,1))].">
      <j1 rule="para" parents="3355 3015"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),w,v5) = T(K(x,(y / (x * z)) \ 1),u)
    ]]></literal>
    <justification jstring="[para(3295(a,1),27(a,2,1))].">
      <j1 rule="para" parents="3295 27"/>
    </justification>
  </clause>

  <clause id="3358">
    <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(3301(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3301 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = (K(v5,v6) * R(K(v6,v5),v7,v8)) * w
    ]]></literal>
    <justification jstring="[para(2664(a,1),2663(a,2,1))].">
      <j1 rule="para" parents="2664 2663"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ u) = x \ (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2980(a,1),2695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2980 2695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(2464(a,1),2701(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2464 2701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,3361,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 3361 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      (x * y) \ R(x * y,z,u) = (y * x) \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2472(a,1),2733(a,1,2,1))].">
      <j1 rule="para" parents="2472 2733"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(245,a,3312,a(flip),b,2775,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 3312 2775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      T(K(x,y),K(x,z) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(245,a,3304,a(flip),b,2775,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="245 3304 2775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(633(a,1),3364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="633 3364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1454(a,1),3364(a,1,2))].">
      <j1 rule="para" parents="1454 3364"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2927(a,1),3364(a,1,2))].">
      <j1 rule="para" parents="2927 3364"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3181(a,1),3364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3181 3364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3225(a,1),3364(a,1,2))].">
      <j1 rule="para" parents="3225 3364"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3337(a,2),3364(a,1,2))].">
      <j1 rule="para" parents="3337 3364"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = z / T(z,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,3370,a(flip),b,2634,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 3370 2634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,3370,a(flip),b,2094,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 3370 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[para(2619(a,1),3365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2619 3365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      T((x \ 1) * y,x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,686,a(flip),b,3367,a),flip(a)].">
      <j1 rule="hyper" parents="65 686 3367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2989,a(flip),b,3371,a),flip(a)].">
      <j1 rule="hyper" parents="65 2989 3371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(85(a,1),3379(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="85 3379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      K(x * (1 / y),z) = z / T(z,x / y)
    ]]></literal>
    <justification jstring="[hyper(201,a,3380,a(flip),b,2634,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 3380 2634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1752(a,1),3380(a,2,2))].">
      <j1 rule="para" parents="1752 3380"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2642,a,b,3374,a),flip(a)].">
      <j1 rule="hyper" parents="325 2642 3374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3100,a,b,3384,a)].">
      <j1 rule="hyper" parents="65 3100 3384"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(1032(a,2),3384(a,1,1))].">
      <j1 rule="para" parents="1032 3384"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1369(a,1),3384(a,1,1,2))].">
      <j1 rule="para" parents="1369 3384"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3182(a,1),3384(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3182 3384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3238(a,1),3384(a,1,1))].">
      <j1 rule="para" parents="3238 3384"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      K(T(K(x,x \ 1) * y,x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(1455(a,2),3385(a,1,1))].">
      <j1 rule="para" parents="1455 3385"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3311(a,2),3387(a,1,1))].">
      <j1 rule="para" parents="3311 3387"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(1454(a,1),3389(a,1,1))].">
      <j1 rule="para" parents="1454 3389"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a,b,3375,a),flip(a)].">
      <j1 rule="hyper" parents="325 2104 3375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,z)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2951,a,3395,a),flip(a)].">
      <j1 rule="hyper" parents="2951 3395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1045(a,1),3395(a,1,2))].">
      <j1 rule="para" parents="1045 3395"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3176(a,2),3395(a,1,2))].">
      <j1 rule="para" parents="3176 3395"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3182(a,1),3395(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3182 3395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3238(a,1),3395(a,1,2))].">
      <j1 rule="para" parents="3238 3395"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3240(a,2),3395(a,1,2))].">
      <j1 rule="para" parents="3240 3395"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3321(a,2),3395(a,1,2))].">
      <j1 rule="para" parents="3321 3395"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(850(a,1),3399(a,1,2))].">
      <j1 rule="para" parents="850 3399"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1452(a,1),3399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1452 3399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      K(x,T(y \ 1,y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2650(a,1),3399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2650 3399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      K(x,y / (K(z \ 1,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3347(a,2),3399(a,1,2))].">
      <j1 rule="para" parents="3347 3399"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(666(a,2),3400(a,1,2))].">
      <j1 rule="para" parents="666 3400"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3337(a,2),3400(a,1,2))].">
      <j1 rule="para" parents="3337 3400"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(3154,a,3377,a)].">
      <j1 rule="hyper" parents="3154 3377"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      K((x \ 1) * y,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,3378,a)].">
      <j1 rule="hyper" parents="57 3378"/>
    </justification>
  </clause>

  <clause id="3412">
    <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(3411(a,1),3245(a,1,1))].">
      <j1 rule="para" parents="3411 3245"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2642,a,b,3382,a),flip(a)].">
      <j1 rule="hyper" parents="325 2642 3382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2630,a(flip),b,3414,a),flip(a)].">
      <j1 rule="hyper" parents="325 2630 3414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),3414(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 3414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = y * K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3416(a,1),2689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3416 2689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3394(a,2),3038(a,1))].">
      <j1 rule="para" parents="3394 3038"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2963,a(flip),b,3397,a)].">
      <j1 rule="hyper" parents="65 2963 3397"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(3397(a,1),3047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3397 3047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      T(x,K(y,z / (u \ 1))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(3397(a,1),3066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3397 3066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2532,a(flip),b,3422,a)].">
      <j1 rule="hyper" parents="65 2532 3422"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3111,a,b,3410,a),flip(a)].">
      <j1 rule="hyper" parents="325 3111 3410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(2619(a,1),3427(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2619 3427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(2488(a,1),3427(a,1,2,2))].">
      <j1 rule="para" parents="2488 3427"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      K(x,T(y,z * K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3109(a,1),3427(a,1,2,2))].">
      <j1 rule="para" parents="3109 3427"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2847(a,1),3431(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2847 3431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2959(a,2),3431(a,1,2,2))].">
      <j1 rule="para" parents="2959 3431"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(115(a,1),3433(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 3433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(1452(a,1),3372(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1452 3372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(312(a,1),3386(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="312 3386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(3236(a,1),3386(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3236 3386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T((x \ 1) * y,x),x)
    ]]></literal>
    <justification jstring="[para(683(a,1),3391(a,1,1,1))].">
      <j1 rule="para" parents="683 3391"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(683(a,1),3392(a,1,1,1))].">
      <j1 rule="para" parents="683 3392"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(1452(a,1),3392(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1452 3392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      K(x,y \ ((1 / z) \ u)) = K(x,y \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2814(a,1),3402(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2814 3402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(633(a,1),3403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="633 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      K(x,(y \ K(z \ 1,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(3227(a,1),3403(a,1,2,1))].">
      <j1 rule="para" parents="3227 3403"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(517(a,1),3407(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="517 3407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      K(x,((1 / (1 / y)) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(1386(a,1),3408(a,1,2,1))].">
      <j1 rule="para" parents="1386 3408"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / u) = K(x,((y \ 1) \ z) / u)
    ]]></literal>
    <justification jstring="[para(2927(a,1),3408(a,1,2,1))].">
      <j1 rule="para" parents="2927 3408"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(1060(a,1),3409(a,1,2,1))].">
      <j1 rule="para" parents="1060 3409"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3222(a,1),3409(a,1,2,1))].">
      <j1 rule="para" parents="3222 3409"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(3136(a,1),3423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3136 3423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      K(x,y / R(1 / z,u,w)) = K(x,y / R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(1060(a,1),3444(a,1,2,2))].">
      <j1 rule="para" parents="1060 3444"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3222(a,1),3444(a,1,2,2))].">
      <j1 rule="para" parents="3222 3444"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,903,a,b,3437,a)].">
      <j1 rule="hyper" parents="65 903 3437"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((x \ 1) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2305,a,b,3439,a)].">
      <j1 rule="hyper" parents="65 2305 3439"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      K(x,((y / (1 / z)) \ 1) \ u) = K(x,((y / (z \ 1)) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(3283(a,1),3443(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3283 3443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(3113(a,1),3450(a,1,2))].">
      <j1 rule="para" parents="3113 3450"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      (x / y) \ (((x / y) * z) * u) = (y \ x) \ (((y \ x) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,2810,a(flip),b,2570,a)].">
      <j1 rule="hyper" parents="132 2810 2570"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[para(2483(a,1),2813(a,1,2))].">
      <j1 rule="para" parents="2483 2813"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      ((x / y) * z) \ ((x / y) * u) = ((y \ x) * z) \ ((y \ x) * u)
    ]]></literal>
    <justification jstring="[para(2591(a,1),2813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2591 2813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(821(a,1),2868(a,1,1,2))].">
      <j1 rule="para" parents="821 2868"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1170(a,1),2868(a,1,1,2))].">
      <j1 rule="para" parents="1170 2868"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(3371(a,1),2908(a,1,2,1))].">
      <j1 rule="para" parents="3371 2908"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      ((x \ y) \ ((y \ x) \ (x \ y))) * (x \ y) = (y \ x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(215,a,2909,a),flip(a)].">
      <j1 rule="hyper" parents="215 2909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      (R(x,y,z) * u) * x = (x * u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2730,a(flip),b,3000,a),flip(a)].">
      <j1 rule="hyper" parents="65 2730 3000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      (R(x,y,z) * u) \ ((x * u) * R(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(3465(a,1),300(a,1,2))].">
      <j1 rule="para" parents="3465 300"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      (x / T(y,x)) * R(y,z,u) = y \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3360,a(flip),b,3055,a),flip(a)].">
      <j1 rule="hyper" parents="65 3360 3055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1752(a,1),3062(a,1,2,1))].">
      <j1 rule="para" parents="1752 3062"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3323(a,2,2,2,1))].">
      <j1 rule="para" parents="9 3323"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = K(x \ 1,x) * (R((x \ 1) \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3324(a,1),3225(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3324 3225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(3339(a,1),3409(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3339 3409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(3348(a,1),3403(a,1,2,1))].">
      <j1 rule="para" parents="3348 3403"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      K(x,R((y \ 1) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(82(a,1),3448(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 3448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(R(1 / y,z,u) * (w / R(1 / y,z,u))) * (R(1 / y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(869(a,1),3452(a,1,2)),flip(a)].">
      <j1 rule="para" parents="869 3452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(135,a,3463,a(flip),b,2652,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="135 3463 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(2287,a,3475,a)].">
      <j1 rule="hyper" parents="2287 3475"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,R(x,v6,v7)) = v5
    ]]></literal>
    <justification jstring="[para(2709(a,2),3063(a,1))].">
      <j1 rule="para" parents="2709 3063"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(478(a,2),2749(a,1,2))].">
      <j1 rule="para" parents="478 2749"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(135,a,2940,a(flip),b,265,a)].">
      <j1 rule="hyper" parents="135 2940 265"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(135,a,2941,a(flip),b,1216,a),flip(a)].">
      <j1 rule="hyper" parents="135 2941 1216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((w * z) * u)),v5,v6) = T(R(x,v5,v6),y / R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,2990,a)].">
      <j1 rule="hyper" parents="65 27 2990"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      K(x,T(y / z,y * u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(3002,a,3041,a)].">
      <j1 rule="hyper" parents="3002 3041"/>
    </justification>
  </clause>

  <clause id="3489">
    <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(325,a,3113,a(flip),b,3271,a),flip(a)].">
      <j1 rule="hyper" parents="325 3113 3271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2054(a,1),3420(a,1))].">
      <j1 rule="para" parents="2054 3420"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2994,a,3489,a)].">
      <j1 rule="hyper" parents="2994 3489"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),3493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 3493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3434,a(flip),b,3494,a)].">
      <j1 rule="hyper" parents="65 3434 3494"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),3495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(192(a,1),3495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="192 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3430,a,b,3498,a)].">
      <j1 rule="hyper" parents="65 3430 3498"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),3499(a,1,2)),flip(a)].">
      <j1 rule="para" parents="115 3499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      (x * ((y \ x) * y)) / x != z * K(y \ x,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ x) * y) = z
    ]]></literal>
    <justification jstring="[para(2578(a,1),46(a,1))].">
      <j1 rule="para" parents="2578 46"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(y,x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2252(a,1),2621(a,1,2))].">
      <j1 rule="para" parents="2252 2621"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * z) / (y * (K(u,x) * z))
    ]]></literal>
    <justification jstring="[hyper(145,a,2696,a),flip(a)].">
      <j1 rule="hyper" parents="145 2696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(2696(a,1),1541(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2696 1541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(2696(a,1),1865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2696 1865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      K(x,T(y,z * (K(u,x) * w))) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(2696(a,1),3429(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2696 3429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      a(x * (T(y,z) * u),w,v5) = a(x * (y * u),w,v5)
    ]]></literal>
    <justification jstring="[para(2114(a,1),3508(a,1,1,2))].">
      <j1 rule="para" parents="2114 3508"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      a(x * (y * z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(2472(a,1),3508(a,1,1,2))].">
      <j1 rule="para" parents="2472 3508"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(3109(a,1),3508(a,1,1,2))].">
      <j1 rule="para" parents="3109 3508"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      a((x * y) * z,u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(2363,a,3512,a)].">
      <j1 rule="hyper" parents="2363 3512"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      a(x * (y * x),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1843,a(flip),b,3512,a),flip(a)].">
      <j1 rule="hyper" parents="325 1843 3512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      a(x * (((y \ 1) * z) * y),u,w) = a(x * L(z,y \ 1,y),u,w)
    ]]></literal>
    <justification jstring="[para(261(a,1),3512(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="261 3512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      a(x * (y * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((z * y) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(3512(a,1),2363(a,1))].">
      <j1 rule="para" parents="3512 2363"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2363,a,3515,a)].">
      <j1 rule="hyper" parents="2363 3515"/>
    </justification>
  </clause>

  <clause id="3519">
    <literal><![CDATA[
      a(L(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((x * y) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3515(a,1),2363(a,1))].">
      <j1 rule="para" parents="3515 2363"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      a(L(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * (x * y),z,u) = w
    ]]></literal>
    <justification jstring="[para(3518(a,1),2363(a,1))].">
      <j1 rule="para" parents="3518 2363"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) = a(y * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,2337,a,b,3513,a),flip(a)].">
      <j1 rule="hyper" parents="325 2337 3513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      a(((x * x) * y) * z,u,w) = a(z * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1882,a(flip),b,3514,a),flip(a)].">
      <j1 rule="hyper" parents="325 1882 3514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      a(x * ((y * y) * z),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2243,a(flip),b,3514,a),flip(a)].">
      <j1 rule="hyper" parents="65 2243 3514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3524">
    <literal><![CDATA[
      a(x * (y * (z * (z * u))),w,v5) = a((L(u,z,z) * y) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,1845,a(flip),b,3514,a),flip(a)].">
      <j1 rule="hyper" parents="65 1845 3514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * y,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(3521(a,2),2363(a,1))].">
      <j1 rule="para" parents="3521 2363"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      a(x * ((1 / y) \ z),u,w) = a((z / y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2420,a(flip),b,3523,a)].">
      <j1 rule="hyper" parents="65 2420 3523"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      a(x * ((1 / y) \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ z) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(3526(a,2),2812(a,1))].">
      <j1 rule="para" parents="3526 2812"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      a(x * (y / z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (z \ y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(1588(a,1),3525(a,1,1,2))].">
      <j1 rule="para" parents="1588 3525"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2026,a(flip),b,2794,a),flip(a)].">
      <j1 rule="hyper" parents="65 2026 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(85(a,1),3531(a,1,1))].">
      <j1 rule="para" parents="85 3531"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(920(a,1),3532(a,1,2))].">
      <j1 rule="para" parents="920 3532"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(85(a,1),2892(a,1,1,1,2,1))].">
      <j1 rule="para" parents="85 2892"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      (x * (y * T(T(y,z),z))) / u = x / (u / (y * T(T(y,z),z)))
    ]]></literal>
    <justification jstring="[para(2880(a,1),2893(a,2,2,2))].">
      <j1 rule="para" parents="2880 2893"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,422,a(flip),b,2955,a),flip(a)].">
      <j1 rule="hyper" parents="137 422 2955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[hyper(3262,a,2311,a),flip(a)].">
      <j1 rule="hyper" parents="3262 2311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3436,a(flip),b,3538,a),flip(a)].">
      <j1 rule="hyper" parents="325 3436 3538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3538(a,2,1,1))].">
      <j1 rule="para" parents="10 3538"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(85(a,1),3538(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="85 3538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(102(a,2),3538(a,2,1))].">
      <j1 rule="para" parents="102 3538"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1428(a,2),3542(a,2,1))].">
      <j1 rule="para" parents="1428 3542"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(104(a,2),3541(a,1,1))].">
      <j1 rule="para" parents="104 3541"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3545(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(3545(a,1),2608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3545 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3548">
    <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(3545(a,1),3303(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3545 3303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(18(a,2),3313(a,2,1))].">
      <j1 rule="para" parents="18 3313"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      K(x,((((y \ 1) * (R((y \ 1) \ 1,z,u) \ 1)) / (1 / y)) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(3324(a,1),3456(a,2,2,1,1))].">
      <j1 rule="para" parents="3324 3456"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      x \ ((x * x) * (((1 / x) * y) * z)) = (x \ 1) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,652,a,b,3458,a)].">
      <j1 rule="hyper" parents="65 652 3458"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) * x) \ ((L(x,y,z) \ 1) * u) = (L(x,y,z) \ x) \ ((1 / L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1780(a,1),3460(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1780 3460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(3483(a,1),2274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3483 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,1228,a(flip),b,3484,a)].">
      <j1 rule="hyper" parents="65 1228 3484"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      (x * y) \ (y * (x * T(K(x,y),z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,2826,a(flip),b,3504,a),flip(a)].">
      <j1 rule="hyper" parents="325 2826 3504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      (x * y) \ (y * T(x,T(y,z))) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(3128(a,1),3556(a,1,2,2))].">
      <j1 rule="para" parents="3128 3556"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      (x * y) \ T(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(2904(a,2),3557(a,1,2))].">
      <j1 rule="para" parents="2904 3557"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2109,a,3558,a)].">
      <j1 rule="hyper" parents="2109 3558"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(3316,a,3559,a)].">
      <j1 rule="hyper" parents="3316 3559"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      K(x,K(y,z / y)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),3559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 3559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(3559(a,1),3316(a,1))].">
      <j1 rule="para" parents="3559 3316"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2836,a,3560,a)].">
      <j1 rule="hyper" parents="2836 3560"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3559,a(flip),b,3560,a),flip(a)].">
      <j1 rule="hyper" parents="325 3559 3560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,3278,a(flip),b,3560,a),flip(a)].">
      <j1 rule="hyper" parents="325 3278 3560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,3560,a,b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 3560 2104"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,z)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,3560,a,b,16,a(flip))].">
      <j1 rule="hyper" parents="137 3560 16"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(136,a,3560,a,b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 3560 2117"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3560(a,1),2827(a,1,2))].">
      <j1 rule="para" parents="3560 2827"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,K(x,y)) = 1
    ]]></literal>
    <justification jstring="[para(3560(a,1),2833(a,1,1))].">
      <j1 rule="para" parents="3560 2833"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3560(a,1),3115(a,1,2))].">
      <j1 rule="para" parents="3560 3115"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(3560(a,1),3214(a,1,1))].">
      <j1 rule="para" parents="3560 3214"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(3563(a,1),2624(a,2,1))].">
      <j1 rule="para" parents="3563 2624"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      K(x,K(y,z / y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3560,a,b,3561,a),flip(a)].">
      <j1 rule="hyper" parents="325 3560 3561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3575">
    <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(89(a,1),3564(a,1,2,2))].">
      <j1 rule="para" parents="89 3564"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3560,a,b,3565,a),flip(a)].">
      <j1 rule="hyper" parents="325 3560 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      T(x,K(y,y * z)) = K(z,K(y,x)) * x
    ]]></literal>
    <justification jstring="[para(3277(a,1),3568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3277 3568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(2628,a,3570,a)].">
      <j1 rule="hyper" parents="2628 3570"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,2833,a,b,3570,a)].">
      <j1 rule="hyper" parents="36 2833 3570"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3560,a,b,3579,a),flip(a)].">
      <j1 rule="hyper" parents="325 3560 3579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3563,a(flip),b,3579,a),flip(a)].">
      <j1 rule="hyper" parents="65 3563 3579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,3579,a(flip),b,2830,a)].">
      <j1 rule="hyper" parents="137 3579 2830"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(3579(a,1),2832(a,1,1))].">
      <j1 rule="para" parents="3579 2832"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(3579(a,1),2837(a,1))].">
      <j1 rule="para" parents="3579 2837"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(3279,a,3580,a),flip(a)].">
      <j1 rule="hyper" parents="3279 3580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,3565,a,b,3580,a)].">
      <j1 rule="hyper" parents="325 3565 3580"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3563,a,b,3580,a)].">
      <j1 rule="hyper" parents="325 3563 3580"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      R(x,T(y,x),T(K(z,K(u,w)),y * x)) \ ((K(u,K(z,w)) * y) * x) = T(y,x) * T(K(u,K(z,w)),y * x)
    ]]></literal>
    <justification jstring="[para(3580(a,1),1481(a,1,1,3,1))].">
      <j1 rule="para" parents="3580 1481"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(3580(a,1),2196(a,1,1))].">
      <j1 rule="para" parents="3580 2196"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3580(a,1),3568(a,1,1))].">
      <j1 rule="para" parents="3580 3568"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3580,a,b,3581,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 3581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3563,a(flip),b,3581,a)].">
      <j1 rule="hyper" parents="65 3563 3581"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(3581(a,1),2837(a,1))].">
      <j1 rule="para" parents="3581 2837"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(3582(a,2),2127(a,1,1))].">
      <j1 rule="para" parents="3582 2127"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(3113(a,1),3582(a,1,2))].">
      <j1 rule="para" parents="3113 3582"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(3582(a,2),3114(a,1,1))].">
      <j1 rule="para" parents="3582 3114"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3582(a,1),3115(a,1,2))].">
      <j1 rule="para" parents="3582 3115"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3582(a,2),3115(a,1,2))].">
      <j1 rule="para" parents="3582 3115"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      x * K(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3582(a,1),3566(a,1,2))].">
      <j1 rule="para" parents="3582 3566"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,3588,a(flip),b,2484,a(flip))].">
      <j1 rule="hyper" parents="136 3588 2484"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(3588(a,1),2837(a,1))].">
      <j1 rule="para" parents="3588 2837"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,3593,a(flip),b,2661,a),flip(a)].">
      <j1 rule="hyper" parents="136 3593 2661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(3593(a,1),2837(a,1))].">
      <j1 rule="para" parents="3593 2837"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(3259,a,3594,a)].">
      <j1 rule="hyper" parents="3259 3594"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3423,a(flip),b,3594,a),flip(a)].">
      <j1 rule="hyper" parents="325 3423 3594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(2759(a,1),3574(a,1,2))].">
      <j1 rule="para" parents="2759 3574"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      T(x,K(y,z * x)) = x * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(3564(a,1),3583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3564 3583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) * K(y,z) = T(T(y,z),K(x,u)) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,3584,a(flip),b,2082,a),flip(a)].">
      <j1 rule="hyper" parents="135 3584 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3580,a,b,3586,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 3586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3582,a,b,3587,a)].">
      <j1 rule="hyper" parents="65 3582 3587"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3580,a,b,3587,a)].">
      <j1 rule="hyper" parents="65 3580 3587"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3568,a(flip),b,3592,a)].">
      <j1 rule="hyper" parents="65 3568 3592"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(2845,a,3617,a),flip(a)].">
      <j1 rule="hyper" parents="2845 3617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2840,a,3617,a)].">
      <j1 rule="hyper" parents="2840 3617"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(2686,a,3617,a)].">
      <j1 rule="hyper" parents="2686 3617"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      R(T(x,K(y,z) * u),K(y,z),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,1954,a,b,3617,a)].">
      <j1 rule="hyper" parents="325 1954 3617"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,3617,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="137 3617 22"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,u),K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(3617(a,1),387(a,1,1))].">
      <j1 rule="para" parents="3617 387"/>
    </justification>
  </clause>

  <clause id="3625">
    <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(3617(a,1),387(a,1))].">
      <j1 rule="para" parents="3617 387"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(3617(a,1),2839(a,1,1))].">
      <j1 rule="para" parents="3617 2839"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(275,a,3619,a)].">
      <j1 rule="hyper" parents="275 3619"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,3619,a(flip),b,2704,a)].">
      <j1 rule="hyper" parents="137 3619 2704"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(3619(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="3619 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(3619(a,1),2840(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3619 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      K(x,K(x \ y,T(z,y))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(2517(a,1),3615(a,2,2))].">
      <j1 rule="para" parents="2517 3615"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(245,a,3629,a,b,xx)].">
      <j1 rule="hyper" parents="245 3629"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(37,a,3163,a,b,3629,a),flip(a)].">
      <j1 rule="hyper" parents="37 3163 3629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      T(K(x \ y,z),y) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,2225,a,b,3629,a),flip(a)].">
      <j1 rule="hyper" parents="37 2225 3629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,3106,a(flip),b,3629,a),flip(a)].">
      <j1 rule="hyper" parents="37 3106 3629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(2223(a,1),3629(a,1,1))].">
      <j1 rule="para" parents="2223 3629"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[para(3069(a,2),3629(a,1,1))].">
      <j1 rule="para" parents="3069 3629"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(3111(a,2),3629(a,1,1))].">
      <j1 rule="para" parents="3111 3629"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      K(x,y \ z) * z = z * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(3124(a,1),3629(a,1,1))].">
      <j1 rule="para" parents="3124 3629"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3218,a,3634,a)].">
      <j1 rule="hyper" parents="3218 3634"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      T(K(T(x,y) \ 1,z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,2288,a(flip),b,3634,a),flip(a)].">
      <j1 rule="hyper" parents="42 2288 3634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(3263,a,3637,a)].">
      <j1 rule="hyper" parents="3263 3637"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(3070,a,3637,a)].">
      <j1 rule="hyper" parents="3070 3637"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,y)) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(2289,a,3637,a)].">
      <j1 rule="hyper" parents="2289 3637"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(275,a,3637,a)].">
      <j1 rule="hyper" parents="275 3637"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(3637(a,1),3128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3637 3128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(3257,a,3642,a)].">
      <j1 rule="hyper" parents="3257 3642"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(3194,a,3642,a),flip(a)].">
      <j1 rule="hyper" parents="3194 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,3143,a,b,3642,a)].">
      <j1 rule="hyper" parents="65 3143 3642"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(235(a,1),3642(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="235 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,3645,a,b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 3645 2104"/>
    </justification>
  </clause>

  <clause id="3654">
    <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),3645(a,1,2))].">
      <j1 rule="para" parents="25 3645"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(235(a,1),3645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="235 3645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(1589(a,1),3645(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1589 3645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(1589(a,1),3645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1589 3645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(2716(a,1),3645(a,1,2))].">
      <j1 rule="para" parents="2716 3645"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      x / K(x / y,z) = K(y \ x,z) \ x
    ]]></literal>
    <justification jstring="[hyper(201,a,3636,a(flip),b,677,a)].">
      <j1 rule="hyper" parents="201 3636 677"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(3636(a,1),302(a,1,2,2))].">
      <j1 rule="para" parents="3636 302"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      K(K(x,y) * z,u) * z = z * K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(3104(a,1),3639(a,1,1))].">
      <j1 rule="para" parents="3104 3639"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(37,a,3282,a,b,3640,a),flip(a)].">
      <j1 rule="hyper" parents="37 3282 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = (z * K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,3640,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 3640 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(3640(a,1),591(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3640 591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(3039,a,3644,a)].">
      <j1 rule="hyper" parents="3039 3644"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      K(x / y,z) * (y \ x) = T(y \ x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(136,a,3644,a(flip),b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 3644 2117"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3647(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3647 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) / x = L(K(y,T(z,x)),u,w)
    ]]></literal>
    <justification jstring="[para(3647(a,1),784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3647 784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(3647(a,1),785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3647 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,3648,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 3648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3648(a,2),2140(a,1))].">
      <j1 rule="para" parents="3648 2140"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,3671,a(flip),b,3220,a),flip(a)].">
      <j1 rule="hyper" parents="137 3671 3220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(115(a,1),3671(a,1,2,1))].">
      <j1 rule="para" parents="115 3671"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(235(a,1),3671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="235 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(251(a,1),3671(a,1,2,1))].">
      <j1 rule="para" parents="251 3671"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1589(a,1),3671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1589 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      T(x,T(y * K(z,y),u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(1592(a,1),3671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1592 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(3671(a,1),3273(a,2,2))].">
      <j1 rule="para" parents="3671 3273"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(2384,a,3649,a)].">
      <j1 rule="hyper" parents="2384 3649"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(14(a,2),3649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      K(L((x \ y) / z,z,x),u) = K((x * z) \ y,T(u,z))
    ]]></literal>
    <justification jstring="[para(795(a,2),3650(a,1,1))].">
      <j1 rule="para" parents="795 3650"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3650(a,1),3194(a,1))].">
      <j1 rule="para" parents="3650 3194"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(3037,a,3652,a)].">
      <j1 rule="hyper" parents="3037 3652"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,T(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(89(a,1),3652(a,1,2,1))].">
      <j1 rule="para" parents="89 3652"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2065(a,1),3653(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2065 3653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2477,a,b,3655,a)].">
      <j1 rule="hyper" parents="65 2477 3655"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(2407(a,1),3675(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2407 3675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      K(x / y,x / (x / z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3121,a(flip),b,3684,a),flip(a)].">
      <j1 rule="hyper" parents="325 3121 3684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(3684(a,2),3167(a,1))].">
      <j1 rule="para" parents="3684 3167"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      K(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3565(a,2),3562(a,1))].">
      <j1 rule="para" parents="3565 3562"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(3588(a,2),3562(a,1))].">
      <j1 rule="para" parents="3588 3562"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,R(y,v6,v7))) = v5
    ]]></literal>
    <justification jstring="[para(2995(a,2),3605(a,1,2))].">
      <j1 rule="para" parents="2995 3605"/>
    </justification>
  </clause>

  <clause id="3695">
    <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(3113(a,1),3605(a,1,2))].">
      <j1 rule="para" parents="3113 3605"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      K(x,K(y / z,T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z \ y)) = w
    ]]></literal>
    <justification jstring="[para(3145(a,2),3605(a,1,2))].">
      <j1 rule="para" parents="3145 3605"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(3416(a,2),3605(a,1,2))].">
      <j1 rule="para" parents="3416 3605"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(3564(a,2),3605(a,1))].">
      <j1 rule="para" parents="3564 3605"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(3069(a,2),3668(a,1))].">
      <j1 rule="para" parents="3069 3668"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(115(a,1),3683(a,1,2,1))].">
      <j1 rule="para" parents="115 3683"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3145(a,1),3683(a,1))].">
      <j1 rule="para" parents="3145 3683"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3149(a,1),3683(a,1))].">
      <j1 rule="para" parents="3149 3683"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(3143(a,2),3683(a,1))].">
      <j1 rule="para" parents="3143 3683"/>
    </justification>
  </clause>

  <clause id="3704">
    <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),3699(a,1,2))].">
      <j1 rule="para" parents="23 3699"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      K(T(x,y),L(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),3699(a,1,2))].">
      <j1 rule="para" parents="25 3699"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3569(a,2),3154(a,1))].">
      <j1 rule="para" parents="3569 3154"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,3497,a,b,3571,a)].">
      <j1 rule="hyper" parents="325 3497 3571"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,3571,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 3571 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3571(a,1),45(a,1))].">
      <j1 rule="para" parents="3571 45"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3592,a(flip),b,3578,a),flip(a)].">
      <j1 rule="hyper" parents="325 3592 3578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3568,a(flip),b,3578,a),flip(a)].">
      <j1 rule="hyper" parents="325 3568 3578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),3712(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 3712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,z)))
    ]]></literal>
    <justification jstring="[hyper(3595,a,3597,a)].">
      <j1 rule="hyper" parents="3595 3597"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(3190(a,1),3597(a,2,2))].">
      <j1 rule="para" parents="3190 3597"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2857,a,3598,a)].">
      <j1 rule="hyper" parents="2857 3598"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x * y,x) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(3614(a,1),3598(a,1,1))].">
      <j1 rule="para" parents="3614 3598"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(u,z \ y)) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(3146(a,1),3599(a,1,2,2))].">
      <j1 rule="para" parents="3146 3599"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      K(x * y,x) * K(x,K(y,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(3614(a,1),3600(a,1,2))].">
      <j1 rule="para" parents="3614 3600"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3583,a(flip),b,3612,a),flip(a)].">
      <j1 rule="hyper" parents="325 3583 3612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),3721(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 3721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3617,a,b,3723,a),flip(a)].">
      <j1 rule="hyper" parents="325 3617 3723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3424,a(flip),b,3723,a)].">
      <j1 rule="hyper" parents="65 3424 3723"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      K(x,y) * (z / K(x,y)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),3618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 3618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * u) = (z * K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,3623,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 3623 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      K(x * y,z) * T(y,K(z,x)) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3721(a,1),3623(a,1,2))].">
      <j1 rule="para" parents="3721 3623"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(3721(a,1),3626(a,1,1))].">
      <j1 rule="para" parents="3721 3626"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(42,a,3361,a,b,3643,a),flip(a)].">
      <j1 rule="hyper" parents="42 3361 3643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(383,a,3646,a)].">
      <j1 rule="hyper" parents="383 3646"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z
    ]]></literal>
    <justification jstring="[para(3646(a,1),1449(a,1,2,1))].">
      <j1 rule="para" parents="3646 1449"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,y \ x))
    ]]></literal>
    <justification jstring="[para(2716(a,1),3646(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2716 3646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3673(a,2),2299(a,1))].">
      <j1 rule="para" parents="3673 2299"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * y) = z * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(3150,a,3679,a)].">
      <j1 rule="hyper" parents="3150 3679"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,3679,a)].">
      <j1 rule="hyper" parents="145 3679"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(135,a,3679,a(flip),b,2185,a(flip))].">
      <j1 rule="hyper" parents="135 3679 2185"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2281,a,b,3680,a),flip(a)].">
      <j1 rule="hyper" parents="325 2281 3680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(3689(a,1),3574(a,1,2))].">
      <j1 rule="para" parents="3689 3574"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,3616,a(flip),b,3714,a),flip(a)].">
      <j1 rule="hyper" parents="65 3616 3714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(3716(a,1),2862(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3716 2862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      L(x \ (y / K(z,u)),x,K(z,u)) = (K(z,u) * x) \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3726(a,1),102(a,2,2))].">
      <j1 rule="para" parents="3726 102"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = K(T(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(2562(a,2),3730(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2562 3730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,262,a(flip),b,3731,a),flip(a)].">
      <j1 rule="hyper" parents="325 262 3731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(3605,a,3740,a),flip(a)].">
      <j1 rule="hyper" parents="3605 3740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,2854,a,b,3746,a)].">
      <j1 rule="hyper" parents="37 2854 3746"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2515(a,1),3748(a,1,2))].">
      <j1 rule="para" parents="2515 3748"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3576,a(flip),b,3747,a),flip(a)].">
      <j1 rule="hyper" parents="325 3576 3747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),3752(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 3752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(3605,a,3753,a)].">
      <j1 rule="hyper" parents="3605 3753"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3594,a,b,3754,a),flip(a)].">
      <j1 rule="hyper" parents="325 3594 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3610,a,b,3754,a)].">
      <j1 rule="hyper" parents="65 3610 3754"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3610,a,b,3755,a)].">
      <j1 rule="hyper" parents="65 3610 3755"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(3605,a,3756,a)].">
      <j1 rule="hyper" parents="3605 3756"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3580,a,b,3756,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2054(a,1),3756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2054 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(2744(a,1),3756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2744 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3756(a,2),3605(a,1))].">
      <j1 rule="para" parents="3756 3605"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(3603,a,3757,a)].">
      <j1 rule="hyper" parents="3603 3757"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(3595,a,3757,a)].">
      <j1 rule="hyper" parents="3595 3757"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,3757,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 3757 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(3757(a,1),3569(a,1,2))].">
      <j1 rule="para" parents="3757 3569"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3580,a,b,3758,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 3758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,3758,a(flip),b,2489,a(flip))].">
      <j1 rule="hyper" parents="132 3758 2489"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(2304(a,2),3758(a,1,2))].">
      <j1 rule="para" parents="2304 3758"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(3758(a,2),3605(a,1))].">
      <j1 rule="para" parents="3758 3605"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(3603,a,3759,a)].">
      <j1 rule="hyper" parents="3603 3759"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3760(a,2),3605(a,1))].">
      <j1 rule="para" parents="3760 3605"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      L(K(x \ 1,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,2307,a,b,3763,a)].">
      <j1 rule="hyper" parents="65 2307 3763"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(3476(a,1),3764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3476 3764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      T(1 / x,y) \ (1 / x) = x \ (T(1 / x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(410,a,3750,a),flip(a)].">
      <j1 rule="hyper" parents="410 3750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3615,a(flip),b,3761,a),flip(a)].">
      <j1 rule="hyper" parents="65 3615 3761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(3761(a,1),3605(a,1))].">
      <j1 rule="para" parents="3761 3605"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = x * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,3776,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 3776 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(85(a,1),3776(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="85 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      K(x,K(x / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3779(a,2),3605(a,1))].">
      <j1 rule="para" parents="3779 3605"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,3765,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 3765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(3631,a,3782,a)].">
      <j1 rule="hyper" parents="3631 3782"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,3782,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 3782 22"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3601,a(flip),b,3778,a),flip(a)].">
      <j1 rule="hyper" parents="325 3601 3778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = K(y,z \ x) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,3787,a(flip),b,3628,a)].">
      <j1 rule="hyper" parents="136 3787 3628"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(3658(a,2),3690(a,1))].">
      <j1 rule="para" parents="3658 3690"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      K(T(x,y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / T(x,y),x) = u
    ]]></literal>
    <justification jstring="[para(185(a,1),3701(a,1,2))].">
      <j1 rule="para" parents="185 3701"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(u / L(x,y,z),x) = w
    ]]></literal>
    <justification jstring="[para(184(a,1),3701(a,1,2))].">
      <j1 rule="para" parents="184 3701"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3113(a,2),3701(a,1))].">
      <j1 rule="para" parents="3113 3701"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * K(y \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(2842(a,1),3702(a,1,2))].">
      <j1 rule="para" parents="2842 3702"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(2755(a,1),3762(a,1,2))].">
      <j1 rule="para" parents="2755 3762"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      K(x / y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3580(a,1),3781(a,1))].">
      <j1 rule="para" parents="3580 3781"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(2559(a,1),3792(a,1,1))].">
      <j1 rule="para" parents="2559 3792"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * K(x \ y,x)) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[para(3633(a,1),3602(a,1,1))].">
      <j1 rule="para" parents="3633 3602"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3594,a,b,3607,a),flip(a)].">
      <j1 rule="hyper" parents="325 3594 3607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      L(K(T(x,y),T(z,y)),u,w) = K(L(x,u / T(x,y),w),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3545,a(flip),b,3651,a)].">
      <j1 rule="hyper" parents="65 3545 3651"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      K(T(x,L(x,y,z) * u),T(w,u)) = K(L(x,u,L(x,y,z)),w)
    ]]></literal>
    <justification jstring="[para(1276(a,1),3651(a,1,1))].">
      <j1 rule="para" parents="1276 3651"/>
    </justification>
  </clause>

  <clause id="3802">
    <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(1276(a,1),3654(a,1,2))].">
      <j1 rule="para" parents="1276 3654"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,y)) = x * K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,3663,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 3663 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[para(3666(a,1),3106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3666 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      K(1 / R(x \ 1,y,z),u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1))
    ]]></literal>
    <justification jstring="[para(3292(a,2),3667(a,1,2))].">
      <j1 rule="para" parents="3292 3667"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      T(x,T(y * K(z,y),u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),3678(a,2,2))].">
      <j1 rule="para" parents="23 3678"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(3715(a,2),3585(a,1))].">
      <j1 rule="para" parents="3715 3585"/>
    </justification>
  </clause>

  <clause id="3808">
    <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(3725(a,1),2639(a,1,1))].">
      <j1 rule="para" parents="3725 2639"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[para(85(a,1),3738(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="85 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(796(a,1),3745(a,1,1,1))].">
      <j1 rule="para" parents="796 3745"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3571,a(flip),b,3766,a),flip(a)].">
      <j1 rule="hyper" parents="65 3571 3766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3154,a,3811,a)].">
      <j1 rule="hyper" parents="3154 3811"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      K(T(x,y \ 1),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(3070,a,3811,a)].">
      <j1 rule="hyper" parents="3070 3811"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(3014,a,3811,a),flip(a)].">
      <j1 rule="hyper" parents="3014 3811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3811(a,1),3128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3811 3128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(3247,a,3812,a)].">
      <j1 rule="hyper" parents="3247 3812"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3201,a(flip),b,3812,a)].">
      <j1 rule="hyper" parents="65 3201 3812"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(2763(a,1),3812(a,1,2))].">
      <j1 rule="para" parents="2763 3812"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      K(x,T(y / R(z \ 1,u,w),z)) = K(x,R(z \ 1,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(2976(a,1),3812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2976 3812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(3132,a,3814,a)].">
      <j1 rule="hyper" parents="3132 3814"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3814(a,2),3154(a,1))].">
      <j1 rule="para" parents="3814 3154"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,3815,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3815(a,2),2140(a,1))].">
      <j1 rule="para" parents="3815 2140"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(3258,a,3822,a),flip(a)].">
      <j1 rule="hyper" parents="3258 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(183(a,1),3817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="183 3817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3818(a,1),3206(a,1))].">
      <j1 rule="para" parents="3818 3206"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      T(x * L(L(y,z,u),w,v5),T(y,x)) = T(x * L(L(y,z,u),w,v5),y)
    ]]></literal>
    <justification jstring="[para(219(a,1),3824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="219 3824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(2763(a,1),3821(a,1,2))].">
      <j1 rule="para" parents="2763 3821"/>
    </justification>
  </clause>

  <clause id="3829">
    <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(3329(a,1),3821(a,1,2))].">
      <j1 rule="para" parents="3329 3821"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      T(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(3355(a,1),3823(a,1))].">
      <j1 rule="para" parents="3355 3823"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      T(x,T(T(T(y,z),z),u)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(1583(a,1),3806(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1583 3806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2288,a,b,3820,a),flip(a)].">
      <j1 rule="hyper" parents="325 2288 3820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3833">
    <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(3741(a,2),3695(a,1))].">
      <j1 rule="para" parents="3741 3695"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(3795,a,3423,a)].">
      <j1 rule="hyper" parents="3795 3423"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),3834(a,2,2,2))].">
      <j1 rule="para" parents="12 3834"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(3585,a,3835,a)].">
      <j1 rule="hyper" parents="3585 3835"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,2298,a,b,3572,a),flip(a)].">
      <j1 rule="hyper" parents="36 2298 3572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(3615(a,1),3572(a,1,1))].">
      <j1 rule="para" parents="3615 3572"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(2299,a,3838,a)].">
      <j1 rule="hyper" parents="2299 3838"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3099,a(flip),b,3838,a)].">
      <j1 rule="hyper" parents="65 3099 3838"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3624,a,3841,a)].">
      <j1 rule="hyper" parents="3624 3841"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(387,a,3841,a)].">
      <j1 rule="hyper" parents="387 3841"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1592,a(flip),b,3841,a),flip(a)].">
      <j1 rule="hyper" parents="65 1592 3841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,274,a(flip),b,3841,a),flip(a)].">
      <j1 rule="hyper" parents="65 274 3841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(3617(a,1),3841(a,1,1))].">
      <j1 rule="para" parents="3617 3841"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ 1) = T(x,T(z \ 1,y))
    ]]></literal>
    <justification jstring="[para(3784(a,1),3841(a,1,1))].">
      <j1 rule="para" parents="3784 3841"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3630,a,3842,a)].">
      <j1 rule="hyper" parents="3630 3842"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3842(a,1),2839(a,1,1))].">
      <j1 rule="para" parents="3842 2839"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      K(T(x,T(y,z)),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3842(a,1),3093(a,1,1))].">
      <j1 rule="para" parents="3842 3093"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      T((x \ y) * (x * x),K(x,z)) = T(y / (x \ 1),T(x,z))
    ]]></literal>
    <justification jstring="[para(595(a,1),3843(a,1,1))].">
      <j1 rule="para" parents="595 3843"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      K(x,T(y,T(z,L(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3843(a,1),3148(a,1,2))].">
      <j1 rule="para" parents="3843 3148"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(3711(a,1),3846(a,1,1))].">
      <j1 rule="para" parents="3711 3846"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3848(a,1),2840(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3848 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(3330(a,1),3850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3330 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(3560(a,1),3840(a,1,1))].">
      <j1 rule="para" parents="3560 3840"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,3845,a(flip),b,2906,a),flip(a)].">
      <j1 rule="hyper" parents="136 3845 2906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(136,a,3856,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 3856 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,L(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(115(a,1),3852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 3852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y \ z) \ 1) = T(x,T((y \ z) \ 1,y))
    ]]></literal>
    <justification jstring="[para(3713(a,1),3847(a,1,1))].">
      <j1 rule="para" parents="3713 3847"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3674(a,1),3849(a,1,1))].">
      <j1 rule="para" parents="3674 3849"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(37,a,3224,a,b,3662,a)].">
      <j1 rule="hyper" parents="37 3224 3662"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3268,a,b,3686,a)].">
      <j1 rule="hyper" parents="65 3268 3686"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x * T(y,u),x) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[para(3113(a,1),3717(a,1,1,2))].">
      <j1 rule="para" parents="3113 3717"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      K(x * y,z) * T(y,K(x,z)) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3617(a,1),3728(a,1,2))].">
      <j1 rule="para" parents="3617 3728"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3809,a(flip),b,3733,a),flip(a)].">
      <j1 rule="hyper" parents="65 3809 3733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(3763(a,1),3773(a,1,1))].">
      <j1 rule="para" parents="3763 3773"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(3771(a,1),3773(a,1,1))].">
      <j1 rule="para" parents="3771 3773"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(137,a,3869,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 3869 18"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,3869,a(flip),b,3870,a),flip(a)].">
      <j1 rule="hyper" parents="65 3869 3870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w))) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(3772,a,3872,a),flip(a)].">
      <j1 rule="hyper" parents="3772 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3874">
    <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(3872(a,2),3585(a,1))].">
      <j1 rule="para" parents="3872 3585"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      T(1 / x,y) \ 1 = x * K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,2526,a(flip),b,3775,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 2526 3775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      1 / T(x \ 1,y) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,2875,a,b,3875,a)].">
      <j1 rule="hyper" parents="325 2875 3875"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(195,a,3876,a)].">
      <j1 rule="hyper" parents="195 3876"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),3877(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 3877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,640,a,b,3878,a)].">
      <j1 rule="hyper" parents="65 640 3878"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      K(x,T((y \ 1) \ 1,z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3878(a,2),3404(a,1,2,1))].">
      <j1 rule="para" parents="3878 3404"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      (x * T(y,z)) / T(T(y,y \ 1),z) = x * K(T(y,z) \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[para(3879(a,2),1213(a,1,2))].">
      <j1 rule="para" parents="3879 1213"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = x * K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3641,a(flip),b,3788,a),flip(a)].">
      <j1 rule="hyper" parents="325 3641 3788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,y)) = T(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,3803,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 3803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      T(x,((y * z) / y) \ 1) = T(x,T(z \ 1,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),3883(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2213,a(flip),b,3884,a),flip(a)].">
      <j1 rule="hyper" parents="325 2213 3884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[para(2562(a,1),3884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2562 3884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2787,a(flip),b,3885,a)].">
      <j1 rule="hyper" parents="65 2787 3885"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,2717,a,b,3887,a(flip))].">
      <j1 rule="hyper" parents="42 2717 3887"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,2983,a,b,3888,a)].">
      <j1 rule="hyper" parents="65 2983 3888"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(3889(a,1),237(a,1,2,2))].">
      <j1 rule="para" parents="3889 237"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(3332,a,3886,a),flip(a)].">
      <j1 rule="hyper" parents="3332 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      T(x,x \ K(x,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2160,a(flip),b,3886,a),flip(a)].">
      <j1 rule="hyper" parents="65 2160 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y))
    ]]></literal>
    <justification jstring="[para(3892(a,1),241(a,1,2,1))].">
      <j1 rule="para" parents="3892 241"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2791,a(flip),b,3891,a)].">
      <j1 rule="hyper" parents="65 2791 3891"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(3825(a,1),1827(a,1,2))].">
      <j1 rule="para" parents="3825 1827"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2108,a,3864,a)].">
      <j1 rule="hyper" parents="2108 3864"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ (((x / (x * L(x \ 1,y,z))) * (x * L(x \ 1,y,z))) / x) = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(1800(a,2),3890(a,1,2))].">
      <j1 rule="para" parents="1800 3890"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(3709,a,3707,a)].">
      <j1 rule="hyper" parents="3709 3707"/>
    </justification>
  </clause>

  <clause id="3899">
    <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(3707(a,2),3706(a,1))].">
      <j1 rule="para" parents="3707 3706"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(109(a,1),3898(a,1,2,2))].">
      <j1 rule="para" parents="109 3898"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(485(a,1),3898(a,1,2,2,1))].">
      <j1 rule="para" parents="485 3898"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(3900(a,1),3598(a,1,1))].">
      <j1 rule="para" parents="3900 3598"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(485(a,1),3899(a,1,2,2,1))].">
      <j1 rule="para" parents="485 3899"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      K(x,K((y * x) / z,T(u,z))) = K(x,K(u,(z / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(3807,a,3048,a)].">
      <j1 rule="hyper" parents="3807 3048"/>
    </justification>
  </clause>

  <clause id="3905">
    <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(3869(a,2),3874(a,1))].">
      <j1 rule="para" parents="3869 3874"/>
    </justification>
  </clause>

  <clause id="3906">
    <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(3580(a,1),3905(a,1,1))].">
      <j1 rule="para" parents="3580 3905"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(1581(a,1),3687(a,1,1,1,2))].">
      <j1 rule="para" parents="1581 3687"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(37,a,3344,a(flip),b,3732,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 3344 3732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(1589(a,1),3908(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1589 3908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(2600(a,1),3909(a,1,1,2))].">
      <j1 rule="para" parents="2600 3909"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(137,a,3910,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 3910 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      K(L(x,y / T(x,z),u),w) = L(K(x,w),y,u)
    ]]></literal>
    <justification jstring="[para(3645(a,1),3800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3645 3800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(194(a,1),3912(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="194 3912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(268(a,1),3912(a,1,1,2))].">
      <j1 rule="para" parents="268 3912"/>
    </justification>
  </clause>

  <clause id="3916">
    <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(3645(a,1),3913(a,1,1))].">
      <j1 rule="para" parents="3645 3913"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,350,a(flip),b,3914,a),flip(a)].">
      <j1 rule="hyper" parents="325 350 3914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z)
    ]]></literal>
    <justification jstring="[hyper(3703,a,3917,a),flip(a)].">
      <j1 rule="hyper" parents="3703 3917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(3699,a,3918,a),flip(a)].">
      <j1 rule="hyper" parents="3699 3918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      K(L(x,x \ K(y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(2615(a,1),3919(a,1,1,2))].">
      <j1 rule="para" parents="2615 3919"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3914,a(flip),b,3921,a)].">
      <j1 rule="hyper" parents="65 3914 3921"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,3922,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 3922 18"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      (x * K(y,z)) * L(K(z,u),w,v5) = x * (K(y,z) * L(K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(3922(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="3922 412"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(489,a,3923,a)].">
      <j1 rule="hyper" parents="489 3923"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2468,a(flip),b,3923,a),flip(a)].">
      <j1 rule="hyper" parents="65 2468 3923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(3086(a,2),3923(a,2,2))].">
      <j1 rule="para" parents="3086 3923"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(1927(a,1),3926(a,1,2))].">
      <j1 rule="para" parents="1927 3926"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(2310(a,1),3926(a,1,2))].">
      <j1 rule="para" parents="2310 3926"/>
    </justification>
  </clause>

  <clause id="3932">
    <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(3930(a,1),506(a,1,1))].">
      <j1 rule="para" parents="3930 506"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,3895,a(flip),b,3927,a),flip(a)].">
      <j1 rule="hyper" parents="132 3895 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = y \ R(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,3301,a(flip),b,3927,a),flip(a)].">
      <j1 rule="hyper" parents="132 3301 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2852(a,1),3928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2852 3928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y \ z) \ 1) = T(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,3883,a(flip),b,3861,a),flip(a)].">
      <j1 rule="hyper" parents="325 3883 3861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y \ z) \ 1) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2787,a(flip),b,3936,a),flip(a)].">
      <j1 rule="hyper" parents="325 2787 3936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(2765,a,3937,a)].">
      <j1 rule="hyper" parents="2765 3937"/>
    </justification>
  </clause>

  <clause id="3939">
    <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(3405(a,1),3938(a,1,1,2))].">
      <j1 rule="para" parents="3405 3938"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(3619(a,1),3938(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3619 3938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(3624,a,3940,a)].">
      <j1 rule="hyper" parents="3624 3940"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(3743,a,3902,a),flip(a)].">
      <j1 rule="hyper" parents="3743 3902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),3942(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(3903,a,3943,a),flip(a)].">
      <j1 rule="hyper" parents="3903 3943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),3944(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 3944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ (u * x)))
    ]]></literal>
    <justification jstring="[hyper(3696,a,3904,a),flip(a)].">
      <j1 rule="hyper" parents="3696 3904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(147,a,3907,a)].">
      <j1 rule="hyper" parents="147 3907"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(3916(a,2),3703(a,1))].">
      <j1 rule="para" parents="3916 3703"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      L(K(x,y),x * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(112(a,1),3948(a,1,2,1))].">
      <j1 rule="para" parents="112 3948"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(201,a,3947,a(flip),b,2618,a)].">
      <j1 rule="hyper" parents="201 3947 2618"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(2286(a,1),3950(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2286 3950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(3106(a,1),3670(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3106 3670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(3704,a,3801,a),flip(a)].">
      <j1 rule="hyper" parents="3704 3801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(3089,a,3934,a)].">
      <j1 rule="hyper" parents="3089 3934"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(3934(a,1),3092(a,1,2))].">
      <j1 rule="para" parents="3934 3092"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * L(x,z,u),x) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3954(a,1),3095(a,1))].">
      <j1 rule="para" parents="3954 3095"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      K(x,y / ((y * (z \ u)) / u)) = (y * u) / (y * (K(z,x) * u))
    ]]></literal>
    <justification jstring="[hyper(3037,a,3505,a)].">
      <j1 rule="hyper" parents="3037 3505"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      (x * y) / (z * T(T(z,u),u)) = x * (y / (z * T(T(z,u),u)))
    ]]></literal>
    <justification jstring="[hyper(136,a,87,a(flip),b,3535,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 87 3535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(3554(a,2),2383(a,1))].">
      <j1 rule="para" parents="3554 2383"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3836,a(flip),b,3774,a),flip(a)].">
      <j1 rule="hyper" parents="65 3836 3774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / w) = T(y,K(x,z)) / w
    ]]></literal>
    <justification jstring="[para(3960(a,2),3596(a,1,1))].">
      <j1 rule="para" parents="3960 3596"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3208,a(flip),b,3893,a),flip(a)].">
      <j1 rule="hyper" parents="325 3208 3893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      x * (T(y,K(z,u)) / w) != y / w
    ]]></literal>
    <literal><![CDATA[
      K((T(y,u) / v5) / (y / v5),z) = x
    ]]></literal>
    <justification jstring="[para(3962(a,1),2675(a,1,2))].">
      <j1 rule="para" parents="3962 2675"/>
    </justification>
  </clause>

  <clause id="3965">
    <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(863(a,1),2890(a,1,1,2))].">
      <j1 rule="para" parents="863 2890"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2388,a(flip),b,2954,a),flip(a)].">
      <j1 rule="hyper" parents="65 2388 2954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(z,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,2388,a(flip),b,2954,a(flip))].">
      <j1 rule="hyper" parents="137 2388 2954"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,1581,a,b,3966,a)].">
      <j1 rule="hyper" parents="201 1581 3966"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      (x * K(y \ z,y)) * (z / y) = x * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(137,a,1588,a(flip),b,3966,a)].">
      <j1 rule="hyper" parents="137 1588 3966"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      ((x * K(y,z)) * L((x * K(y,z)) \ x,u,w)) * y = (x * K(y,z)) * (y * L(y \ (y * K(z,y)),u,w))
    ]]></literal>
    <justification jstring="[para(3966(a,1),1737(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3966 1737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      (x / y) * (y * K(y \ x,y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(1588(a,1),3967(a,1,1))].">
      <j1 rule="para" parents="1588 3967"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(2504(a,1),3967(a,1,1))].">
      <j1 rule="para" parents="2504 3967"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(2847(a,1),3967(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2847 3967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(1613,a,3973,a),flip(a)].">
      <j1 rule="hyper" parents="1613 3973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      T(x,y) * (T(z,x) * K(T(x,y),T(z,x))) = T(T(x,z),y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(2507(a,1),3973(a,2,1))].">
      <j1 rule="para" parents="2507 3973"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      R(1 / T(x,y),T(x,y),y) = y / (x * ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(201,a,3975,a(flip),b,365,a),flip(a)].">
      <j1 rule="hyper" parents="201 3975 365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      (T(x,y) * T(x,y)) * (y / (x * ((x * y) / x))) = R(T(x,y),T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3975(a,1),693(a,1,2,2))].">
      <j1 rule="para" parents="3975 693"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      R(T(x / y,y * ((y * z) / y)),y,(y * z) / y) = (T(y,z) * z) \ (x * ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(3975(a,2),825(a,2,1))].">
      <j1 rule="para" parents="3975 825"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      R(T(K(x,y),z) * z,u,w) = K(x,y) * R((K(x,y) * z) / K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(3975(a,2),1057(a,1,1))].">
      <j1 rule="para" parents="3975 1057"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(375,a,3969,a)].">
      <j1 rule="hyper" parents="375 3969"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1184,a(flip),b,3969,a)].">
      <j1 rule="hyper" parents="65 1184 3969"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      x \ (y * (x * K(z,x))) = T(y * K(z,x),x)
    ]]></literal>
    <justification jstring="[hyper(284,a,3974,a),flip(a)].">
      <j1 rule="hyper" parents="284 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * (z * K(y,z))) = z
    ]]></literal>
    <justification jstring="[hyper(140,a,3974,a)].">
      <j1 rule="hyper" parents="140 3974"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,1654,a,b,3974,a),flip(a)].">
      <j1 rule="hyper" parents="37 1654 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(325,a,2550,a(flip),b,3981,a),flip(a)].">
      <j1 rule="hyper" parents="325 2550 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      T(x,y) = (x / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2550,a(flip),b,3981,a),flip(a)].">
      <j1 rule="hyper" parents="136 2550 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,189,a(flip),b,3987,a),flip(a)].">
      <j1 rule="hyper" parents="38 189 3987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      (x / y) \ T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,3988,a,b,1586,a(flip))].">
      <j1 rule="hyper" parents="132 3988 1586"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      x \ T(x * y,y) = y * K(x * y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3991(a,1,1))].">
      <j1 rule="para" parents="11 3991"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      (x * ((y * z) / y)) * K(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(11(a,1),3982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      L(T(x,K(y,x)),K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(773,a,3985,a)].">
      <j1 rule="hyper" parents="773 3985"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[para(2456(a,1),3996(a,1,1))].">
      <j1 rule="para" parents="2456 3996"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      L(x,K(y,x),z) = u \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,9,a,b,3997,a),flip(a)].">
      <j1 rule="hyper" parents="325 9 3997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3997(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="3997 412"/>
    </justification>
  </clause>

  <clause id="4000">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(489,a,3986,a)].">
      <j1 rule="hyper" parents="489 3986"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(455,a,3986,a)].">
      <j1 rule="hyper" parents="455 3986"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,3986,a(flip),b,2087,a)].">
      <j1 rule="hyper" parents="136 3986 2087"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,3986,a(flip),b,89,a),flip(a)].">
      <j1 rule="hyper" parents="131 3986 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(1588(a,1),3986(a,2,2))].">
      <j1 rule="para" parents="1588 3986"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(3147(a,1),4003(a,1,3))].">
      <j1 rule="para" parents="3147 4003"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(3949,a,4001,a)].">
      <j1 rule="hyper" parents="3949 4001"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,((u * y) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2748,a,b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="325 2748 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      K(L(x,y / x,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3545,a,b,4001,a)].">
      <j1 rule="hyper" parents="65 3545 4001"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3546,a(flip),b,4001,a)].">
      <j1 rule="hyper" parents="65 3546 4001"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      L(L(K(x,y),z,u),y,w) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4001(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4001 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,4006,a)].">
      <j1 rule="hyper" parents="54 4006"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(u,y),w,v5) = x * (T(y,z) * L(K(u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(4012(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="4012 412"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[para(3992(a,2),2506(a,1,1))].">
      <j1 rule="para" parents="3992 2506"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(3992(a,2),3656(a,1,1))].">
      <j1 rule="para" parents="3992 3656"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ (x * z) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,3994,a)].">
      <j1 rule="hyper" parents="140 3994"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3994(a,1,1,2,1))].">
      <j1 rule="para" parents="10 3994"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      K(x,x \ T(x * y,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4014(a,1),3011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4014 3011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4008(a,1),216(a,1))].">
      <j1 rule="para" parents="4008 216"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(K(x,y),z,u),y,v5) = w
    ]]></literal>
    <justification jstring="[para(4011(a,1),1542(a,1))].">
      <j1 rule="para" parents="4011 1542"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4008(a,2),4023(a,1))].">
      <j1 rule="para" parents="4008 4023"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(3540(a,1),4025(a,1))].">
      <j1 rule="para" parents="3540 4025"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(2691(a,2),3972(a,1,2))].">
      <j1 rule="para" parents="2691 3972"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4027(a,1),1148(a,1,1))].">
      <j1 rule="para" parents="4027 1148"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      ((x \ T(y,x)) * T(x,y)) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(2644(a,1),4028(a,1,1,1))].">
      <j1 rule="para" parents="2644 4028"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      x \ (y * ((z * x) / z)) = T(y * K(z,x),x)
    ]]></literal>
    <justification jstring="[para(1581(a,2),3983(a,1,2,2))].">
      <j1 rule="para" parents="1581 3983"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = x * R(y,x,y)
    ]]></literal>
    <justification jstring="[para(3990(a,1),753(a,1,1))].">
      <j1 rule="para" parents="3990 753"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      (x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y))
    ]]></literal>
    <justification jstring="[para(4031(a,1),95(a,1,1))].">
      <j1 rule="para" parents="4031 95"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(1588(a,1),4002(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1588 4002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z * K(y,z),y)
    ]]></literal>
    <justification jstring="[para(4002(a,1),1608(a,1,2))].">
      <j1 rule="para" parents="4002 1608"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(3701,a,4015,a)].">
      <j1 rule="hyper" parents="3701 4015"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = R(x,z / y,y) * z
    ]]></literal>
    <justification jstring="[hyper(325,a,418,a,b,4033,a),flip(a)].">
      <j1 rule="hyper" parents="325 418 4033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      x / (y * ((y * x) / y)) = T(x,y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3353,a(flip),b,3977,a),flip(a)].">
      <j1 rule="hyper" parents="65 3353 3977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      R(x,y / z,z) * (u * (u \ y)) = (x * (z \ y)) * T(z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,156,a,b,4039,a)].">
      <j1 rule="hyper" parents="325 156 4039"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(489,a,3999,a)].">
      <j1 rule="hyper" parents="489 3999"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(3147(a,1),4043(a,1,2))].">
      <j1 rule="para" parents="3147 4043"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(153(a,1),4044(a,1,3))].">
      <j1 rule="para" parents="153 4044"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(2863,a,4045,a)].">
      <j1 rule="hyper" parents="2863 4045"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(4045(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="4045 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      K(x,y) = (x * R(y,x,y)) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4022,a(flip),b,4032,a)].">
      <j1 rule="hyper" parents="325 4022 4032"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),w,v5) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3111,a,b,3357,a),flip(a)].">
      <j1 rule="hyper" parents="325 3111 3357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(3111(a,2),3665(a,1,1))].">
      <j1 rule="para" parents="3111 3665"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(3130(a,1),3952(a,1,1))].">
      <j1 rule="para" parents="3130 3952"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(3959,a,2275,a)].">
      <j1 rule="hyper" parents="3959 2275"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(3248,a,4053,a),flip(a)].">
      <j1 rule="hyper" parents="3248 4053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[hyper(776,a,4042,a(flip))].">
      <j1 rule="hyper" parents="776 4042"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      K(x,T((y / (x * z)) \ 1,u)) = K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3119,a(flip),b,4050,a),flip(a)].">
      <j1 rule="hyper" parents="65 3119 4050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3285,a(flip),b,4058,a),flip(a)].">
      <j1 rule="hyper" parents="65 3285 4058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      K(x,y \ (x * (z \ y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),4059(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 4059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      R(K(T(T(x,y),y * z),u),w,v5) = ((y * z) \ ((y * K(u,x)) * z)) \ 1
    ]]></literal>
    <justification jstring="[para(4051(a,1),2910(a,2,1))].">
      <j1 rule="para" parents="4051 2910"/>
    </justification>
  </clause>

  <clause id="4063">
    <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(3944(a,1),4052(a,1,1,1))].">
      <j1 rule="para" parents="3944 4052"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),2067(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 2067"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2755,a(flip),b,4064,a),flip(a)].">
      <j1 rule="hyper" parents="325 2755 4064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(4064(a,2),2756(a,1))].">
      <j1 rule="para" parents="4064 2756"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(4065(a,1),497(a,1,1))].">
      <j1 rule="para" parents="4065 497"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      ((1 / (x * y)) * x) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3291,a,b,2268,a)].">
      <j1 rule="hyper" parents="65 3291 2268"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (x * T(x,x \ (x \ 1))) * (y / z) = (((1 / x) \ x) * y) / z
    ]]></literal>
    <justification jstring="[para(3288(a,1),2314(a,2,1,1))].">
      <j1 rule="para" parents="3288 2314"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      (x * (1 / (1 / x))) * (y / z) = (((1 / x) \ x) * y) / z
    ]]></literal>
    <justification jstring="[para(1644(a,1),4070(a,1,1,2))].">
      <j1 rule="para" parents="1644 4070"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      (((1 / x) \ x) * y) / z = ((1 / x) \ x) * (y / z)
    ]]></literal>
    <justification jstring="[para(3288(a,1),4071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3288 4071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      K(x,y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(2993(a,1),2599(a,1,1))].">
      <j1 rule="para" parents="2993 2599"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      T(x,x \ 1) \ ((1 * x) \ 1) = ((1 * x) \ 1) * ((1 * x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),2793(a,1,1,1))].">
      <j1 rule="para" parents="7 2793"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      T(x,x \ 1) \ (x \ 1) = ((1 * x) \ 1) * ((1 * x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),4075(a,1,2,1))].">
      <j1 rule="para" parents="7 4075"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      x \ T(x \ 1,x) = ((1 * x) \ 1) * ((1 * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2644,a(flip),b,4076,a)].">
      <j1 rule="hyper" parents="65 2644 4076"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      x \ T(x \ 1,x) = (x \ 1) * ((1 * x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),4077(a,2,1,1))].">
      <j1 rule="para" parents="7 4077"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      x \ T(x \ 1,x) = (x \ 1) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),4078(a,2,2,1))].">
      <j1 rule="para" parents="7 4078"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      x * ((x \ 1) / x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,420,a(flip),b,4079,a)].">
      <j1 rule="hyper" parents="137 420 4079"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      R(x \ (y / ((x \ 1) / x)),x,(x \ 1) / x) = T(y / T(x \ 1,x),x)
    ]]></literal>
    <justification jstring="[para(4080(a,1),616(a,2,1,2))].">
      <j1 rule="para" parents="4080 616"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      R((x * T(T(x,y),y)) * z,u,w) = (x * T(T(x,y),y)) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(2880(a,1),2894(a,1,1,1))].">
      <j1 rule="para" parents="2880 2894"/>
    </justification>
  </clause>

  <clause id="4083">
    <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(2584(a,1),3198(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2584 3198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(2092(a,1),3534(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2092 3534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(137,a,4084,a,b,xx)].">
      <j1 rule="hyper" parents="137 4084"/>
    </justification>
  </clause>

  <clause id="4086">
    <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(2390(a,1),4084(a,2,1))].">
      <j1 rule="para" parents="2390 4084"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(2169(a,1),4085(a,1,2,2))].">
      <j1 rule="para" parents="2169 4085"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(4085(a,1),2849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4085 2849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2847(a,1),4087(a,1,1,1))].">
      <j1 rule="para" parents="2847 4087"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3928,a(flip),b,4089,a),flip(a)].">
      <j1 rule="hyper" parents="325 3928 4089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,4089,a(flip),b,2870,a)].">
      <j1 rule="hyper" parents="135 4089 2870"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(455,a,4090,a)].">
      <j1 rule="hyper" parents="455 4090"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(4092(a,1),298(a,1,2))].">
      <j1 rule="para" parents="4092 298"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      (x * K(y,z)) * L(K(u,y),w,v5) = x * (K(y,z) * L(K(u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(4092(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="4092 412"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(2234,a,4091,a)].">
      <j1 rule="hyper" parents="2234 4091"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2855(a,1),4095(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2855 4095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      ((x / T(y,z)) * K(y,u)) \ (x * K(y,u)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(195,a,4096,a)].">
      <j1 rule="hyper" parents="195 4096"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      ((x \ y) * K(x,z)) \ (y * K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(268(a,1),4097(a,1,1,1))].">
      <j1 rule="para" parents="268 4097"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * y) * z) = x \ ((((x * x) / x) * y) * z)
    ]]></literal>
    <justification jstring="[para(769(a,1),3552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="769 3552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * y) * z) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4099(a,2,2,1,1))].">
      <j1 rule="para" parents="11 4099"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      ((K(x,y) * z) \ 1) \ ((((K(x,y) * z) \ 1) * u) * w) = z \ (K(y,x) * (((K(x,y) * z) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,2674,a(flip),b,4100,a),flip(a)].">
      <j1 rule="hyper" parents="325 2674 4100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      (x \ 1) \ (L(x \ 1,y,z) * u) = x \ ((x * (x \ L(x,y,z))) * u)
    ]]></literal>
    <justification jstring="[para(1313(a,1),4100(a,1,2,1))].">
      <j1 rule="para" parents="1313 4100"/>
    </justification>
  </clause>

  <clause id="4103">
    <literal><![CDATA[
      L(x \ (y \ ((y * z) * u)),x,y) = ((y \ 1) * x) \ (((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(4100(a,1),1501(a,1,1,2))].">
      <j1 rule="para" parents="4100 1501"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3676,a(flip),b,3688,a)].">
      <j1 rule="hyper" parents="65 3676 3688"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2786,a(flip),b,4104,a),flip(a)].">
      <j1 rule="hyper" parents="325 2786 4104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,3367,a(flip),b,4105,a),flip(a)].">
      <j1 rule="hyper" parents="325 3367 4105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      T(x,T(y,z)) * K(z \ y,z) = K(z \ y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3858,a(flip),b,3798,a)].">
      <j1 rule="hyper" parents="65 3858 3798"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      (x * T(y,z)) / T(T(y,y \ 1),z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3646(a,1),3881(a,2,2))].">
      <j1 rule="para" parents="3646 3881"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      (x * T(y,z)) / T((y \ 1) \ 1,z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),4109(a,1,2,1))].">
      <j1 rule="para" parents="114 4109"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * T((y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4110(a,1),256(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4110 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(4112,a,3230,a),flip(a)].">
      <j1 rule="hyper" parents="4112 3230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(3963(a,1),4113(a,1,2))].">
      <j1 rule="para" parents="3963 4113"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      (x \ K(x,y)) * T(x,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3233,a,4114,a)].">
      <j1 rule="hyper" parents="3233 4114"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ K(x,y)) * x
    ]]></literal>
    <justification jstring="[para(4115(a,1),1041(a,1,1))].">
      <j1 rule="para" parents="4115 1041"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      (x \ K(x,y)) * x = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3200,a(flip),b,4116,a),flip(a)].">
      <j1 rule="hyper" parents="65 3200 4116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,2082,a,b,4117,a)].">
      <j1 rule="hyper" parents="37 2082 4117"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2846,a,b,4118,a)].">
      <j1 rule="hyper" parents="65 2846 4118"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,4119,a(flip),b,2618,a)].">
      <j1 rule="hyper" parents="201 4119 2618"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4119(a,1),2678(a,1,2))].">
      <j1 rule="para" parents="4119 2678"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      (x * K(y,z)) * L(K(z,u),w,v5) = x * (L(K(z,u),w,v5) * K(y,z))
    ]]></literal>
    <justification jstring="[para(3090(a,2),3925(a,2,2))].">
      <j1 rule="para" parents="3090 3925"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      T(x,y) * (T(z,x) * K(x,T(T(z,x),y))) = T(T(x,z),y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(3113(a,1),3976(a,1,2,2))].">
      <j1 rule="para" parents="3113 3976"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[para(1989(a,2),4069(a,1,1))].">
      <j1 rule="para" parents="1989 4069"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      K(x,y) * R((y * T(T(y,x),x)) * z,u,w) = (y * T(y,x)) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(4082(a,2),2898(a,1,2))].">
      <j1 rule="para" parents="4082 2898"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * L(K(u,z),w,v5)) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[para(2847(a,1),4094(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2847 4094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      x \ ((x * (x \ L(x,y,z))) * u) = L(x \ 1,y,z) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1246,a(flip),b,4102,a),flip(a)].">
      <j1 rule="hyper" parents="65 1246 4102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      T(x,y) * (T(z,x) * K(x,T(z,y))) = T(T(x,z),y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(2530(a,1),4126(a,1,2,2))].">
      <j1 rule="para" parents="2530 4126"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = x \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),4130(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1246,a(flip),b,4133,a),flip(a)].">
      <j1 rule="hyper" parents="325 1246 4133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(2277,a,2273,a),flip(a)].">
      <j1 rule="hyper" parents="2277 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2275,a(flip),b,4137,a),flip(a)].">
      <j1 rule="hyper" parents="325 2275 4137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(3248,a,4138,a)].">
      <j1 rule="hyper" parents="3248 4138"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(201,a,4139,a(flip),b,2608,a),flip(a)].">
      <j1 rule="hyper" parents="201 4139 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(T(x,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2611,a(flip),b,4140,a),flip(a)].">
      <j1 rule="hyper" parents="325 2611 4140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(4141(a,2),3205(a,1))].">
      <j1 rule="para" parents="4141 3205"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      L(x,y,z * (z * (R(z,u,w) * v5))) = L(x,y,L(v5,z,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(956(a,1),2385(a,1,3,2))].">
      <j1 rule="para" parents="956 2385"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      L(x,y,z * (z * (L(z,u,w) * v5))) = L(x,y,L(v5,z,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1249(a,1),2386(a,1,3,2))].">
      <j1 rule="para" parents="1249 2386"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      ((K(x,y) * (z / (x * y))) * x) \ (K(x,y) * z) = L(y,x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(666(a,1),2734(a,1,1,1))].">
      <j1 rule="para" parents="666 2734"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(3017,a,2189,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3017 2189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3306,a(flip),b,3549,a)].">
      <j1 rule="hyper" parents="65 3306 3549"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(37,a,1773,a(flip),b,4148,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 1773 4148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1628,a,b,4148,a(flip))].">
      <j1 rule="hyper" parents="36 1628 4148"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,1040,a,b,4150,a)].">
      <j1 rule="hyper" parents="325 1040 4150"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4150(a,2),2307(a,1,1))].">
      <j1 rule="para" parents="4150 2307"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(2308,a,4152,a)].">
      <j1 rule="hyper" parents="2308 4152"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2308,a,4153,a)].">
      <j1 rule="hyper" parents="2308 4153"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,4154,a(flip),b,4155,a),flip(a)].">
      <j1 rule="hyper" parents="325 4154 4155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) * K(L(x,v5,v6),x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(136,a,4156,a,b,2611,a)].">
      <j1 rule="hyper" parents="136 4156 2611"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      L(K(x \ 1,x) * (L(x,y,z) \ u),x,x) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1945,a(flip),b,4149,a),flip(a)].">
      <j1 rule="hyper" parents="325 1945 4149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(3181(a,1),4149(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3181 4149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,3181,a,b,4160,a),flip(a)].">
      <j1 rule="hyper" parents="36 3181 4160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1381(a,1),4162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1381 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4164(a,1),3241(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4164 3241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(4164(a,1),3293(a,1,1))].">
      <j1 rule="para" parents="4164 3293"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(1270,a,4165,a)].">
      <j1 rule="hyper" parents="1270 4165"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1523,a(flip),b,4167,a),flip(a)].">
      <j1 rule="hyper" parents="65 1523 4167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(132,a,4167,a(flip),b,1523,a(flip))].">
      <j1 rule="hyper" parents="132 4167 1523"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      K(L(x,y,z),L(x,u,w) \ 1) = K(L(x,v5,v6),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2628,a,4158,a)].">
      <j1 rule="hyper" parents="2628 4158"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      K(L(x,y,z),L(x,u,w) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,4009,a(flip),b,4170,a),flip(a)].">
      <j1 rule="hyper" parents="325 4009 4170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,4171,a(flip),b,1366,a(flip))].">
      <j1 rule="hyper" parents="132 4171 1366"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,4172,a(flip),b,1373,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 4172 1373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4174">
    <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(1471(a,2),3681(a,1,1))].">
      <j1 rule="para" parents="1471 3681"/>
    </justification>
  </clause>

  <clause id="4175">
    <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(325,a,3571,a,b,3685,a)].">
      <j1 rule="hyper" parents="325 3571 3685"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3832,a(flip),b,3810,a),flip(a)].">
      <j1 rule="hyper" parents="325 3832 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(3964,a,2835,a)].">
      <j1 rule="hyper" parents="3964 2835"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      (x * T(T(x,y),y)) * (y / (x * ((x * y) / x))) = R(T(x,y),T(x,y),y)
    ]]></literal>
    <justification jstring="[para(2880(a,1),3978(a,1,1))].">
      <j1 rule="para" parents="2880 3978"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      R(K(T(x,y),T(z,y * u)),w,v5) = ((y * u) \ ((y * K(z,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(3113(a,1),4062(a,1,1))].">
      <j1 rule="para" parents="3113 4062"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(3637(a,1),4063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3637 4063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(147,a,4180,a)].">
      <j1 rule="hyper" parents="147 4180"/>
    </justification>
  </clause>

  <clause id="4183">
    <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),4181(a,1,1,1,1))].">
      <j1 rule="para" parents="9 4181"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      ((x \ 1) * y) \ (((x \ 1) * z) * u) = (x * y) \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,308,a(flip),b,4103,a),flip(a)].">
      <j1 rule="hyper" parents="65 308 4103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      ((x \ 1) * y) \ (L(x \ 1,z,u) * w) = (x * y) \ ((x * (x \ L(x,z,u))) * w)
    ]]></literal>
    <justification jstring="[para(1313(a,1),4184(a,1,2,1))].">
      <j1 rule="para" parents="1313 4184"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      a(x * ((y * (y \ 1)) \ ((y * z) * u)),w,v5) = a(x * (((y \ 1) * z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(4184(a,1),2359(a,1,1,2))].">
      <j1 rule="para" parents="4184 2359"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,z,z)) = L(x,y,L(v5,z,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1491,a(flip),b,4143,a)].">
      <j1 rule="hyper" parents="65 1491 4143"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w) * v5,z,z)) = L(x,y,L(v5,z,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1491,a(flip),b,4144,a)].">
      <j1 rule="hyper" parents="65 1491 4144"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      (K(x,y) * ((z / (x * y)) * x)) \ (K(x,y) * z) = L(y,x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(287(a,1),4145(a,1,1))].">
      <j1 rule="para" parents="287 4145"/>
    </justification>
  </clause>

  <clause id="4191">
    <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(4174(a,1),3756(a,2,2))].">
      <j1 rule="para" parents="4174 3756"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      (x * T(T(x,y),y)) * (T(y,x) / (x * y)) = R(T(x,y),T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4041(a,1),4178(a,1,2))].">
      <j1 rule="para" parents="4041 4178"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),w,v5) = ((z * u) \ ((z * K(y,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(3142(a,1),4179(a,1,1))].">
      <j1 rule="para" parents="3142 4179"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,470,a(flip),b,4189,a),flip(a)].">
      <j1 rule="hyper" parents="65 470 4189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      L(x \ y,x,((x \ y) * x) \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),4194(a,2,1,1,2))].">
      <j1 rule="para" parents="10 4194"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4051,a(flip),b,4193,a),flip(a)].">
      <j1 rule="hyper" parents="65 4051 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(4088(a,2),4197(a,1,1))].">
      <j1 rule="para" parents="4088 4197"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = (y * u) \ ((y * K(x,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(2625,a,4198,a)].">
      <j1 rule="hyper" parents="2625 4198"/>
    </justification>
  </clause>

  <clause id="4200">
    <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(2093(a,1),2178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2093 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4201">
    <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(4200(a,2),490(a,1))].">
      <j1 rule="para" parents="4200 490"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      R(x,y,T(z,y * z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4201,a,4000,a)].">
      <j1 rule="hyper" parents="4201 4000"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(4201,a,31,a),flip(a)].">
      <j1 rule="hyper" parents="4201 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      T(x,y) * L(K(z,T(x,y)),u,w) = T(x * L(K(z,x),u,w),y)
    ]]></literal>
    <justification jstring="[para(2310(a,1),2312(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2310 2312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      T(x * L(K(y,x),z,u),y) = T(x,y) * L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(2517(a,1),4204(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2517 4204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      ((x \ 1) * (K(x,y) * ((x \ 1) \ z))) * (z \ u) = K(x,y) * u
    ]]></literal>
    <justification jstring="[para(2211(a,1),2423(a,2,1))].">
      <j1 rule="para" parents="2211 2423"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      (x \ 1) \ (K(x,y) * z) = K(x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,4206,a(flip),b,177,a(flip))].">
      <j1 rule="hyper" parents="132 4206 177"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,157,a(flip),b,4207,a),flip(a)].">
      <j1 rule="hyper" parents="137 157 4207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,4208,a,b,389,a)].">
      <j1 rule="hyper" parents="137 4208 389"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,4208,a),flip(a)].">
      <j1 rule="hyper" parents="65 233 4208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(683(a,1),4209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="683 4209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(3318(a,1),4214(a,1,1))].">
      <j1 rule="para" parents="3318 4214"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(245,a,287,a,b,4210,a)].">
      <j1 rule="hyper" parents="245 287 4210"/>
    </justification>
  </clause>

  <clause id="4217">
    <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),4216(a,2,2))].">
      <j1 rule="para" parents="25 4216"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(514,a,4215,a)].">
      <j1 rule="hyper" parents="514 4215"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      (x / y) * (y \ (x * R(x \ y,z,u))) = R(K(y,y \ x) * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1057,a,b,2811,a),flip(a)].">
      <j1 rule="hyper" parents="325 1057 2811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      R((x * y) * ((x \ 1) * (x * x)),z,u) = (R(y * K(x,y),z,u) * x) * x
    ]]></literal>
    <justification jstring="[para(34(a,1),2936(a,1,1))].">
      <j1 rule="para" parents="34 2936"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      K(x / y,T(z,u)) \ T(x / (K(y \ x,z) \ x),u) = K(K(x / y,z) \ x,T(K(x / y,z),u))
    ]]></literal>
    <justification jstring="[para(3660(a,1),3134(a,1,2,1,2))].">
      <j1 rule="para" parents="3660 3134"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(113(a,1),3461(a,1,1,2,2))].">
      <j1 rule="para" parents="113 3461"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1791(a,2),4222(a,1,1))].">
      <j1 rule="para" parents="1791 4222"/>
    </justification>
  </clause>

  <clause id="4224">
    <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(3545(a,1),3548(a,1,1))].">
      <j1 rule="para" parents="3545 3548"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3950,a(flip),b,3951,a),flip(a)].">
      <j1 rule="hyper" parents="325 3950 3951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),4225(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="85 4225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      R(T(K(x,y),z) * z,u,w) = K(x,y) * R(T(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(3628(a,1),3980(a,2,2,1))].">
      <j1 rule="para" parents="3628 3980"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      R(T(K(x,y),z) * z,u,w) = R(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,243,a(flip),b,4227,a),flip(a)].">
      <j1 rule="hyper" parents="325 243 4227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      R(x * K(y,z),u,w) = R(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3629(a,1),4228(a,1,1))].">
      <j1 rule="para" parents="3629 4228"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      L(x,y,R(z * K(u,w),v5,v6)) = L(x,y,R(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(4229(a,2),2324(a,1,3))].">
      <j1 rule="para" parents="4229 2324"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      a(R(x * K(y,z),u,w),v5,v6) = a(R(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(4229(a,2),2340(a,1,1))].">
      <j1 rule="para" parents="4229 2340"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * w) * u)) = L(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1636,a(flip),b,4230,a)].">
      <j1 rule="hyper" parents="65 1636 4230"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1874,a(flip),b,4231,a)].">
      <j1 rule="hyper" parents="65 1874 4231"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4233(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      a((T(x,y) * y) \ ((x * z) * ((x * y) / x)),u,w) = a(R(z,x,(x * y) / x),u,w)
    ]]></literal>
    <justification jstring="[para(3975(a,2),4234(a,1,1,1))].">
      <j1 rule="para" parents="3975 4234"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      R(K(x,y) * ((y * T(T(y,x),x)) * z),u,w) = (y * T(y,x)) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1057,a,b,4128,a)].">
      <j1 rule="hyper" parents="65 1057 4128"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      (x / y) * (y \ (x * R(x \ y,z,u))) = R(x / y,z,u)
    ]]></literal>
    <justification jstring="[para(2455(a,1),4219(a,2,1))].">
      <j1 rule="para" parents="2455 4219"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(140,a,4240,a)].">
      <j1 rule="hyper" parents="140 4240"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      R(x,y,z) * ((y * z) \ (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w))) = R(((x * y) * z) / (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),4240(a,1,1))].">
      <j1 rule="para" parents="20 4240"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      y \ (x * R(x \ y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(4240(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4240 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) = (y \ x) \ R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1403,a,b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="325 1403 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (y \ x) \ R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(4241(a,2),1405(a,1))].">
      <j1 rule="para" parents="4241 1405"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (y \ x) \ R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1077,a,b,4244,a)].">
      <j1 rule="hyper" parents="65 1077 4244"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      ((x \ 1) \ R(x \ 1,y,z)) * L(u,R((1 / x) \ 1,y,z),x) = (1 / x) * (R((1 / x) \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(4246(a,1),1496(a,1,1))].">
      <j1 rule="para" parents="4246 1496"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      (R(x * K(y,x),z,u) * y) * y = R((y * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(221(a,1),4220(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="221 4220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      R((x * y) * x,z,u) = (x * R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1599(a,1),4248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1599 4248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      R((x * T(x,y)) * z,u,w) = (x * T(x,y)) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(2898(a,1),4239(a,1,1))].">
      <j1 rule="para" parents="2898 4239"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y / (x \ 1)) / y) = (x * K(y,x)) * ((T(y,x) * x) \ y)
    ]]></literal>
    <justification jstring="[para(2529(a,1),2594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2529 2594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4253">
    <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(2642(a,2),2926(a,2,1))].">
      <j1 rule="para" parents="2642 2926"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      L(T(x,y),T(z,x),K(x,z)) * z = K(x,z) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(2642(a,2),4253(a,1,1,3))].">
      <j1 rule="para" parents="2642 4253"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * T(y,x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(153(a,1),4254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="153 4254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(2185(a,2),4255(a,1,2))].">
      <j1 rule="para" parents="2185 4255"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(x,x \ y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3839,a(flip),b,4257,a)].">
      <j1 rule="hyper" parents="65 3839 4257"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      (T(x,y) * z) \ (K(x,z) * u) = (K(x,y) * (z * x)) \ u
    ]]></literal>
    <justification jstring="[para(4257(a,1),470(a,1,1))].">
      <j1 rule="para" parents="4257 470"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      K(x,y) * (y * T(x,z)) = T(x,T(z,y)) * y
    ]]></literal>
    <justification jstring="[para(3679(a,1),4257(a,1,2))].">
      <j1 rule="para" parents="3679 4257"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,1619,a,b,4260,a(flip))].">
      <j1 rule="hyper" parents="37 1619 4260"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(140,a,4261,a)].">
      <j1 rule="hyper" parents="140 4261"/>
    </justification>
  </clause>

  <clause id="4263">
    <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(4262(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4262 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      (T(x,y) * z) \ (K(x,z) * u) = (z * x) \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2674,a(flip),b,4259,a),flip(a)].">
      <j1 rule="hyper" parents="325 2674 4259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      x * ((y * x) * T((y * x) \ 1,x)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[hyper(291,a,2942,a),flip(a)].">
      <j1 rule="hyper" parents="291 2942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      x * (y * (x * T(x \ (y \ 1),x))) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(821(a,1),4265(a,1,2))].">
      <j1 rule="para" parents="821 4265"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      (((x \ (1 / y)) * x) * y) * x = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[para(113(a,1),4266(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4268">
    <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(325,a,2510,a(flip),b,3485,a),flip(a)].">
      <j1 rule="hyper" parents="325 2510 3485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4269">
    <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),4183(a,2,2,1,1))].">
      <j1 rule="para" parents="9 4183"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,4269,a)].">
      <j1 rule="hyper" parents="145 4269"/>
    </justification>
  </clause>

  <clause id="4271">
    <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(4269(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4269 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4273">
    <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(325,a,27,a,b,4268,a),flip(a)].">
      <j1 rule="hyper" parents="325 27 4268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      x * (x * T(T(x,T(y,x)) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(22(a,2),2740(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="22 2740"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(2500(a,1),4274(a,1,2,2,1,1))].">
      <j1 rule="para" parents="2500 4274"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ y,z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),4275(a,1,2,2,1,2))].">
      <j1 rule="para" parents="11 4275"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),z) = (x * (y * T(y \ x,z))) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,1169,a(flip),b,2823,a),flip(a)].">
      <j1 rule="hyper" parents="65 1169 2823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(113(a,1),4277(a,2,1,2))].">
      <j1 rule="para" parents="113 4277"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      x * K(((x * y) / x) \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(2609(a,1),4278(a,1,2,1))].">
      <j1 rule="para" parents="2609 4278"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = L(K(z,u),y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(2860,a,3932,a)].">
      <j1 rule="hyper" parents="2860 3932"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,3097,a(flip),b,4280,a),flip(a)].">
      <j1 rule="hyper" parents="325 3097 4280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(2847(a,1),4281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2847 4281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4283">
    <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(325,a,4012,a(flip),b,3358,a),flip(a)].">
      <j1 rule="hyper" parents="325 4012 3358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4285">
    <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(138,a,3412,a),flip(a)].">
      <j1 rule="hyper" parents="138 3412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3378(a,1),4285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3378 4285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3435,a(flip),b,3939,a)].">
      <j1 rule="hyper" parents="65 3435 3939"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3938,a(flip),b,4287,a),flip(a)].">
      <j1 rule="hyper" parents="65 3938 4287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      ((x \ 1) * y) \ (L(x \ 1,z,u) * w) = (x * y) \ (L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),4185(a,2,2,1))].">
      <j1 rule="para" parents="10 4185"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      a(x * (((y \ 1) * z) * u),w,v5) = a(x * ((y * z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(170(a,1),4186(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="170 4186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      (((x \ 1) * y) / L(y,x \ 1,x)) * x = x \ R(1 / (1 / x),x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1204(a,1),2938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1204 2938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      (((x \ 1) * y) / L(y,x \ 1,x)) * x = (x \ 1) * R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1539,a(flip),b,4293,a),flip(a)].">
      <j1 rule="hyper" parents="325 1539 4293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / ((z * K(x \ 1,x)) * u) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[hyper(3307,a,109,a(flip))].">
      <j1 rule="hyper" parents="3307 109"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(3051,a,4067,a),flip(a)].">
      <j1 rule="hyper" parents="3051 4067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(206(a,1),2132(a,1,2))].">
      <j1 rule="para" parents="206 2132"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      T((x * y) \ (K(z,y) * T(y,T(z,x))),x \ 1) = (x * T(y,T(z,x))) \ T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,2681,a(flip),b,3275,a)].">
      <j1 rule="hyper" parents="65 2681 3275"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((x * y) * T((x * y) \ 1,x)) * x
    ]]></literal>
    <justification jstring="[para(890(a,1),2581(a,2,1))].">
      <j1 rule="para" parents="890 2581"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(1100(a,1),4308(a,2,1))].">
      <j1 rule="para" parents="1100 4308"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[hyper(325,a,4267,a(flip),b,4309,a),flip(a)].">
      <j1 rule="hyper" parents="325 4267 4309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = y * ((x \ (y \ 1)) * x)
    ]]></literal>
    <justification jstring="[hyper(36,a,4127,a(flip),b,4310,a(flip))].">
      <j1 rule="hyper" parents="36 4127 4310"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * y) = ((y \ x) * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),4311(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 4311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4218,a(flip),b,4312,a),flip(a)].">
      <j1 rule="hyper" parents="65 4218 4312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(2818,a,4313,a),flip(a)].">
      <j1 rule="hyper" parents="2818 4313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (K(x \ 1,x) * (z * u)) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[para(3230(a,1),4295(a,1,2))].">
      <j1 rule="para" parents="3230 4295"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * ((y * z) * u)) / (z * u)) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3347,a(flip),b,4315,a)].">
      <j1 rule="hyper" parents="65 3347 4315"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[para(981(a,1),4316(a,1,2))].">
      <j1 rule="para" parents="981 4316"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(2723,a,4317,a),flip(a)].">
      <j1 rule="hyper" parents="2723 4317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1197(a,1),4318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1197 4318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(742,a,4320,a),flip(a)].">
      <j1 rule="hyper" parents="742 4320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2084,a,b,4320,a)].">
      <j1 rule="hyper" parents="65 2084 4320"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4320(a,1),2294(a,1,2))].">
      <j1 rule="para" parents="4320 2294"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      K(T(x,y \ 1),R(z,y \ 1,y)) = K(x,((1 / y) * z) * y)
    ]]></literal>
    <justification jstring="[para(4322(a,1),3645(a,1,2))].">
      <j1 rule="para" parents="4322 3645"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((1 / x) \ y) / y)
    ]]></literal>
    <justification jstring="[para(4321(a,2),96(a,1,2,2))].">
      <j1 rule="para" parents="4321 96"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      K(x,((1 / y) * z) * y) = K(T(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(3002,a,4324,a),flip(a)].">
      <j1 rule="hyper" parents="3002 4324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      ((1 / x) \ y) \ (y * R(1 / (1 / x),x \ 1,(1 / x) \ y)) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(325,a,3447,a(flip),b,4325,a),flip(a)].">
      <j1 rule="hyper" parents="325 3447 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(4323(a,1),4328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4323 4328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(325,a,3454,a(flip),b,4329,a)].">
      <j1 rule="hyper" parents="325 3454 4329"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2759,a(flip),b,4330,a),flip(a)].">
      <j1 rule="hyper" parents="325 2759 4330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4331(a,2),3038(a,1))].">
      <j1 rule="para" parents="4331 3038"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      K(((x \ 1) \ y) * (x \ 1),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(4333,a,3034,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4333 3034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3437(a,2),4333(a,1))].">
      <j1 rule="para" parents="3437 4333"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      K(((1 / x) \ y) * (1 / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(3284(a,2),4334(a,1,1))].">
      <j1 rule="para" parents="3284 4334"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      K((x \ y) * x,x \ 1) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3289(a,1),4334(a,1,1))].">
      <j1 rule="para" parents="3289 4334"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4336(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = (x \ y) * K(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4337(a,1),3418(a,2,2))].">
      <j1 rule="para" parents="4337 3418"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,3415,a(flip),b,4338,a),flip(a)].">
      <j1 rule="hyper" parents="325 3415 4338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      K((1 / x) * (y * x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),4341(a,2,1))].">
      <j1 rule="para" parents="22 4341"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),4341(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 4341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[para(750(a,1),4342(a,1,1))].">
      <j1 rule="para" parents="750 4342"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      K((x / ((1 / x) \ y)) \ 1,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(4335,a,2688,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4335 2688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4346">
    <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(4345(a,1),3896(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4345 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3438,a(flip),b,4344,a)].">
      <j1 rule="hyper" parents="65 3438 4344"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4347(a,1),2610(a,1,1))].">
      <j1 rule="para" parents="4347 2610"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(2698,a,4348,a),flip(a)].">
      <j1 rule="hyper" parents="2698 4348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3404,a(flip),b,4349,a),flip(a)].">
      <j1 rule="hyper" parents="65 3404 4349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      K(x,x \ ((x \ 1) \ y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4349(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 4349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3425,a(flip),b,4351,a)].">
      <j1 rule="hyper" parents="65 3425 4351"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      x * T(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(2148,a,4355,a)].">
      <j1 rule="hyper" parents="2148 4355"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4355(a,2),2710(a,2,2))].">
      <j1 rule="para" parents="4355 2710"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2145,a,b,4356,a),flip(a)].">
      <j1 rule="hyper" parents="36 2145 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4359">
    <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(4358(a,1),1691(a,1,2,1,1))].">
      <j1 rule="para" parents="4358 1691"/>
    </justification>
  </clause>

  <clause id="4360">
    <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),x * y)
    ]]></literal>
    <justification jstring="[para(4358(a,2),1691(a,1,1))].">
      <j1 rule="para" parents="4358 1691"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,3896,a(flip),b,4346,a),flip(a)].">
      <j1 rule="hyper" parents="325 3896 4346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      K(T(x,((y \ 1) / (y \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),4362(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="82 4362"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3855,a(flip),b,4364,a)].">
      <j1 rule="hyper" parents="65 3855 4364"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3789,a,4366,a)].">
      <j1 rule="hyper" parents="3789 4366"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((1 / L(x,y,z)) * u) = (L(x,y,z) * x) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1516,a(flip),b,3553,a),flip(a)].">
      <j1 rule="hyper" parents="65 1516 3553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((1 / L(x,y,z)) * u) = L(x \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,102,a,b,4368,a),flip(a)].">
      <j1 rule="hyper" parents="325 102 4368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T(L((x \ 1) \ (x \ x),y,z),u)
    ]]></literal>
    <justification jstring="[para(952(a,2),2278(a,2,2,1))].">
      <j1 rule="para" parents="952 2278"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      L(x,y,L((T(z,u) * w) * v5,K(u,z),K(u,z)) * v6) = L(x,y,v6 * ((z * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,3507,a(flip),b,2897,a),flip(a)].">
      <j1 rule="hyper" parents="325 3507 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      L(x,y,((T(z,u) * w) * v5) * v6) = L(x,y,v6 * ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(153(a,1),4371(a,1,3,1))].">
      <j1 rule="para" parents="153 4371"/>
    </justification>
  </clause>

  <clause id="4375">
    <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(287(a,1),3350(a,1,2))].">
      <j1 rule="para" parents="287 3350"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T(L((x \ 1) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(69(a,1),4370(a,2,2,1,1,2))].">
      <j1 rule="para" parents="69 4370"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * L(T((x \ 1) \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),4376(a,2,2))].">
      <j1 rule="para" parents="25 4376"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = L(T(x,u),y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(818,a,4377,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="818 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4380">
    <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(3340,a,4375,a)].">
      <j1 rule="hyper" parents="3340 4375"/>
    </justification>
  </clause>

  <clause id="4381">
    <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(3352(a,1),4380(a,1,1))].">
      <j1 rule="para" parents="3352 4380"/>
    </justification>
  </clause>

  <clause id="4382">
    <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),4381(a,1,1,1))].">
      <j1 rule="para" parents="14 4381"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2862,a,4382,a)].">
      <j1 rule="hyper" parents="2862 4382"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(680(a,1),4383(a,1,2))].">
      <j1 rule="para" parents="680 4383"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(846(a,1),4383(a,1,2))].">
      <j1 rule="para" parents="846 4383"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      L(x,y,z) / ((x \ L(x,u,w)) \ 1) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),2022(a,1,1,1))].">
      <j1 rule="para" parents="10 2022"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      L(x,y,z) / (L(x,u,w) \ x) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(2015(a,1),4388(a,1,2))].">
      <j1 rule="para" parents="2015 4388"/>
    </justification>
  </clause>

  <clause id="4390">
    <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(3310,a,3309,a),flip(a)].">
      <j1 rule="hyper" parents="3310 3309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(3312(a,1),4390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3312 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,18,a,b,4391,a),flip(a)].">
      <j1 rule="hyper" parents="325 18 4391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1020(a,1),4392(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1020 4392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      L(x,L(y,y,y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(848(a,2),4394(a,1,2))].">
      <j1 rule="para" parents="848 4394"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      (x \ 1) \ (L(y,x,x) * 1) = ((x \ 1) \ 1) * T(y,1)
    ]]></literal>
    <justification jstring="[para(4396(a,1),1504(a,1,2,1))].">
      <j1 rule="para" parents="4396 1504"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x) = ((x \ 1) \ 1) * T(y,1)
    ]]></literal>
    <justification jstring="[hyper(304,a,4397,a)].">
      <j1 rule="hyper" parents="304 4397"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(203(a,1),4398(a,2,2))].">
      <j1 rule="para" parents="203 4398"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      (x \ K(y,z)) \ ((((K(z,y) * x) \ 1) * u) * w) = x \ (K(y,z) * (((K(z,y) * x) * u) * w))
    ]]></literal>
    <justification jstring="[para(2616(a,1),4101(a,1,1))].">
      <j1 rule="para" parents="2616 4101"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      (x \ K(y,z)) \ (((x \ K(y,z)) * u) * w) = x \ (K(y,z) * (((K(z,y) * x) * u) * w))
    ]]></literal>
    <justification jstring="[para(2616(a,1),4400(a,1,2,1,1))].">
      <j1 rule="para" parents="2616 4400"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      (x \ K(y,z)) \ (((x \ K(y,z)) * u) * w) = x \ (K(y,z) * ((K(z,y) * (x * u)) * w))
    ]]></literal>
    <justification jstring="[para(287(a,1),4401(a,2,2,2,1))].">
      <j1 rule="para" parents="287 4401"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      (x \ K(y,z)) \ (((x \ K(y,z)) * u) * w) = x \ ((x * u) * w)
    ]]></literal>
    <justification jstring="[para(2665(a,1),4402(a,2,2))].">
      <j1 rule="para" parents="2665 4402"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(x / y,T(z,u)) \ T(K(y \ x,z),u)
    ]]></literal>
    <justification jstring="[para(82(a,1),4221(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 4221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(x / y,T(z,u)) \ K(y \ x,T(z,u))
    ]]></literal>
    <justification jstring="[para(3111(a,2),4407(a,2,2))].">
      <j1 rule="para" parents="3111 4407"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      K(K(x / y,z) \ x,T(K(x / y,z),u)) = K(z,T(x / y,u)) * K(y \ x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3140,a(flip),b,4409,a),flip(a)].">
      <j1 rule="hyper" parents="325 3140 4409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      (T(x,y) * z) \ R((x * T(x,y)) * ((1 / x) * z),u,w) = (1 / ((1 / x) * z)) * R((1 / x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4250(a,2),2430(a,1,2))].">
      <j1 rule="para" parents="4250 2430"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(y,z) \ (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(910(a,1),2865(a,1,1))].">
      <j1 rule="para" parents="910 2865"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      ((x * (y * (z * K(u \ 1,u)))) \ ((x * y) * z)) * K(u \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = w
    ]]></literal>
    <justification jstring="[para(3313(a,1),3302(a,1))].">
      <j1 rule="para" parents="3313 3302"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      ((x * K(y,z)) * L((x * K(y,z)) \ x,u,w)) * y = (x * K(y,z)) * (y * L(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),3971(a,2,2,2,1))].">
      <j1 rule="para" parents="9 3971"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,R((1 / x) \ 1,y,z),x) = (1 / x) * (R((1 / x) \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(1081(a,1),4247(a,1,1))].">
      <j1 rule="para" parents="1081 4247"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,R(x,y,z),x) = (1 / x) * (R((1 / x) \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(85(a,1),4416(a,1,2,2,1))].">
      <j1 rule="para" parents="85 4416"/>
    </justification>
  </clause>

  <clause id="4418">
    <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(944(a,1),4359(a,2,1))].">
      <j1 rule="para" parents="944 4359"/>
    </justification>
  </clause>

  <clause id="4419">
    <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(65,a,4418,a(flip),b,4360,a),flip(a)].">
      <j1 rule="hyper" parents="65 4418 4360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(944(a,1),4419(a,1,1)),flip(a)].">
      <j1 rule="para" parents="944 4419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4421">
    <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(4420(a,1),4177(a,1,1,1,1))].">
      <j1 rule="para" parents="4420 4177"/>
    </justification>
  </clause>

  <clause id="4422">
    <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(3475(a,2),4421(a,1,1))].">
      <j1 rule="para" parents="3475 4421"/>
    </justification>
  </clause>

  <clause id="4423">
    <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(3692,a,4422,a)].">
      <j1 rule="hyper" parents="3692 4422"/>
    </justification>
  </clause>

  <clause id="4424">
    <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(3697,a,4423,a)].">
      <j1 rule="hyper" parents="3697 4423"/>
    </justification>
  </clause>

  <clause id="4425">
    <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),4424(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 4424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4426">
    <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(4425(a,1),3562(a,1))].">
      <j1 rule="para" parents="4425 3562"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      (T(x,y) * z) \ R(((x * T(x,y)) / x) * z,u,w) = (1 / ((1 / x) * z)) * R((1 / x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(2313(a,1),4411(a,1,2,1))].">
      <j1 rule="para" parents="2313 4411"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      (T(x,y) * z) \ R(T(x,y) * z,u,w) = (1 / ((1 / x) * z)) * R((1 / x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(269(a,1),4427(a,1,2,1,1))].">
      <j1 rule="para" parents="269 4427"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      (1 / ((1 / x) * y)) * R((1 / x) * y,z,u) = (x * y) \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2415,a(flip),b,4428,a),flip(a)].">
      <j1 rule="hyper" parents="65 2415 4428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      ((1 / x) * y) \ R((1 / x) * y,z,u) = (x * y) \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3267,a,4429,a)].">
      <j1 rule="hyper" parents="3267 4429"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(2618(a,1),4412(a,1,1,2,2,1))].">
      <j1 rule="para" parents="2618 4412"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(2849(a,1),4431(a,2,2,1,2,2))].">
      <j1 rule="para" parents="2849 4431"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * K(w,v5) = x * R(x \ (y * K(w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(2662(a,1),4432(a,1,1,2))].">
      <j1 rule="para" parents="2662 4432"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (T(x * y,z) * u) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(2114(a,1),2408(a,1,2))].">
      <j1 rule="para" parents="2114 2408"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R(1 / y,y,x) * R(R(1 / y,y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2923(a,1),2924(a,2,2,1,1))].">
      <j1 rule="para" parents="2923 2924"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(z,K(u,w)),x)) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3377(a,1),3590(a,1,1,3))].">
      <j1 rule="para" parents="3377 3590"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      (x * (y * (z * K(u \ 1,u)))) \ (K(u \ 1,u) * ((x * y) * z)) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[para(1027(a,1),3308(a,1,1,2))].">
      <j1 rule="para" parents="1027 3308"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      ((x * (y * (z * K(u \ 1,u)))) \ ((x * y) * z)) * K(u \ 1,u) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(3342,a,4439,a)].">
      <j1 rule="hyper" parents="3342 4439"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u \ 1,u)) = a(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(4413,a,4440,a),flip(a)].">
      <j1 rule="hyper" parents="4413 4440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(216,a,4441,a),flip(a)].">
      <j1 rule="hyper" parents="216 4441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(3155(a,1),4442(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3155 4442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4448">
    <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),1073(a,1,2,1,1))].">
      <j1 rule="para" parents="100 1073"/>
    </justification>
  </clause>

  <clause id="4449">
    <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(1066,a,4448,a),flip(a)].">
      <j1 rule="hyper" parents="1066 4448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <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(909(a,1),4449(a,2,2))].">
      <j1 rule="para" parents="909 4449"/>
    </justification>
  </clause>

  <clause id="4451">
    <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(455,a,4450,a),flip(a)].">
      <j1 rule="hyper" parents="455 4450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1413(a,2,2,1))].">
      <j1 rule="para" parents="18 1413"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ (x \ (x * y)),u,w))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(908(a,1),4452(a,1,2))].">
      <j1 rule="para" parents="908 4452"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ y,u,w))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),4453(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="9 4453"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(907(a,1),4454(a,1,2,2))].">
      <j1 rule="para" parents="907 4454"/>
    </justification>
  </clause>

  <clause id="4456">
    <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="[hyper(325,a,1310,a,b,4455,a),flip(a)].">
      <j1 rule="hyper" parents="325 1310 4455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ L(z,u,w)))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(1310(a,1),4455(a,1,2,2,2))].">
      <j1 rule="para" parents="1310 4455"/>
    </justification>
  </clause>

  <clause id="4458">
    <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(456,a,4457,a),flip(a)].">
      <j1 rule="hyper" parents="456 4457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(4457(a,1),456(a,1))].">
      <j1 rule="para" parents="4457 456"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,w),y,z) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(30(a,1),4458(a,1,2))].">
      <j1 rule="para" parents="30 4458"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      L(x \ 1,x,y) \ L((y * x) \ y,z,u) = L((x \ 1) \ L(x \ 1,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(225(a,1),4458(a,1,2,1))].">
      <j1 rule="para" parents="225 4458"/>
    </justification>
  </clause>

  <clause id="4462">
    <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(4458(a,1),1767(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4458 1767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4463">
    <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(4458(a,1),2015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4458 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,u,w),y,z) \ L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(4458(a,1),2024(a,1,1))].">
      <j1 rule="para" parents="4458 2024"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ L(L(T(y,x),z,u),x,x) = L(T(y,x) \ L(T(y,x),z,u),x,x)
    ]]></literal>
    <justification jstring="[para(655(a,1),4460(a,1,1))].">
      <j1 rule="para" parents="655 4460"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) \ 1 = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,824,a(flip),b,4463,a),flip(a)].">
      <j1 rule="hyper" parents="65 824 4463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      L(x,y,z) \ (L(x \ L(x,u,w),y,z) \ 1) = L(L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,4463,a(flip),b,1257,a)].">
      <j1 rule="hyper" parents="132 4463 1257"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,u,w) = L(x \ L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(30(a,1),4463(a,1,1))].">
      <j1 rule="para" parents="30 4463"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w),x \ 1,x) \ L(L(x,y,z),u,w) = L((x \ 1) * (x * (L(x,y,z) \ L(x,y,z))),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(1929(a,2),4463(a,2,1,1))].">
      <j1 rule="para" parents="1929 4463"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,w),y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(30(a,1),4459(a,1,2))].">
      <j1 rule="para" parents="30 4459"/>
    </justification>
  </clause>

  <clause id="4471">
    <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(325,a,1768,a(flip),b,4462,a),flip(a)].">
      <j1 rule="hyper" parents="325 1768 4462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      L(x \ 1,x,y) \ L((y * x) \ y,z,u) = L(x \ (1 * L(1 \ x,z,u)),x,y)
    ]]></literal>
    <justification jstring="[para(1410(a,1),4461(a,2,1))].">
      <j1 rule="para" parents="1410 4461"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      L(x \ 1,x,y) \ L((y * x) \ y,z,u) = L(x \ (1 * L(x,z,u)),x,y)
    ]]></literal>
    <justification jstring="[para(67(a,1),4472(a,2,1,2,2,1))].">
      <j1 rule="para" parents="67 4472"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      L(x \ 1,x,y) \ L((y * x) \ y,z,u) = L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),4473(a,2,1,2))].">
      <j1 rule="para" parents="7 4473"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      (L(x \ 1,x,x \ y) \ L(((x \ y) * x) \ (x \ y),z,u)) * y = (y / x) * (x * T(x \ L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(4474(a,2),1580(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4474 1580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4476">
    <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(456,a,4456,a),flip(a)].">
      <j1 rule="hyper" parents="456 4456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4477">
    <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(2410(a,1),4476(a,1,1))].">
      <j1 rule="para" parents="2410 4476"/>
    </justification>
  </clause>

  <clause id="4478">
    <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(2410(a,1),4477(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2410 4477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4479">
    <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(325,a,4476,a(flip),b,4478,a),flip(a)].">
      <j1 rule="hyper" parents="325 4476 4478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4481">
    <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(944(a,1),4479(a,2,1))].">
      <j1 rule="para" parents="944 4479"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(944(a,1),4481(a,1,1))].">
      <j1 rule="para" parents="944 4481"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      L(x,y,(y * x) \ 1) \ R(L(x,y,(y * x) \ 1),z,u) = ((1 / (y * x)) * y) * R(L(x,y,y * x),z,u)
    ]]></literal>
    <justification jstring="[para(1499(a,1),1823(a,2,2,1))].">
      <j1 rule="para" parents="1499 1823"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      L(x,y,(y * x) \ 1) \ R(L(x,y,(y * x) \ 1),z,u) = ((1 / (y * x)) * y) * L(R(x,z,u),y,y * x)
    ]]></literal>
    <justification jstring="[para(29(a,1),4483(a,2,2))].">
      <j1 rule="para" parents="29 4483"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      L(x,y,(y * x) \ 1) \ R(L(x,y,(y * x) \ 1),z,u) = (1 / (y * x)) * (y * R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1496,a(flip),b,4484,a),flip(a)].">
      <j1 rule="hyper" parents="325 1496 4484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      L(x,y,y * x) \ R(L(x,y,(y * x) \ 1),z,u) = (1 / (y * x)) * (y * R(x,z,u))
    ]]></literal>
    <justification jstring="[para(1499(a,1),4485(a,1,1))].">
      <j1 rule="para" parents="1499 4485"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      L(x,y,y * x) \ R(L(x,y,y * x),z,u) = (1 / (y * x)) * (y * R(x,z,u))
    ]]></literal>
    <justification jstring="[para(1499(a,1),4486(a,1,2,1))].">
      <j1 rule="para" parents="1499 4486"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      L(x,y,y * x) \ L(R(x,z,u),y,y * x) = (1 / (y * x)) * (y * R(x,z,u))
    ]]></literal>
    <justification jstring="[para(29(a,1),4487(a,1,2))].">
      <j1 rule="para" parents="29 4487"/>
    </justification>
  </clause>

  <clause id="4489">
    <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(325,a,1956,a(flip),b,1959,a),flip(a)].">
      <j1 rule="hyper" parents="325 1956 1959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4490">
    <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(2946(a,2),4489(a,1,1))].">
      <j1 rule="para" parents="2946 4489"/>
    </justification>
  </clause>

  <clause id="4491">
    <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(4490(a,1),291(a,1))].">
      <j1 rule="para" parents="4490 291"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(4491,a,2260,a)].">
      <j1 rule="hyper" parents="4491 2260"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3354(a,1),4492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3354 4492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(2080(a,1),4493(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2080 4493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2080(a,1),4494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2080 4494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(135,a,157,a(flip),b,4496,a(flip))].">
      <j1 rule="hyper" parents="135 157 4496"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,106,a,b,4498,a)].">
      <j1 rule="hyper" parents="65 106 4498"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(2104(a,2),4499(a,1,2))].">
      <j1 rule="para" parents="2104 4499"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4500(a,1),408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4500 408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(455,a,4501,a)].">
      <j1 rule="hyper" parents="455 4501"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(2135(a,1),4501(a,1,1))].">
      <j1 rule="para" parents="2135 4501"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(4502(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="4502 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      L(x,K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(153(a,1),4504(a,1,3))].">
      <j1 rule="para" parents="153 4504"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(4505,a,2110,a)].">
      <j1 rule="hyper" parents="4505 2110"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(325,a,2618,a(flip),b,4506,a),flip(a)].">
      <j1 rule="hyper" parents="325 2618 4506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      T(x,y) \ (x * (T(x,y) * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(325,a,2184,a(flip),b,4506,a),flip(a)].">
      <j1 rule="hyper" parents="325 2184 4506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      (x * y) / (x * (T(x,z) \ y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,2126,a,b,4506,a)].">
      <j1 rule="hyper" parents="201 2126 4506"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,2618,a(flip),b,4506,a)].">
      <j1 rule="hyper" parents="201 2618 4506"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      T(x,y) * (K(x,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(148,a,4506,a)].">
      <j1 rule="hyper" parents="148 4506"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(137,a,2126,a,b,4506,a)].">
      <j1 rule="hyper" parents="137 2126 4506"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,22,a,b,4506,a)].">
      <j1 rule="hyper" parents="137 22 4506"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2647,a(flip),b,4506,a)].">
      <j1 rule="hyper" parents="137 2647 4506"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(137,a,2618,a(flip),b,4506,a)].">
      <j1 rule="hyper" parents="137 2618 4506"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2485,a(flip),b,4506,a)].">
      <j1 rule="hyper" parents="137 2485 4506"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,9,a(flip),b,4506,a),flip(a)].">
      <j1 rule="hyper" parents="137 9 4506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,76,a(flip),b,4506,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 76 4506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),4506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 4506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,2662,a(flip),b,4507,a),flip(a)].">
      <j1 rule="hyper" parents="137 2662 4507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      T(x,y) \ (z * x) = K(y,x) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,232,a(flip),b,4507,a)].">
      <j1 rule="hyper" parents="65 232 4507"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,4507,a(flip),b,2648,a),flip(a)].">
      <j1 rule="hyper" parents="137 4507 2648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      x * (K(x * y,x) * y) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,4507,a(flip),b,2644,a(flip))].">
      <j1 rule="hyper" parents="137 4507 2644"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),4507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 4507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      T(x / y,z) \ x = K(z,x / y) * y
    ]]></literal>
    <justification jstring="[para(12(a,1),4507(a,1,2))].">
      <j1 rule="para" parents="12 4507"/>
    </justification>
  </clause>

  <clause id="4528">
    <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),4507(a,1,1))].">
      <j1 rule="para" parents="25 4507"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(2094(a,2),4507(a,1,2))].">
      <j1 rule="para" parents="2094 4507"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      T(x,y) / (K(z,x) * K(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2094(a,2),4510(a,1,1))].">
      <j1 rule="para" parents="2094 4510"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(132,a,77,a(flip),b,4511,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 77 4511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(549,a,4515,a),flip(a)].">
      <j1 rule="hyper" parents="549 4515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      R(T(x,y),K(y,x) * z,(x * z) \ u) \ u = (K(y,x) * z) * ((T(x,y) * (K(y,x) * z)) \ u)
    ]]></literal>
    <justification jstring="[para(4515(a,1),483(a,1,1,3,1))].">
      <j1 rule="para" parents="4515 483"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      x * (K(x,y) * L(T(x,y) \ z,u,w)) = L(z / T(x,y),u,w) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,587,a,b,4517,a),flip(a)].">
      <j1 rule="hyper" parents="325 587 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      x * (K(x,y) * L(x \ K(y,x),z,u)) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2639,a(flip),b,4517,a),flip(a)].">
      <j1 rule="hyper" parents="325 2639 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(325,a,2125,a(flip),b,4517,a),flip(a)].">
      <j1 rule="hyper" parents="325 2125 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(245,a,2236,a,b,4517,a)].">
      <j1 rule="hyper" parents="245 2236 4517"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,u)) = x \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,2227,a(flip),b,4517,a),flip(a)].">
      <j1 rule="hyper" parents="132 2227 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2739,a,b,4517,a)].">
      <j1 rule="hyper" parents="36 2739 4517"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(36,a,3882,a(flip),b,4517,a),flip(a)].">
      <j1 rule="hyper" parents="36 3882 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      L(x,y,z) * (K(L(x,y,z),u) * w) = L(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),4517(a,2,1))].">
      <j1 rule="para" parents="25 4517"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      (x * (K(x,y) * (z * u))) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4517(a,1),626(a,1,2,1))].">
      <j1 rule="para" parents="4517 626"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(2125(a,2),4517(a,1,2))].">
      <j1 rule="para" parents="2125 4517"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(3640(a,1),4517(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3640 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      T(x,T(y,z)) * (z * x) = x * (z * T(x,y))
    ]]></literal>
    <justification jstring="[para(3679(a,1),4517(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3679 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      (x \ y) / (T(x,z) \ y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(202,a,4519,a)].">
      <j1 rule="hyper" parents="202 4519"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,3604,a(flip),b,4519,a)].">
      <j1 rule="hyper" parents="65 3604 4519"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      (x \ y) \ (K(x,z) * u) = (T(x,z) \ y) \ u
    ]]></literal>
    <justification jstring="[para(4519(a,1),674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4519 674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[para(4519(a,1),2653(a,1,2))].">
      <j1 rule="para" parents="4519 2653"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      K(x,y) * ((y \ z) * u) = (T(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(4519(a,1),2667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4519 2667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,3161,a,b,4526,a)].">
      <j1 rule="hyper" parents="65 3161 4526"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,4526,a(flip),b,2116,a)].">
      <j1 rule="hyper" parents="136 4526 2116"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      L(x,y,T(z,u) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(4526(a,1),1541(a,1,3))].">
      <j1 rule="para" parents="4526 1541"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      L(x,y,T(z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(4526(a,1),1542(a,1,3))].">
      <j1 rule="para" parents="4526 1542"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      a(T(x,y) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4526(a,1),1865(a,1,1))].">
      <j1 rule="para" parents="4526 1865"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      a(T(x,y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(4526(a,1),1866(a,1,1))].">
      <j1 rule="para" parents="4526 1866"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u
    ]]></literal>
    <justification jstring="[para(4526(a,1),2665(a,1,2,1))].">
      <j1 rule="para" parents="4526 2665"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      K(R(x,y,z),u) * (R(T(x,u),y,z) \ w) = R(x,y,z) \ w
    ]]></literal>
    <justification jstring="[para(27(a,2),4532(a,1,2,1))].">
      <j1 rule="para" parents="27 4532"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) \ y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(114(a,1),4532(a,1,2,1))].">
      <j1 rule="para" parents="114 4532"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(4532(a,1),2236(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4532 2236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4532(a,1),2677(a,1,2))].">
      <j1 rule="para" parents="4532 2677"/>
    </justification>
  </clause>

  <clause id="4569">
    <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),4551(a,1,2,1))].">
      <j1 rule="para" parents="25 4551"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      T(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(4508(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4508 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      (x * (T(x,y) \ z)) * R((x * (T(x,y) \ z)) \ (x * z),u,w) = R(T(x,y),u,w) * (x * (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(4509(a,1),592(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4509 592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      T(x,y) * (R(T(x,y),z,u) * (x * (T(x,y) \ w))) = R(T(x,y),z,u) * (x * w)
    ]]></literal>
    <justification jstring="[para(4512(a,1),956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4512 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      K(x,y) * ((y * (x * z)) / u) = (y * (T(x,y) * z)) / u
    ]]></literal>
    <justification jstring="[para(4514(a,1),2707(a,1,2,1))].">
      <j1 rule="para" parents="4514 2707"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4515(a,1),4514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4515 4514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      T(x,y) * (y * (y * x)) = x * (y * (x * y))
    ]]></literal>
    <justification jstring="[para(4516(a,1),4514(a,1,2))].">
      <j1 rule="para" parents="4516 4514"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2705,a,b,4523,a)].">
      <j1 rule="hyper" parents="65 2705 4523"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(2815,a,4524,a),flip(a)].">
      <j1 rule="hyper" parents="2815 4524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2462,a,b,4524,a)].">
      <j1 rule="hyper" parents="65 2462 4524"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * (((x \ y) \ 1) \ z)) = y * ((((x \ y) \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2916,a(flip),b,4524,a),flip(a)].">
      <j1 rule="hyper" parents="65 2916 4524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2476,a(flip),b,4524,a)].">
      <j1 rule="hyper" parents="65 2476 4524"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      ((x / y) * z) / (K(y,y \ x) * z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(135,a,2566,a(flip),b,4524,a(flip))].">
      <j1 rule="hyper" parents="135 2566 4524"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4524(a,1),2496(a,1,2))].">
      <j1 rule="para" parents="4524 2496"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(3035(a,1),4525(a,1,2,1))].">
      <j1 rule="para" parents="3035 4525"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      x * (y * K(x * y,x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(3162(a,1),4525(a,1,2))].">
      <j1 rule="para" parents="3162 4525"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,3157,a(flip),b,4527,a),flip(a)].">
      <j1 rule="hyper" parents="325 3157 4527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,3600,a(flip),b,4529,a)].">
      <j1 rule="hyper" parents="137 3600 4529"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      x / (K(y,x * K(z,x)) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(1589(a,1),4531(a,1,1))].">
      <j1 rule="para" parents="1589 4531"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      K(x,y) * (x \ ((x / z) * u)) = x \ ((T(x,y) / z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,2197,a(flip),b,4539,a),flip(a)].">
      <j1 rule="hyper" parents="132 2197 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[hyper(36,a,2593,a,b,4539,a),flip(a)].">
      <j1 rule="hyper" parents="36 2593 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2821,a(flip),b,4541,a),flip(a)].">
      <j1 rule="hyper" parents="65 2821 4541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,3537,a(flip),b,4541,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 3537 4541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4541(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4594">
    <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),4541(a,2,2))].">
      <j1 rule="para" parents="25 4541"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),4544(a,1,1))].">
      <j1 rule="para" parents="1581 4544"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(132,a,2317,a(flip),b,4548,a)].">
      <j1 rule="hyper" parents="132 2317 4548"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y)
    ]]></literal>
    <justification jstring="[para(4548(a,1),2747(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4548 2747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      T(x,y) \ (y \ T(x,y)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(2644(a,1),4555(a,1,2))].">
      <j1 rule="para" parents="2644 4555"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      (x \ L(T(x,y),z,u)) * K(w,x) = T(x,w) \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(220(a,1),4557(a,1,2,2))].">
      <j1 rule="para" parents="220 4557"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      L(x,y,R(T(z,u),w,v5) \ v6) = L(x,y,R(z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(27(a,2),4560(a,1,3,1))].">
      <j1 rule="para" parents="27 4560"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      L(x,y,(z / u) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(115(a,1),4560(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="115 4560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      a((x / y) \ z,u,w) = a((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(115(a,1),4562(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="115 4562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      a((((x * x) \ y) * x) \ z,u,w) = a((y * (x \ 1)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(885(a,1),4562(a,1,1,1))].">
      <j1 rule="para" parents="885 4562"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,3537,a(flip),b,4576,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 3537 4576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(455,a,4578,a)].">
      <j1 rule="hyper" parents="455 4578"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y / (x \ 1)) / y) = x * (K(y,x) * ((T(y,x) * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,4252,a,b,4578,a)].">
      <j1 rule="hyper" parents="65 4252 4578"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(2691(a,2),4578(a,1,1))].">
      <j1 rule="para" parents="2691 4578"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      L(x,K(y,z),z) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,153,a,b,4607,a),flip(a)].">
      <j1 rule="hyper" parents="325 153 4607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,2850,a(flip),b,4580,a),flip(a)].">
      <j1 rule="hyper" parents="65 2850 4580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K((y * z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4580,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="132 4580 93"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      R(x \ y,z,u) * (K(x,R(x \ y,z,u)) * w) = R(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[para(613(a,1),4580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="613 4580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[para(2548(a,1),4580(a,2,2))].">
      <j1 rule="para" parents="2548 4580"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(140,a,4584,a)].">
      <j1 rule="hyper" parents="140 4584"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,2875,a,b,4585,a)].">
      <j1 rule="hyper" parents="325 2875 4585"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      T(T(x,y),z) * T(y,x) = T(x,z) * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(4586(a,1),4132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4586 4132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ K(y,z)) = T(x \ K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2283,a,b,4593,a)].">
      <j1 rule="hyper" parents="65 2283 4593"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,4593,a(flip),b,926,a),flip(a)].">
      <j1 rule="hyper" parents="132 4593 926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) = K(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,4606,a,b,4517,a)].">
      <j1 rule="hyper" parents="132 4606 4517"/>
    </justification>
  </clause>

  <clause id="4622">
    <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(3638(a,2),4615(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3638 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(82(a,1),4616(a,2,1,1))].">
      <j1 rule="para" parents="82 4616"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(85(a,1),4616(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 4616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(114(a,2),4624(a,1,2,1))].">
      <j1 rule="para" parents="114 4624"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      L(x,y,z) / T(x,u) = T(x,u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1754(a,1),4624(a,1,2,1))].">
      <j1 rule="para" parents="1754 4624"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      x / (x / T(y,z)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(202,a,4625,a)].">
      <j1 rule="hyper" parents="202 4625"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(3593(a,1),4568(a,1,1))].">
      <j1 rule="para" parents="3593 4568"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(3582(a,2),4545(a,1,1))].">
      <j1 rule="para" parents="3582 4545"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      L((x * y) \ 1,x * y,T(y,T(z,x))) = (y * (x * T(y,z))) \ T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(4550(a,1),225(a,2,1))].">
      <j1 rule="para" parents="4550 225"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      T(x,y) \ (x * ((x \ z) * u)) = (T(x,y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,4507,a,b,4556,a)].">
      <j1 rule="hyper" parents="65 4507 4556"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = z \ ((x \ z) * x)
    ]]></literal>
    <justification jstring="[para(4564(a,1),2235(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4564 2235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,94,a(flip),b,4637,a),flip(a)].">
      <j1 rule="hyper" parents="325 94 4637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(3790,a,4638,a)].">
      <j1 rule="hyper" parents="3790 4638"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      K(x \ (T(x,y) * z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(3031,a,4638,a),flip(a)].">
      <j1 rule="hyper" parents="3031 4638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      (x / T(y,z)) * K(y \ x,y) = T(x / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(137,a,4640,a(flip),b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 4640 2104"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(4518(a,1),4641(a,1,1))].">
      <j1 rule="para" parents="4518 4641"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3100,a(flip),b,4646,a)].">
      <j1 rule="hyper" parents="65 3100 4646"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(2114(a,1),4646(a,1,1))].">
      <j1 rule="para" parents="2114 4646"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(4646(a,1),2248(a,1,1))].">
      <j1 rule="para" parents="4646 2248"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(2472(a,1),4646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2472 4646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(2619(a,1),4646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2619 4646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      K(T(x,y) * z,y) = K(x * z,y)
    ]]></literal>
    <justification jstring="[para(2650(a,1),4646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2650 4646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(3679(a,1),4646(a,1,1))].">
      <j1 rule="para" parents="3679 4646"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      K(((x * y) / x) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(4544(a,2),4646(a,1,1))].">
      <j1 rule="para" parents="4544 4646"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      T(x * K(y,x),y * K(x,z)) = x
    ]]></literal>
    <justification jstring="[para(4647(a,1),1589(a,1,1,2))].">
      <j1 rule="para" parents="4647 1589"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4647(a,1),2608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4647 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2847(a,1),4647(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2847 4647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * K(z,u)) = T(y * K(z,u),K(x,z))
    ]]></literal>
    <justification jstring="[para(4647(a,1),3584(a,1,1,2))].">
      <j1 rule="para" parents="4647 3584"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(4648(a,1),3031(a,1))].">
      <j1 rule="para" parents="4648 3031"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,3035,a(flip),b,4651,a),flip(a)].">
      <j1 rule="hyper" parents="325 3035 4651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4651(a,1),1597(a,1,1,2))].">
      <j1 rule="para" parents="4651 1597"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4651(a,1),2773(a,1,1))].">
      <j1 rule="para" parents="4651 2773"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(3147(a,1),4652(a,1,1,1))].">
      <j1 rule="para" parents="3147 4652"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x * K(w,u),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2993,a,b,4661,a)].">
      <j1 rule="hyper" parents="325 2993 4661"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      K(x \ T(x * y,x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(4615(a,2),4661(a,1,1))].">
      <j1 rule="para" parents="4615 4661"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4659(a,1),1592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4659 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(93(a,1),4674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="93 4674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(312(a,1),4674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="312 4674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(314(a,1),4674(a,1,2))].">
      <j1 rule="para" parents="314 4674"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,x),u,w) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(4674(a,1),242(a,1,2,1))].">
      <j1 rule="para" parents="4674 242"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(2093(a,1),4674(a,1,2))].">
      <j1 rule="para" parents="2093 4674"/>
    </justification>
  </clause>

  <clause id="4680">
    <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(4674(a,1),2509(a,1,2,1))].">
      <j1 rule="para" parents="4674 2509"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(4674(a,1),3649(a,1,2))].">
      <j1 rule="para" parents="4674 3649"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      T(x,T(y * K(x,z),u)) = (u * T(x,y)) / T(u,x)
    ]]></literal>
    <justification jstring="[para(4674(a,1),3737(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4674 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      T(x,T(y,x) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4557(a,1),4674(a,1,2))].">
      <j1 rule="para" parents="4557 4674"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(4675(a,2),603(a,1,2))].">
      <j1 rule="para" parents="4675 603"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      T(x,x * T(y / x,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(423(a,1),4675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="423 4675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(4675(a,2),608(a,1,2,1))].">
      <j1 rule="para" parents="4675 608"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4676(a,1),292(a,1,2))].">
      <j1 rule="para" parents="4676 292"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4676(a,1),756(a,1,1))].">
      <j1 rule="para" parents="4676 756"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4676(a,1),2503(a,1,1,2))].">
      <j1 rule="para" parents="4676 2503"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      L(T(x,y / x),y / x,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,599,a,b,4677,a)].">
      <j1 rule="hyper" parents="65 599 4677"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2608,a(flip),b,4660,a),flip(a)].">
      <j1 rule="hyper" parents="325 2608 4660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2951,a,4702,a),flip(a)].">
      <j1 rule="hyper" parents="2951 4702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(93(a,1),4702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="93 4702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2847(a,1),4702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2847 4702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2848(a,2),4702(a,1,2))].">
      <j1 rule="para" parents="2848 4702"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3105(a,1),4702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3105 4702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3106(a,1),4702(a,1,2))].">
      <j1 rule="para" parents="3106 4702"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4557(a,1),4702(a,1,2))].">
      <j1 rule="para" parents="4557 4702"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4010,a,b,4705,a)].">
      <j1 rule="hyper" parents="65 4010 4705"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(89(a,1),4705(a,2,2))].">
      <j1 rule="para" parents="89 4705"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,y * z))
    ]]></literal>
    <justification jstring="[para(4705(a,2),3580(a,1,2))].">
      <j1 rule="para" parents="4705 3580"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,y * K(w,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,2957,a,b,4707,a)].">
      <j1 rule="hyper" parents="325 2957 4707"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      K(x,K(x,y) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3074(a,1),4707(a,1,2))].">
      <j1 rule="para" parents="3074 4707"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      K(x,y / (K(z,x) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2962,a(flip),b,4708,a)].">
      <j1 rule="hyper" parents="65 2962 4708"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      K(T(x,y),K(z,x) * u) = K(T(x,y),u)
    ]]></literal>
    <justification jstring="[para(3147(a,1),4709(a,1,2,1))].">
      <j1 rule="para" parents="3147 4709"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(4710(a,1),3580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4710 3580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      K(x,K(K(x,y) \ z,u)) = K(K(x,z),u)
    ]]></literal>
    <justification jstring="[para(4719(a,1),3563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4719 3563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3390,a,b,4666,a)].">
      <j1 rule="hyper" parents="65 3390 4666"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      K(x,y) = T(y * x,y) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1117,a,b,4672,a),flip(a)].">
      <j1 rule="hyper" parents="65 1117 4672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4675,a(flip),b,4679,a),flip(a)].">
      <j1 rule="hyper" parents="325 4675 4679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      K(x,y \ L(K(z,x),u,w)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(2310(a,1),4704(a,1,2,2))].">
      <j1 rule="para" parents="2310 4704"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(115(a,1),4711(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(4731(a,1),3769(a,2,2))].">
      <j1 rule="para" parents="4731 3769"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 4734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(2472(a,1),4665(a,1,1))].">
      <j1 rule="para" parents="2472 4665"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2467,a,4668,a)].">
      <j1 rule="hyper" parents="2467 4668"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(4668(a,1),4046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4668 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4671(a,1),2994(a,1))].">
      <j1 rule="para" parents="4671 2994"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,1595,a,b,4686,a(flip))].">
      <j1 rule="hyper" parents="37 1595 4686"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,y * T(T(y,x) \ x,z)) = L(y,T(x / T(y,x),z),y) * T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2722(a,1),4686(a,1,2,2))].">
      <j1 rule="para" parents="2722 4686"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,114,a(flip),b,4693,a),flip(a)].">
      <j1 rule="hyper" parents="325 114 4693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      L(T(x,x \ y),y / x,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2510(a,1),4695(a,1,1))].">
      <j1 rule="para" parents="2510 4695"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4718(a,1),3002(a,1))].">
      <j1 rule="para" parents="4718 3002"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4744,a(flip),b,4517,a),flip(a)].">
      <j1 rule="hyper" parents="132 4744 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4744,a(flip),b,3927,a),flip(a)].">
      <j1 rule="hyper" parents="132 4744 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4744(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4744 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * x) = L(x,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(2831(a,1),4748(a,1,1))].">
      <j1 rule="para" parents="2831 4748"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(4750(a,1),2960(a,1,2,1))].">
      <j1 rule="para" parents="4750 2960"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(93(a,1),4754(a,1,2))].">
      <j1 rule="para" parents="93 4754"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(4010(a,2),4761(a,1))].">
      <j1 rule="para" parents="4010 4761"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      (x * ((y \ x) * y)) / x = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4657(a,1),4279(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4657 4279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[para(2650(a,1),4669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2650 4669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(2472(a,1),4720(a,1,2,2))].">
      <j1 rule="para" parents="2472 4720"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(2488(a,1),4720(a,1,2,2))].">
      <j1 rule="para" parents="2488 4720"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3580,a,b,4726,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      K(x,K(K(x,y) \ z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3563,a(flip),b,4728,a),flip(a)].">
      <j1 rule="hyper" parents="325 3563 4728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,4048,a(flip),b,4732,a(flip))].">
      <j1 rule="hyper" parents="41 4048 4732"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,4773,a)].">
      <j1 rule="hyper" parents="140 4773"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4773,a(flip),b,2980,a)].">
      <j1 rule="hyper" parents="132 4773 2980"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4773(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4773 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      x \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(4773(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4773 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      K(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(R(x,L(y,z,u),x),R(x,L(y,z,u),x) * y)
    ]]></literal>
    <justification jstring="[para(4773(a,1),4146(a,1,2))].">
      <j1 rule="para" parents="4773 4146"/>
    </justification>
  </clause>

  <clause id="4779">
    <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(4773(a,1),4451(a,2,1))].">
      <j1 rule="para" parents="4773 4451"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4774(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(4774(a,1),466(a,1,1))].">
      <j1 rule="para" parents="4774 466"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,29,a,b,4781,a)].">
      <j1 rule="hyper" parents="65 29 4781"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      (L(x,y,x) * y) * x = x * (y * x)
    ]]></literal>
    <justification jstring="[para(4781(a,1),408(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4781 408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[para(4782(a,1),309(a,1,1,1))].">
      <j1 rule="para" parents="4782 309"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4782(a,1),2957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4782 2957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4782(a,1),2973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4782 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4782(a,1),2993(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4782 2993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(4782(a,1),2979(a,1,2))].">
      <j1 rule="para" parents="4782 2979"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,w,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2957,a,b,4785,a)].">
      <j1 rule="hyper" parents="325 2957 4785"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      T(x,K(y,L(z,u,z))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(4785(a,2),3617(a,1,2))].">
      <j1 rule="para" parents="4785 3617"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4610(a,1),4785(a,1,2))].">
      <j1 rule="para" parents="4610 4785"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4610(a,1),4786(a,1,2))].">
      <j1 rule="para" parents="4610 4786"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(325,a,3164,a,b,4787,a),flip(a)].">
      <j1 rule="hyper" parents="325 3164 4787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,w,x),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2993,a,b,4787,a)].">
      <j1 rule="hyper" parents="325 2993 4787"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3914,a(flip),b,4787,a)].">
      <j1 rule="hyper" parents="65 3914 4787"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(4787(a,1),2112(a,1,1))].">
      <j1 rule="para" parents="4787 2112"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,2957,a,b,4795,a),flip(a)].">
      <j1 rule="hyper" parents="325 2957 4795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1545,a,b,4795,a)].">
      <j1 rule="hyper" parents="65 1545 4795"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,4795,a(flip),b,4391,a(flip))].">
      <j1 rule="hyper" parents="137 4795 4391"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(469(a,1),4791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="469 4791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = v6
    ]]></literal>
    <justification jstring="[para(4791(a,2),3585(a,1,2))].">
      <j1 rule="para" parents="4791 3585"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ (K(y,z) * w)) = T(x,u \ w)
    ]]></literal>
    <justification jstring="[para(102(a,1),4792(a,1,2))].">
      <j1 rule="para" parents="102 4792"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,z) = T(x,y) \ K(x,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,4799,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 4799 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      K(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4789(a,1),3002(a,1))].">
      <j1 rule="para" parents="4789 3002"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4794(a,1),2994(a,1))].">
      <j1 rule="para" parents="4794 2994"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4798(a,2),3002(a,1))].">
      <j1 rule="para" parents="4798 3002"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(1556(a,1),4806(a,1,2))].">
      <j1 rule="para" parents="1556 4806"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4780(a,1),2993(a,1,1))].">
      <j1 rule="para" parents="4780 2993"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4780(a,1),2994(a,1,1))].">
      <j1 rule="para" parents="4780 2994"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(245,a,4783,a,b,xx)].">
      <j1 rule="hyper" parents="245 4783"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4784(a,1),2562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4784 2562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) = (x * (x * T(T(x,y) \ y,z))) / x
    ]]></literal>
    <justification jstring="[para(2722(a,1),4784(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2722 4784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      K(K(x,y) \ z,K(x,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(3585,a,4772,a)].">
      <j1 rule="hyper" parents="3585 4772"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(137,a,4788,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 4788 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      K(x,y) \ T(x,x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,599,a(flip),b,4797,a)].">
      <j1 rule="hyper" parents="132 599 4797"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      K(x,y) * (x \ L(x,z,x)) = x \ L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4797,a(flip),b,4539,a),flip(a)].">
      <j1 rule="hyper" parents="132 4797 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4797,a(flip),b,2125,a)].">
      <j1 rule="hyper" parents="132 4797 2125"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(2684,a,4820,a)].">
      <j1 rule="hyper" parents="2684 4820"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2467,a,4823,a)].">
      <j1 rule="hyper" parents="2467 4823"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(4823(a,1),4046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4823 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,4824,a(flip),b,3927,a),flip(a)].">
      <j1 rule="hyper" parents="132 4824 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(489,a,4801,a)].">
      <j1 rule="hyper" parents="489 4801"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4513,a,b,4801,a)].">
      <j1 rule="hyper" parents="325 4513 4801"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,4801,a(flip),b,2087,a)].">
      <j1 rule="hyper" parents="136 4801 2087"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(4827(a,1),408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4827 408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4827(a,1),4203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4827 4203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4055,a(flip),b,4832,a)].">
      <j1 rule="hyper" parents="65 4055 4832"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      R(x,y,(x \ z) \ z) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),4832(a,1,3))].">
      <j1 rule="para" parents="114 4832"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4833(a,2,2))].">
      <j1 rule="para" parents="9 4833"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(236(a,1),4836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="236 4836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      K(K(x,y) \ z,T(K(x,u),w)) = K(x,K(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(3111(a,1),4818(a,1,2))].">
      <j1 rule="para" parents="3111 4818"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4651(a,2),4756(a,1,2))].">
      <j1 rule="para" parents="4651 4756"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4757(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(4757(a,1),2849(a,1,1))].">
      <j1 rule="para" parents="4757 2849"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(4757(a,1),3089(a,1))].">
      <j1 rule="para" parents="4757 3089"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      K(x,T(T(y,z),z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,w,x),y) = u
    ]]></literal>
    <justification jstring="[para(4793(a,1),3683(a,1))].">
      <j1 rule="para" parents="4793 3683"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4793(a,1),4807(a,1))].">
      <j1 rule="para" parents="4793 4807"/>
    </justification>
  </clause>

  <clause id="4848">
    <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(2082(a,1),4841(a,1,2,1))].">
      <j1 rule="para" parents="2082 4841"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(137,a,4567,a(flip),b,1918,a),flip(a)].">
      <j1 rule="hyper" parents="137 4567 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      ((x \ y) \ y) * ((x \ y) * z) = x * ((x \ y) * (K(x,x \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,319,a(flip),b,4574,a)].">
      <j1 rule="hyper" parents="325 319 4574"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      a(x * (y * (z * (z * y))),u,w) = a(x * (y * (z * (y * z))),u,w)
    ]]></literal>
    <justification jstring="[para(4575(a,1),3511(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4575 3511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(132,a,10,a(flip),b,4577,a),flip(a)].">
      <j1 rule="hyper" parents="132 10 4577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(2114(a,1),4577(a,1,2))].">
      <j1 rule="para" parents="2114 4577"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      (x \ y) * (R(T(x,x \ y),z,u) * w) = (y / x) * (R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(2131(a,1),4577(a,1,2))].">
      <j1 rule="para" parents="2131 4577"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      (K(x,x \ y) * z) * K((K(x,x \ y) * z) \ ((y / x) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(4581(a,1),2691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4581 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,4590,a(flip),b,2652,a),flip(a)].">
      <j1 rule="hyper" parents="132 4590 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      L(x,y,z * ((u / w) \ v5)) = L(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(4590(a,1),3507(a,1,3,2))].">
      <j1 rule="para" parents="4590 3507"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      a(x * ((y / z) \ u),w,v5) = a(x * ((z \ y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(4590(a,1),3508(a,1,1,2))].">
      <j1 rule="para" parents="4590 3508"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      a(x * R(y,y,x),z,u) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2342,a,b,4604,a)].">
      <j1 rule="hyper" parents="65 2342 4604"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(2885,a,4609,a),flip(a)].">
      <j1 rule="hyper" parents="2885 4609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(530,a,4609,a)].">
      <j1 rule="hyper" parents="530 4609"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[hyper(535,a,4614,a),flip(a)].">
      <j1 rule="hyper" parents="535 4614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      (T(x,L(x,y,z)) \ L(x,y,z)) * R(x,u,w) = x \ (L(x,y,z) * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(4628(a,1),3467(a,1,1))].">
      <j1 rule="para" parents="4628 3467"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      (K(x,y / z) * K(K(x,z \ y),u)) / T(K(x,z \ y),u) = R(K(x,K(z,y)),K(x,z \ y),K(K(x,z \ y),u))
    ]]></literal>
    <justification jstring="[para(4634(a,1),2102(a,1,1,1))].">
      <j1 rule="para" parents="4634 2102"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      K(x,T(T(y / z,y),u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),4760(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="85 4760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      T(x,(y \ x) * y) = x
    ]]></literal>
    <justification jstring="[hyper(3503,a,4763,a)].">
      <j1 rule="hyper" parents="3503 4763"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      T(x,y * (x / y)) = x
    ]]></literal>
    <justification jstring="[para(85(a,1),4870(a,1,2,1))].">
      <j1 rule="para" parents="85 4870"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4872(a,1),3069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4872 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4873(a,1,2,2))].">
      <j1 rule="para" parents="11 4873"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      (x * y) * K(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(4874(a,1),292(a,1,2))].">
      <j1 rule="para" parents="4874 292"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = T(T(x,u),w) \ T(T(x,u) * K(x * z,T(x,u)),w)
    ]]></literal>
    <justification jstring="[para(4764(a,1),1620(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4764 1620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      (T(x,y) \ K(x,z)) \ (T(x,y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(4805(a,1),2859(a,1,1))].">
      <j1 rule="para" parents="4805 2859"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x / y,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,154,a(flip),b,4828,a),flip(a)].">
      <j1 rule="hyper" parents="325 154 4828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(4829(a,1),2096(a,1,2))].">
      <j1 rule="para" parents="4829 2096"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(4853(a,1),4771(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4853 4771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3546,a(flip),b,4650,a)].">
      <j1 rule="hyper" parents="65 3546 4650"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4646,a(flip),b,4890,a),flip(a)].">
      <j1 rule="hyper" parents="325 4646 4890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(308(a,1),4891(a,1,1))].">
      <j1 rule="para" parents="308 4891"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,4746,a(flip),b,2087,a),flip(a)].">
      <j1 rule="hyper" parents="136 4746 2087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4900">
    <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="[para(3618(a,1),4759(a,1,1))].">
      <j1 rule="para" parents="3618 4759"/>
    </justification>
  </clause>

  <clause id="4901">
    <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(3580(a,1),4813(a,1,2))].">
      <j1 rule="para" parents="3580 4813"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3935,a,b,4825,a)].">
      <j1 rule="hyper" parents="65 3935 4825"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4532(a,1),4521(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4532 4521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(4756(a,1),4611(a,1,2))].">
      <j1 rule="para" parents="4756 4611"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = (y \ R(y,x \ 1,y)) / (T(y * (x \ 1),y) / y)
    ]]></literal>
    <justification jstring="[hyper(201,a,4907,a(flip),b,379,a),flip(a)].">
      <j1 rule="hyper" parents="201 4907 379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      T(T(x,y),z) * T(y,x) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,4513,a(flip),b,4617,a),flip(a)].">
      <j1 rule="hyper" parents="325 4513 4617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      K(x \ K(y,z),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,2095,a(flip),b,4618,a)].">
      <j1 rule="hyper" parents="37 2095 4618"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      T(x,y) \ (z * L(u,x \ z,x)) = (T(x,y) \ z) * u
    ]]></literal>
    <justification jstring="[para(414(a,2),4636(a,1,2))].">
      <j1 rule="para" parents="414 4636"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      T(x,T(y * K(x,z),u)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3737,a(flip),b,4684,a),flip(a)].">
      <j1 rule="hyper" parents="325 3737 4684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(93(a,1),4912(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="93 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(T(y,x) / x,z))
    ]]></literal>
    <justification jstring="[para(2644(a,2),4687(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2644 4687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,1108,a(flip),b,4694,a),flip(a)].">
      <j1 rule="hyper" parents="37 1108 4694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(147,a,4915,a)].">
      <j1 rule="hyper" parents="147 4915"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4916(a,1),4029(a,1,1))].">
      <j1 rule="para" parents="4916 4029"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      (R(x,y,z) * u) \ ((x * u) * R(x,y,z)) = L(R(x,u,x),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2980(a,1),4776(a,1,2))].">
      <j1 rule="para" parents="2980 4776"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(2618(a,1),4802(a,1,2,1))].">
      <j1 rule="para" parents="2618 4802"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      K(x,T(y / z,u)) * K(z \ y,T(x,u)) = K(y / z,K(y,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,4410,a(flip),b,4838,a)].">
      <j1 rule="hyper" parents="65 4410 4838"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(4845,a,4035,a(flip))].">
      <j1 rule="hyper" parents="4845 4035"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(4807,a,4921,a),flip(a)].">
      <j1 rule="hyper" parents="4807 4921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),4922(a,1,1,1,1))].">
      <j1 rule="para" parents="10 4922"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = K(y \ x,z \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(4923(a,1),3280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4923 3280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4648,a(flip),b,4893,a),flip(a)].">
      <j1 rule="hyper" parents="325 4648 4893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[para(93(a,1),4927(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="93 4927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(2847(a,1),4927(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2847 4927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(3105(a,1),4927(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3105 4927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(3645(a,1),4927(a,1,1,1,2))].">
      <j1 rule="para" parents="3645 4927"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (w * K(y \ u,x)) \ w
    ]]></literal>
    <justification jstring="[para(4930(a,1),2849(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4930 2849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(470(a,1),4931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="470 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(2483(a,1),4935(a,1,1,2))].">
      <j1 rule="para" parents="2483 4935"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(4526(a,1),4935(a,1,1,2))].">
      <j1 rule="para" parents="4526 4935"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ z) = K(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(2095(a,2),4919(a,2,2,2))].">
      <j1 rule="para" parents="2095 4919"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2849,a(flip),b,4934,a),flip(a)].">
      <j1 rule="hyper" parents="325 2849 4934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(93(a,1),4943(a,1,2,1))].">
      <j1 rule="para" parents="93 4943"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(2269(a,1),4943(a,1,2,1))].">
      <j1 rule="para" parents="2269 4943"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      K(x,(y * L(K(z,x),u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(2310(a,1),4943(a,1,2,1,2))].">
      <j1 rule="para" parents="2310 4943"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(2847(a,1),4943(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2847 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(4018(a,1),4943(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4018 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4942,a(flip),b,4945,a)].">
      <j1 rule="hyper" parents="65 4942 4945"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4919,a(flip),b,4945,a)].">
      <j1 rule="hyper" parents="65 4919 4945"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(2582(a,1),4945(a,1,2,1))].">
      <j1 rule="para" parents="2582 4945"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(4142,a,4949,a)].">
      <j1 rule="hyper" parents="4142 4949"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      T(x,(y * K(x,z)) \ u) = x * K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(137,a,4947,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 4947 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(2472(a,1),4950(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2472 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      K(x,y \ (((z / x) * u) * w)) = K(x,y \ (((x \ z) * u) * w))
    ]]></literal>
    <justification jstring="[para(2810(a,1),4950(a,1,2,2))].">
      <j1 rule="para" parents="2810 4950"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(2696(a,1),4950(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2696 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3640(a,1),4950(a,1,2,2))].">
      <j1 rule="para" parents="3640 4950"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(4532(a,1),4950(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4532 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3702,a,4952,a),flip(a)].">
      <j1 rule="hyper" parents="3702 4952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,4060,a(flip),b,4955,a),flip(a)].">
      <j1 rule="hyper" parents="325 4060 4955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(4004(a,1),4958(a,1,2,2))].">
      <j1 rule="para" parents="4004 4958"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      T(x,(y * K(x,z)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,4953,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 4953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3105(a,1),4963(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3105 4963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4804,a(flip),b,4964,a),flip(a)].">
      <j1 rule="hyper" parents="65 4804 4964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      T(x,y \ (z * x)) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(2472(a,1),4965(a,1,2,2))].">
      <j1 rule="para" parents="2472 4965"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2483(a,1),4965(a,1,2,2))].">
      <j1 rule="para" parents="2483 4965"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      T(x,y \ (z / x)) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(2554(a,1),4965(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2554 4965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(2635(a,1),4965(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2635 4965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(3207,a,4970,a)].">
      <j1 rule="hyper" parents="3207 4970"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u \ (x * w)),y,z) = K(L(x,y,z),u \ (w * x))
    ]]></literal>
    <justification jstring="[para(4967(a,1),2106(a,1,2,1))].">
      <j1 rule="para" parents="4967 2106"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4968(a,2),2888(a,1))].">
      <j1 rule="para" parents="4968 2888"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(2842(a,1),4960(a,1,2,1))].">
      <j1 rule="para" parents="2842 4960"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      K(x,(y * (z * K(u,x))) \ w) = K(x,(y * z) \ w)
    ]]></literal>
    <justification jstring="[para(100(a,1),4946(a,1,2,1))].">
      <j1 rule="para" parents="100 4946"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(4948(a,1),4122(a,1,2,2))].">
      <j1 rule="para" parents="4948 4122"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      K(x,y \ (z * (K(x,u) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(2619(a,1),4957(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2619 4957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,x)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(3109(a,1),4957(a,1,2,2,2))].">
      <j1 rule="para" parents="3109 4957"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(65,a,3331,a(flip),b,4962,a),flip(a)].">
      <j1 rule="hyper" parents="65 3331 4962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      K(x,(y * (K(x,z) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(3073(a,1),4975(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3073 4975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      K(x,(y * (K(x,z) * u)) \ (y * (u * w))) = K(x,L(w,K(x,z) * u,y))
    ]]></literal>
    <justification jstring="[para(629(a,1),4977(a,1,2)),flip(a)].">
      <j1 rule="para" parents="629 4977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      K(x \ (y * (z * K(u,w))),w) = (v5 * K(w,x \ (y * z))) \ v5
    ]]></literal>
    <justification jstring="[para(4978(a,1),2849(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4978 2849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4690(a,1),1944(a,1,1))].">
      <j1 rule="para" parents="4690 1944"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(4692,a,4917,a),flip(a)].">
      <j1 rule="hyper" parents="4692 4917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      L(x,x \ y,x) = y / (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,414,a,b,4984,a)].">
      <j1 rule="hyper" parents="36 414 4984"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4629,a(flip),b,4985,a)].">
      <j1 rule="hyper" parents="325 4629 4985"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(195,a,4985,a(flip))].">
      <j1 rule="hyper" parents="195 4985"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      (x / (x / y)) \ L(y,y \ x,y) = K(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4986,a(flip),b,2094,a(flip))].">
      <j1 rule="hyper" parents="132 4986 2094"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(2883,a,4895,a)].">
      <j1 rule="hyper" parents="2883 4895"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      L((T(x,y) \ z) \ u,x \ z,x) = z \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(36,a,1242,a(flip),b,4911,a(flip))].">
      <j1 rule="hyper" parents="36 1242 4911"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4911(a,1),74(a,1,2))].">
      <j1 rule="para" parents="4911 74"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1577,a,4991,a)].">
      <j1 rule="hyper" parents="1577 4991"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1931,a(flip),b,4992,a)].">
      <j1 rule="hyper" parents="65 1931 4992"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      T(L(L(x * K(y,x),y,x * K(y,x)),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(2513(a,1),4983(a,2,2))].">
      <j1 rule="para" parents="2513 4983"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      (x / (x / y)) \ L(y,y \ x,y) = K((x / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2461,a(flip),b,4988,a),flip(a)].">
      <j1 rule="hyper" parents="325 2461 4988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,3923,a(flip),b,4989,a)].">
      <j1 rule="hyper" parents="65 3923 4989"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      K(x,y) = (y / (y / x)) \ L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,644,a(flip),b,4996,a)].">
      <j1 rule="hyper" parents="325 644 4996"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(4826(a,1),4997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4826 4997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3269,a,5000,a)].">
      <j1 rule="hyper" parents="3269 5000"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,5001,a(flip),b,962,a)].">
      <j1 rule="hyper" parents="132 5001 962"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      L(x \ 1,y,x) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,1312,a(flip),b,5002,a)].">
      <j1 rule="hyper" parents="65 1312 5002"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      L(x \ 1,y,x) * L((R(x,y,x) \ 1) \ 1,z,u) = L(R(x,y,x),z,u) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5003(a,2),589(a,1,1))].">
      <j1 rule="para" parents="5003 589"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      (x * y) \ ((y * (T(x,y) * z)) / u) = (y * x) \ ((y * (x * z)) / u)
    ]]></literal>
    <justification jstring="[hyper(132,a,4573,a(flip),b,2494,a)].">
      <j1 rule="hyper" parents="132 4573 2494"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3862,a,b,4591,a)].">
      <j1 rule="hyper" parents="65 3862 4591"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(2956,a,4598,a),flip(a)].">
      <j1 rule="hyper" parents="2956 4598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5007(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5009">
    <literal><![CDATA[
      T(x * K(y,z),K(u,y)) = T(x,K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(3591,a,4664,a),flip(a)].">
      <j1 rule="hyper" parents="3591 4664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4932,a(flip),b,4683,a)].">
      <j1 rule="hyper" parents="65 4932 4683"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(3701,a,5010,a),flip(a)].">
      <j1 rule="hyper" parents="3701 5010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(4085(a,1),5011(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4085 5011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(3073(a,1),5013(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3073 5013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = ((v5 * x) / v5) / ((v5 * (x * K(y / (u * w),x))) / v5)
    ]]></literal>
    <justification jstring="[para(5014(a,1),3950(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5014 3950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(455,a,4831,a)].">
      <j1 rule="hyper" parents="455 4831"/>
    </justification>
  </clause>

  <clause id="5017">
    <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(4831(a,1),2859(a,1,1))].">
      <j1 rule="para" parents="4831 2859"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(3949,a,5016,a)].">
      <j1 rule="hyper" parents="3949 5016"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      x * K(L(x,y,L(x,z,u)),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,5018,a,b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 5018 2104"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3953,a(flip),b,5018,a),flip(a)].">
      <j1 rule="hyper" parents="65 3953 5018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),5020(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3859,a,b,5022,a)].">
      <j1 rule="hyper" parents="65 3859 5022"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(507(a,1),5023(a,1,2,2))].">
      <j1 rule="para" parents="507 5023"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(1157,a,4849,a)].">
      <j1 rule="hyper" parents="1157 4849"/>
    </justification>
  </clause>

  <clause id="5032">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) \ w)) = L(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2428,a(flip),b,4859,a),flip(a)].">
      <j1 rule="hyper" parents="65 2428 4859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      a(x * ((y \ 1) \ z),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(3529,a,4860,a),flip(a)].">
      <j1 rule="hyper" parents="3529 4860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      a(x * ((y \ 1) \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ z) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(4860(a,1),3529(a,1))].">
      <j1 rule="para" parents="4860 3529"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(2363,a,5033,a)].">
      <j1 rule="hyper" parents="2363 5033"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      a(L(L(x,x,y),y,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2358,a,b,5033,a)].">
      <j1 rule="hyper" parents="65 2358 5033"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      a(((L(x,y,y) \ 1) \ x) * z,u,w) = a(a(y,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(824(a,1),5035(a,2,1,1))].">
      <j1 rule="para" parents="824 5035"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3158,a(flip),b,4862,a)].">
      <j1 rule="hyper" parents="65 3158 4862"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(114(a,2),4865(a,1,2,2,1))].">
      <j1 rule="para" parents="114 4865"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(z,x / y)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(3617(a,1),4881(a,1,2))].">
      <j1 rule="para" parents="3617 4881"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),u) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1917,a(flip),b,4906,a)].">
      <j1 rule="hyper" parents="65 1917 4906"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),y) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1829,a(flip),b,4906,a)].">
      <j1 rule="hyper" parents="65 1829 4906"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      T(x,y * R(y \ 1,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,5043,a)].">
      <j1 rule="hyper" parents="56 5043"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),u) = (1 / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(85(a,1),5043(a,2,2,1))].">
      <j1 rule="para" parents="85 5043"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(966(a,1),5046(a,1,2))].">
      <j1 rule="para" parents="966 5046"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u = u * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1998,a,5050,a),flip(a)].">
      <j1 rule="hyper" parents="1998 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      x / (y \ R(y,z,u)) = (y \ R(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,5050,a),flip(a)].">
      <j1 rule="hyper" parents="376 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      K(x \ R(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,5050,a,b,2635,a),flip(a)].">
      <j1 rule="hyper" parents="133 5050 2635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,5050,a)].">
      <j1 rule="hyper" parents="57 5050"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      x / (y \ R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (y \ R(y,z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(5050(a,1),376(a,1))].">
      <j1 rule="para" parents="5050 376"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      x * ((y \ R(y,z,u)) * K(x,w)) = T(x,w) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5050(a,1),4549(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5050 4549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(K(w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(325,a,35,a,b,5054,a),flip(a)].">
      <j1 rule="hyper" parents="325 35 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(v5,v6),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(65,a,4177,a(flip),b,5060,a)].">
      <j1 rule="hyper" parents="65 4177 5060"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ L(x,u,w)) = R(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1347,a(flip),b,5051,a),flip(a)].">
      <j1 rule="hyper" parents="325 1347 5051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,4907,a(flip),b,5051,a)].">
      <j1 rule="hyper" parents="135 4907 5051"/>
    </justification>
  </clause>

  <clause id="5067">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,w)) = a(K(v5,v6),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(65,a,3761,a,b,5064,a)].">
      <j1 rule="hyper" parents="65 3761 5064"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,5006,a(flip),b,4517,a)].">
      <j1 rule="hyper" parents="132 5006 4517"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(3724(a,1),5041(a,1,2))].">
      <j1 rule="para" parents="3724 5041"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(T(y,x),K(x,z)) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(2519(a,2),5072(a,2,2,1))].">
      <j1 rule="para" parents="2519 5072"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(4875,a,2497,a(flip))].">
      <j1 rule="hyper" parents="4875 2497"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2665,a,b,5077,a(flip))].">
      <j1 rule="hyper" parents="36 2665 5077"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      a(L(L(x,x,y),y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2358(a,2),5034(a,1))].">
      <j1 rule="para" parents="2358 5034"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      a((x * y) \ ((y * y) * z),u,w) = a((x * (y \ 1)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(691(a,1),4605(a,1,1))].">
      <j1 rule="para" parents="691 4605"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3650,a(flip),b,4612,a),flip(a)].">
      <j1 rule="hyper" parents="325 3650 4612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(4619(a,1),2867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4619 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(173(a,1),5082(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="173 5082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5082,a,b,5083,a)].">
      <j1 rule="hyper" parents="65 5082 5083"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,2867,a,b,5083,a)].">
      <j1 rule="hyper" parents="41 2867 5083"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,2849,a,b,5083,a),flip(a)].">
      <j1 rule="hyper" parents="41 2849 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,3405,a(flip),b,5084,a),flip(a)].">
      <j1 rule="hyper" parents="325 3405 5084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,4615,a(flip),b,5086,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 4615 5086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5086(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(3582(a,2),5086(a,2,2))].">
      <j1 rule="para" parents="3582 5086"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      K(x,y \ T(y * z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5086(a,2),4754(a,1,2))].">
      <j1 rule="para" parents="5086 4754"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(5088(a,1),2424(a,1,1))].">
      <j1 rule="para" parents="5088 2424"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(5088(a,1),3538(a,1,1))].">
      <j1 rule="para" parents="5088 3538"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),5091(a,1,2,2,1))].">
      <j1 rule="para" parents="10 5091"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(2616(a,2),5087(a,1,2,1))].">
      <j1 rule="para" parents="2616 5087"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(725,a,5085,a),flip(a)].">
      <j1 rule="hyper" parents="725 5085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      x * (y \ K((y * (x \ 1)) \ 1,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2206,a,b,5085,a(flip))].">
      <j1 rule="hyper" parents="137 2206 5085"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(137,a,5085,a(flip),b,2656,a)].">
      <j1 rule="hyper" parents="137 5085 2656"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      K(((x \ 1) / y) \ 1,z) = (x \ T(x * y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,5085,a(flip),b,2205,a),flip(a)].">
      <j1 rule="hyper" parents="135 5085 2205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5085(a,2,2,1))].">
      <j1 rule="para" parents="10 5085"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(5085(a,1),1102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5085 1102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(5085(a,1),1155(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5085 1155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      K(((x \ 1) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(5085(a,1),3455(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5085 3455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),5098(a,1,2,2,1))].">
      <j1 rule="para" parents="10 5098"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2857,a,5089,a)].">
      <j1 rule="hyper" parents="2857 5089"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,313,a(flip),b,5089,a)].">
      <j1 rule="hyper" parents="65 313 5089"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(2275(a,2),5089(a,1,2))].">
      <j1 rule="para" parents="2275 5089"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      L(x,y,z \ T(u,w)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(5089(a,1),2324(a,1,3))].">
      <j1 rule="para" parents="5089 2324"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      a(x \ T(y,z),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(5089(a,1),2340(a,1,1))].">
      <j1 rule="para" parents="5089 2340"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      a(x * (y \ T(z,u)),w,v5) = a(x * (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(5089(a,1),3513(a,1,1,2))].">
      <j1 rule="para" parents="5089 3513"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = (x * (y / x)) \ (T(x,x \ y) * (x \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(5089(a,1),2743(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5089 2743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(5089(a,1),4747(a,1,1))].">
      <j1 rule="para" parents="5089 4747"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      L(x,y,z \ (u / w)) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(115(a,1),5111(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="115 5111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      T(x,y) * L(z,u,u \ x) = (T(x,y) / u) * (u * z)
    ]]></literal>
    <justification jstring="[para(5111(a,1),1561(a,1,2))].">
      <j1 rule="para" parents="5111 1561"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      a(x \ (y / z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(115(a,1),5112(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="115 5112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),5115(a,1,1,2))].">
      <j1 rule="para" parents="22 5115"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) \ w)) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1567,a(flip),b,5116,a),flip(a)].">
      <j1 rule="hyper" parents="65 1567 5116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      L(x,y,z \ (((u * u) * w) / u)) = L(x,y,z \ ((1 / u) \ w))
    ]]></literal>
    <justification jstring="[para(652(a,1),5116(a,2,3,2))].">
      <j1 rule="para" parents="652 5116"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      a(x \ ((y * y) \ z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1883,a(flip),b,5118,a),flip(a)].">
      <j1 rule="hyper" parents="65 1883 5118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5123">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * w)) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),5120(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 5120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      a(x \ ((y * y) * z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),5122(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      a(x \ (((y * y) \ z) * u),w,v5) = a(x \ (z * u),w,v5)
    ]]></literal>
    <justification jstring="[para(391(a,1),5122(a,1,1,2))].">
      <j1 rule="para" parents="391 5122"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(652(a,1),5123(a,1,3))].">
      <j1 rule="para" parents="652 5123"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4603,a(flip),b,5126,a)].">
      <j1 rule="hyper" parents="65 4603 5126"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      a(x \ ((y \ 1) * (y \ z)),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(663(a,1),5124(a,1,1,2))].">
      <j1 rule="para" parents="663 5124"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3109(a,1),5095(a,1,2,1,1))].">
      <j1 rule="para" parents="3109 5095"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(946(a,1),5096(a,1,2,1,2))].">
      <j1 rule="para" parents="946 5096"/>
    </justification>
  </clause>

  <clause id="5131">
    <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(962(a,1),5096(a,1,2,1,2))].">
      <j1 rule="para" parents="962 5096"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(39,a,3476,a(flip),b,5099,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 3476 5099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(148,a,5132,a),flip(a)].">
      <j1 rule="hyper" parents="148 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,5132,a,b,xx)].">
      <j1 rule="hyper" parents="136 5132"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      x * T(x \ (y / (1 / x)),z) = T(y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,751,a(flip),b,5132,a)].">
      <j1 rule="hyper" parents="65 751 5132"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5132(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(81(a,1),5132(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      x \ T(T(x,y) * y,z) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(3975(a,2),5132(a,1,2,1))].">
      <j1 rule="para" parents="3975 5132"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(135,a,5133,a,b,2587,a)].">
      <j1 rule="hyper" parents="135 5133 2587"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5133(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 5133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(115(a,1),5133(a,2,2,1))].">
      <j1 rule="para" parents="115 5133"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5134(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 5134"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(81(a,1),5134(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="81 5134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(136,a,2955,a(flip),b,5136,a)].">
      <j1 rule="hyper" parents="136 2955 5136"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(5136(a,1),115(a,1,1))].">
      <j1 rule="para" parents="5136 115"/>
    </justification>
  </clause>

  <clause id="5154">
    <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(5136(a,1),3257(a,1,1))].">
      <j1 rule="para" parents="5136 3257"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(5136(a,1),3555(a,1,2))].">
      <j1 rule="para" parents="5136 3555"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5138(a,1),115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5138 115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      (x \ T(L(y,x \ 1,x),z)) * x = T(((x \ 1) * y) * x,z)
    ]]></literal>
    <justification jstring="[para(261(a,1),5146(a,1,1,2,1))].">
      <j1 rule="para" parents="261 5146"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(3626(a,1),5141(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3626 5141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[hyper(137,a,5144,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 5144 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5162">
    <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(5152(a,1),3700(a,1,2))].">
      <j1 rule="para" parents="5152 3700"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(5086(a,1),5152(a,1,1))].">
      <j1 rule="para" parents="5086 5152"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2205,a,b,5100,a)].">
      <j1 rule="hyper" parents="65 2205 5100"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(5100(a,1),3455(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5100 3455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5107(a,1),4950(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5107 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(85(a,1),5166(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="85 5166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ ((T(y,x) / z) \ y)) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(410,a,5108,a),flip(a)].">
      <j1 rule="hyper" parents="410 5108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = (((x / y) \ 1) \ y) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(85(a,1),5109(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="85 5109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = (((x / y) \ 1) \ T(y,z)) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(2166(a,1),5109(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2166 5109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      a(x * (y \ (z / u)),w,v5) = a(x * (y \ (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),5113(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 5113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),5128(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      a(x * R(y,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4861,a,b,5172,a)].">
      <j1 rule="hyper" parents="65 4861 5172"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3472,a(flip),b,5129,a)].">
      <j1 rule="hyper" parents="65 3472 5129"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(4491,a,5161,a),flip(a)].">
      <j1 rule="hyper" parents="4491 5161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      (x * (((y * z) / (y * u)) / x)) * (y * u) = (y * u) * (x * (L(u \ z,u,y) / x))
    ]]></literal>
    <justification jstring="[para(102(a,2),5161(a,2,2,2,1))].">
      <j1 rule="para" parents="102 5161"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1230(a,1),5174(a,1,2,1,1))].">
      <j1 rule="para" parents="1230 5174"/>
    </justification>
  </clause>

  <clause id="5179">
    <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),5090(a,1,2,1))].">
      <j1 rule="para" parents="12 5090"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(2804(a,1),5097(a,1,2,2))].">
      <j1 rule="para" parents="2804 5097"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5180(a,1),1482(a,2,2,1))].">
      <j1 rule="para" parents="5180 1482"/>
    </justification>
  </clause>

  <clause id="5182">
    <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),5110(a,2,2))].">
      <j1 rule="para" parents="27 5110"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      a(x \ (((y * (y \ 1)) \ (y * z)) * u),w,v5) = a(x \ (((y \ 1) * z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(1516(a,1),5125(a,1,1,2,1))].">
      <j1 rule="para" parents="1516 5125"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      (x \ L(T(y,z),x \ 1,x)) * x = T(((x \ 1) * y) * x,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),5158(a,1,1,2))].">
      <j1 rule="para" parents="25 5158"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      T(((x \ 1) * y) * x,z) = ((x \ 1) * T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(389(a,1),5187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="389 5187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2392,a,4678,a)].">
      <j1 rule="hyper" parents="2392 4678"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3753,a(flip),b,4739,a),flip(a)].">
      <j1 rule="hyper" parents="325 3753 4739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(85(a,1),5190(a,1,2,2,1,2))].">
      <j1 rule="para" parents="85 5190"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3401,a(flip),b,5191,a)].">
      <j1 rule="hyper" parents="65 3401 5191"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4012,a(flip),b,4758,a),flip(a)].">
      <j1 rule="hyper" parents="325 4012 4758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      T(x,T(x * T(y / x,z),x)) = T(x,x * T(T(x,y) \ y,z))
    ]]></literal>
    <justification jstring="[para(1181(a,2),4914(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1181 4914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      K(x \ (y * (z * K(u,w))),w) = K(x \ (y * z),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2849,a(flip),b,4982,a),flip(a)].">
      <j1 rule="hyper" parents="325 2849 4982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(93(a,1),5196(a,1,1,2,2))].">
      <j1 rule="para" parents="93 5196"/>
    </justification>
  </clause>

  <clause id="5198">
    <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(451(a,1),5197(a,2,1))].">
      <j1 rule="para" parents="451 5197"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1820,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="325 1820 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(42,a,2979,a,b,5199,a),flip(a)].">
      <j1 rule="hyper" parents="42 2979 5199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,5038,a(flip),b,5070,a),flip(a)].">
      <j1 rule="hyper" parents="325 5038 5070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      a((x * (y \ 1)) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5124,a(flip),b,5080,a),flip(a)].">
      <j1 rule="hyper" parents="65 5124 5080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      1 / ((1 / x) * (y \ T(y * x,z))) = K(z,((x \ 1) * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(201,a,5105,a(flip),b,2608,a)].">
      <j1 rule="hyper" parents="201 5105 2608"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * (w / u))) = L(x,y,z \ ((1 / u) \ w))
    ]]></literal>
    <justification jstring="[para(556(a,1),5121(a,1,3,2))].">
      <j1 rule="para" parents="556 5121"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5130(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),5209(a,2,2))].">
      <j1 rule="para" parents="25 5209"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),5211(a,1,1))].">
      <j1 rule="para" parents="25 5211"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4379,a,b,5212,a)].">
      <j1 rule="hyper" parents="65 4379 5212"/>
    </justification>
  </clause>

  <clause id="5214">
    <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),5148(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5218">
    <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="[para(5189(a,1),443(a,1,2))].">
      <j1 rule="para" parents="5189 443"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(2537,a,5195,a),flip(a)].">
      <j1 rule="hyper" parents="2537 5195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,4687,a(flip),b,5219,a),flip(a)].">
      <j1 rule="hyper" parents="325 4687 5219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,5009,a(flip),b,5214,a(flip))].">
      <j1 rule="hyper" parents="37 5009 5214"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(3617(a,1),5221(a,2,2))].">
      <j1 rule="para" parents="3617 5221"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(3631,a,5222,a)].">
      <j1 rule="hyper" parents="3631 5222"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,3537,a(flip),b,5223,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 3537 5223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,3729,a(flip),b,5224,a),flip(a)].">
      <j1 rule="hyper" parents="325 3729 5224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / T(K(y,z),x * K(y,z * x))
    ]]></literal>
    <justification jstring="[para(5225(a,1),2536(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5225 2536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(709,a,4882,a),flip(a)].">
      <j1 rule="hyper" parents="709 4882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5228">
    <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(325,a,4286,a(flip),b,4538,a),flip(a)].">
      <j1 rule="hyper" parents="325 4286 4538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(2114(a,1),4582(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2114 4582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,239,a(flip),b,5229,a),flip(a)].">
      <j1 rule="hyper" parents="325 239 5229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(216,a,5229,a)].">
      <j1 rule="hyper" parents="216 5229"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,153,a(flip),b,5229,a(flip))].">
      <j1 rule="hyper" parents="137 153 5229"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,239,a(flip),b,5231,a)].">
      <j1 rule="hyper" parents="325 239 5231"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      (x * y) * L(L(z,x,y),u,w) = y * (T(x,y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,30,a,b,5231,a(flip))].">
      <j1 rule="hyper" parents="137 30 5231"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5231(a,2,2,2))].">
      <j1 rule="para" parents="10 5231"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * (T(y,z) * u))) = L(L(u,y,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(5231(a,2),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5231 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      (x * y) \ (y * (x * z)) = L(K(y,x) * z,x,y)
    ]]></literal>
    <justification jstring="[para(4515(a,1),5231(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4515 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),5233(a,1,2)),flip(a)].">
      <j1 rule="para" parents="115 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      ((x * y) / z) * L(z,x,y) = (y * (T(x,y) * z)) / z
    ]]></literal>
    <justification jstring="[hyper(135,a,5232,a(flip),b,1709,a),flip(a)].">
      <j1 rule="hyper" parents="135 5232 1709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      L(T(T(x,y),z) \ u,T(x,z),y) = (T(x,z) * y) \ (y * u)
    ]]></literal>
    <justification jstring="[para(23(a,1),5236(a,1,1,1))].">
      <j1 rule="para" parents="23 5236"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      L(R(T(x,y) \ z,u,w),x,y) = R((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(5236(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5236 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w),x,y) = L((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(5236(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5236 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      L((x * y) \ (y * R(T(x,y),z,u)),T(x,y),u * z) = L(a(T(x,y),z,u),x,y)
    ]]></literal>
    <justification jstring="[para(5236(a,1),2346(a,1,1))].">
      <j1 rule="para" parents="5236 2346"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(5230(a,1),216(a,1))].">
      <j1 rule="para" parents="5230 216"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5230(a,1),4791(a,1,2))].">
      <j1 rule="para" parents="5230 4791"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      L(x,T(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(1545(a,2),5248(a,1))].">
      <j1 rule="para" parents="1545 5248"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(115(a,1),5249(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 5249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      L(x,y \ z,T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z / y,y) = w
    ]]></literal>
    <justification jstring="[para(115(a,1),5250(a,1,2))].">
      <j1 rule="para" parents="115 5250"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      ((x * y) \ y) * (x * x) = L(K(y,x) * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,390,a(flip),b,5238,a)].">
      <j1 rule="hyper" parents="65 390 5238"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      ((x * y) \ y) * (x * x) = L(x * K(y,x),x,y)
    ]]></literal>
    <justification jstring="[para(2452(a,1),5253(a,2,1))].">
      <j1 rule="para" parents="2452 5253"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      ((x * y) \ y) * (x * x) = (y / (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(325,a,1723,a(flip),b,5254,a),flip(a)].">
      <j1 rule="hyper" parents="325 1723 5254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5256">
    <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(5236(a,1),5235(a,1,2,1))].">
      <j1 rule="para" parents="5236 5235"/>
    </justification>
  </clause>

  <clause id="5257">
    <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(137,a,5245,a(flip),b,5231,a(flip))].">
      <j1 rule="hyper" parents="137 5245 5231"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      L((x * T(y,z)) \ x,y,z) = L((y * z) \ (z * 1),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(225(a,1),5246(a,1,1))].">
      <j1 rule="para" parents="225 5246"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      L((x * T(y,z)) \ x,y,z) = L((y * z) \ z,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(8(a,1),5258(a,2,1,2))].">
      <j1 rule="para" parents="8 5258"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(3657(a,1),4588(a,1,2,1))].">
      <j1 rule="para" parents="3657 4588"/>
    </justification>
  </clause>

  <clause id="5261">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(2633(a,1),5260(a,1,2,2))].">
      <j1 rule="para" parents="2633 5260"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(195,a,5261,a)].">
      <j1 rule="hyper" parents="195 5261"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(1581(a,2),5262(a,1,1,1))].">
      <j1 rule="para" parents="1581 5262"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,3086,a,b,5264,a),flip(a)].">
      <j1 rule="hyper" parents="325 3086 5264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      K(x,y) * K(T(L(x,z,u) * y,y),x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(1274(a,1),5265(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1274 5265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(3322(a,1),5266(a,1,2))].">
      <j1 rule="para" parents="3322 5266"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(3095,a,5267,a)].">
      <j1 rule="hyper" parents="3095 5267"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5002(a,1),4597(a,2,2))].">
      <j1 rule="para" parents="5002 4597"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      ((x \ y) \ y) * ((x \ y) * z) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(4577(a,1),4850(a,2,2))].">
      <j1 rule="para" parents="4577 4850"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      (x / y) * ((x / (x / y)) * z) = (y \ x) * (((x / y) \ x) * z)
    ]]></literal>
    <justification jstring="[para(85(a,1),5270(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="85 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      (x / y) * ((x / (x / y)) * z) = (y \ x) * (y * z)
    ]]></literal>
    <justification jstring="[para(85(a,1),5271(a,2,2,1))].">
      <j1 rule="para" parents="85 5271"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      a(x * (y * (z * (z * y))),u,w) = a(x * a(y,z,y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1906,a(flip),b,4851,a),flip(a)].">
      <j1 rule="hyper" parents="325 1906 4851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      a((L(x,y,y) * x) * z,u,w) = a(z * a(x,y,x * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,3524,a(flip),b,5273,a)].">
      <j1 rule="hyper" parents="65 3524 5273"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      a((x * L(x,y,y)) * z,u,w) = a(z * a(x,y,x * y),u,w)
    ]]></literal>
    <justification jstring="[para(249(a,1),5274(a,1,1,1))].">
      <j1 rule="para" parents="249 5274"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      (x * x) * (R(T(x \ 1,(x \ 1) \ x),y,z) * u) = (x / (x \ 1)) * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(272(a,1),4855(a,1,1))].">
      <j1 rule="para" parents="272 4855"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      K(x,T(y / z,u)) * K(z \ y,T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(x,u))) = w
    ]]></literal>
    <justification jstring="[para(4920(a,2),3796(a,1))].">
      <j1 rule="para" parents="4920 3796"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = T(x / y,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3192,a(flip),b,4924,a),flip(a)].">
      <j1 rule="hyper" parents="325 3192 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[para(3026(a,1),5279(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3026 5279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(4976(a,1),4123(a,1))].">
      <j1 rule="para" parents="4976 4123"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5072,a(flip),b,5073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5072 5073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5283">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(x,z)) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(3843(a,1),5073(a,1,2))].">
      <j1 rule="para" parents="3843 5073"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,(y * x) / y),u)
    ]]></literal>
    <justification jstring="[para(1616(a,1),5282(a,1,1,1))].">
      <j1 rule="para" parents="1616 5282"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(325,a,5155,a(flip),b,5101,a),flip(a)].">
      <j1 rule="hyper" parents="325 5155 5101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,5030,a(flip),b,5285,a)].">
      <j1 rule="hyper" parents="65 5030 5285"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1792,a(flip),b,5286,a),flip(a)].">
      <j1 rule="hyper" parents="65 1792 5286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(5287(a,1),2230(a,1,2))].">
      <j1 rule="para" parents="5287 2230"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(5287(a,1),3462(a,1,1,2))].">
      <j1 rule="para" parents="5287 3462"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      K((x / y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(5288(a,1),2301(a,1))].">
      <j1 rule="para" parents="5288 2301"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2077,a(flip),b,5169,a),flip(a)].">
      <j1 rule="hyper" parents="65 2077 5169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(3965,a,5289,a),flip(a)].">
      <j1 rule="hyper" parents="3965 5289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5292(a,2,2,1))].">
      <j1 rule="para" parents="10 5292"/>
    </justification>
  </clause>

  <clause id="5294">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(82(a,1),5292(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 5292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(348(a,1),5294(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="348 5294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(2870(a,1),5295(a,1,2,1))].">
      <j1 rule="para" parents="2870 5295"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4974,a,b,5296,a)].">
      <j1 rule="hyper" parents="65 4974 5296"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2516(a,1),5296(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2516 5296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4919,a(flip),b,5297,a)].">
      <j1 rule="hyper" parents="65 4919 5297"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(2587(a,1),5300(a,1,2,2))].">
      <j1 rule="para" parents="2587 5300"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(82(a,1),5301(a,1,2,2,2))].">
      <j1 rule="para" parents="82 5301"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      (T(x,y) * (z * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4517(a,1),4547(a,1,1))].">
      <j1 rule="para" parents="4517 4547"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      a(x,K(x,y) * z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(709,a,5303,a),flip(a)].">
      <j1 rule="hyper" parents="709 5303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2635(a,1),5304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2635 5304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1876,a,5305,a)].">
      <j1 rule="hyper" parents="1876 5305"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      R(x \ y,z,u) * (K(x,x \ y) * w) = R(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[para(2957(a,1),4613(a,1,2,1))].">
      <j1 rule="para" parents="2957 4613"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(R(y \ x,z,u),K(y,y \ x) * w)
    ]]></literal>
    <justification jstring="[hyper(135,a,5308,a(flip),b,1585,a)].">
      <j1 rule="hyper" parents="135 5308 1585"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(4702(a,1),4848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4702 4848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(4655(a,1),5311(a,2,2))].">
      <j1 rule="para" parents="4655 5311"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,4841,a(flip),b,5312,a),flip(a)].">
      <j1 rule="hyper" parents="325 4841 5312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(4918(a,1),3466(a,1))].">
      <j1 rule="para" parents="4918 3466"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      K(L(x,y,z),u \ (w * x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u \ (x * w)) = v5
    ]]></literal>
    <justification jstring="[para(4972(a,1),2161(a,1))].">
      <j1 rule="para" parents="4972 2161"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,4980,a(flip),b,4981,a),flip(a)].">
      <j1 rule="hyper" parents="65 4980 4981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(18(a,2),5318(a,2,2))].">
      <j1 rule="para" parents="18 5318"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(2619(a,1),5320(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2619 5320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(5320(a,1),4122(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5320 4122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4122,a(flip),b,5322,a),flip(a)].">
      <j1 rule="hyper" parents="325 4122 5322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(2635(a,1),5323(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2635 5323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(L(x,y,z),u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2211(a,1),5213(a,1,2))].">
      <j1 rule="para" parents="2211 5213"/>
    </justification>
  </clause>

  <clause id="5326">
    <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(325,a,2398,a,b,4622,a),flip(a)].">
      <j1 rule="hyper" parents="325 2398 4622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,1990,a,b,5102,a)].">
      <j1 rule="hyper" parents="65 1990 5102"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5167,a(flip),b,5168,a)].">
      <j1 rule="hyper" parents="65 5167 5168"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(137,a,5178,a(flip),b,5328,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 5178 5328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,T(x,y)),u)
    ]]></literal>
    <justification jstring="[para(3675(a,1),5284(a,2,1,2))].">
      <j1 rule="para" parents="3675 5284"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4625(a,1),5326(a,2,1))].">
      <j1 rule="para" parents="4625 5326"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(137,a,5335,a(flip),b,4622,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 5335 4622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(2519(a,2),5336(a,2,2,1))].">
      <j1 rule="para" parents="2519 5336"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(515(a,1),5327(a,1,2,1))].">
      <j1 rule="para" parents="515 5327"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,5134,a(flip),b,5338,a),flip(a)].">
      <j1 rule="hyper" parents="325 5134 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z)
    ]]></literal>
    <justification jstring="[para(516(a,1),5345(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="516 5345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      K(x,T(K(y \ 1,y) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(5348(a,2),3400(a,1,2))].">
      <j1 rule="para" parents="5348 3400"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(633(a,1),5350(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="633 5350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      K(x,T(y * K(z \ 1,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(3159(a,1),5350(a,1,2,1))].">
      <j1 rule="para" parents="3159 5350"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      K(x,T(y / (1 / (1 / z)),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(1809(a,1),5352(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1809 5352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(4314(a,1),5351(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4314 5351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2969,a(flip),b,5353,a)].">
      <j1 rule="hyper" parents="65 2969 5353"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(82(a,1),5355(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 5355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(4809,a,5356,a),flip(a)].">
      <j1 rule="hyper" parents="4809 5356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(3111(a,2),5354(a,2,2))].">
      <j1 rule="para" parents="3111 5354"/>
    </justification>
  </clause>

  <clause id="5359">
    <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(5358(a,2),3833(a,1))].">
      <j1 rule="para" parents="5358 3833"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ T(x,T(z,y)) = L((y * x) \ 1,y * x,x)
    ]]></literal>
    <justification jstring="[hyper(1574,a,4635,a),flip(a)].">
      <j1 rule="hyper" parents="1574 4635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      x \ (L(x,y,z) * R(x,u,w)) = (x \ L(x,y,z)) * R(x,u,w)
    ]]></literal>
    <justification jstring="[para(184(a,1),4866(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="184 4866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(x,u,w) = L(x,y,z) * (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1246,a(flip),b,5362,a),flip(a)].">
      <j1 rule="hyper" parents="65 1246 5362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      L(T((x \ 1) * x,x \ 1),y,z) = a(1 / L(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(979,a,4779,a),flip(a)].">
      <j1 rule="hyper" parents="979 4779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      a(1 / L(x,y,z),x,x \ 1) = L(K(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(3173(a,1),5364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3173 5364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5366">
    <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(135,a,5365,a(flip),b,978,a)].">
      <j1 rule="hyper" parents="135 5365 978"/>
    </justification>
  </clause>

  <clause id="5368">
    <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(2307(a,1),5366(a,1,1))].">
      <j1 rule="para" parents="2307 5366"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      1 / ((x * (L(x,y,z) \ 1)) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4073,a(flip),b,5368,a)].">
      <j1 rule="hyper" parents="65 4073 5368"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      1 / ((L(x,y,z) \ x) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1257(a,1),5369(a,1,2,1))].">
      <j1 rule="para" parents="1257 5369"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(195,a,5370,a),flip(a)].">
      <j1 rule="hyper" parents="195 5370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(338,a,5371,a)].">
      <j1 rule="hyper" parents="338 5371"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,1669,a(flip),b,5039,a),flip(a)].">
      <j1 rule="hyper" parents="325 1669 5039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2917,a(flip),b,5373,a),flip(a)].">
      <j1 rule="hyper" parents="325 2917 5373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(4627(a,1),5374(a,1,2))].">
      <j1 rule="para" parents="4627 5374"/>
    </justification>
  </clause>

  <clause id="5376">
    <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(5375(a,1),606(a,1,2))].">
      <j1 rule="para" parents="5375 606"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5131(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5269,a,b,5377,a)].">
      <j1 rule="hyper" parents="65 5269 5377"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2267(a,1),5378(a,1,2))].">
      <j1 rule="para" parents="2267 5378"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(4797(a,1),5379(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4797 5379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      (T(x,y) / T(R(x,z,x),u)) * K(x \ L(T(x,y),z,x),R(x,z,x)) = T(T(x,y) / T(R(x,z,x),u),R(x,z,x))
    ]]></literal>
    <justification jstring="[para(5380(a,1),4644(a,1,2,1))].">
      <j1 rule="para" parents="5380 4644"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(4583(a,1),5181(a,1,1,1))].">
      <j1 rule="para" parents="4583 5181"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(135,a,5066,a(flip),b,5382,a(flip))].">
      <j1 rule="hyper" parents="135 5066 5382"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      a(x \ (((y \ 1) * z) * u),w,v5) = a(x \ ((y * z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(170(a,1),5183(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="170 5183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5386">
    <literal><![CDATA[
      a(x \ (T(y * (z \ 1),K(z \ 1,u)) * w),v5,v6) = a(x \ ((z * T(y,T(z \ 1,u))) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(2904(a,2),5384(a,1,1,2,1))].">
      <j1 rule="para" parents="2904 5384"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      L((x * y) \ (R(x,z,u) * y),T(x,y),u * z) = L(a(T(x,y),z,u),x,y)
    ]]></literal>
    <justification jstring="[para(243(a,1),5247(a,1,1,2))].">
      <j1 rule="para" parents="243 5247"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(1741,a,5256,a),flip(a)].">
      <j1 rule="hyper" parents="1741 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      T(x,y) * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(2644(a,1),5388(a,1,2,1))].">
      <j1 rule="para" parents="2644 5388"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (y * z),u,w) = y * (x * R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(4906(a,1),5257(a,2,2))].">
      <j1 rule="para" parents="4906 5257"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * y) * (x * R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,909,a(flip),b,5390,a),flip(a)].">
      <j1 rule="hyper" parents="65 909 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = y * (x * R(x \ (y \ z),u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),5390(a,1,2,1,2))].">
      <j1 rule="para" parents="10 5390"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * x)),u,w)) = (y * R(y \ z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,1811,a(flip),b,5392,a),flip(a)].">
      <j1 rule="hyper" parents="65 1811 5392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      x * (y * R(y \ T(z,x),u,w)) = (y * R(y \ z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(22(a,2),5394(a,1,2,2,1,2))].">
      <j1 rule="para" parents="22 5394"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      K(x,y) * (z * R(z \ x,u,w)) = (z * R(z \ x,u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2119(a,1),5396(a,1,2,2,1,2))].">
      <j1 rule="para" parents="2119 5396"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ (x * K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,4434,a(flip),b,5397,a),flip(a)].">
      <j1 rule="hyper" parents="325 4434 5397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(2094(a,2),5398(a,2,2,1,2))].">
      <j1 rule="para" parents="2094 5398"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      ((x * R(x \ y,z,u)) * ((y * w) / y)) \ (w * (x * R(x \ T(y,w),z,u))) = K(w,T(x * R(x \ y,z,u),y))
    ]]></literal>
    <justification jstring="[para(5399(a,1),5081(a,1,2,2))].">
      <j1 rule="para" parents="5399 5081"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      (x * y) * (x * R(x \ 1,z,u)) = x * ((x * R(x \ 1,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1457(a,1),5391(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1457 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      x * ((x * R(x \ 1,y,z)) * u) = (x * u) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1077(a,1),5401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1077 5401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      (x * y) * (x \ R(x,z,u)) = x * ((x \ R(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1077(a,1),5402(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1077 5402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x * u) = x * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5051,a,b,5403,a)].">
      <j1 rule="hyper" parents="65 5051 5403"/>
    </justification>
  </clause>

  <clause id="5405">
    <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(5404(a,1),1472(a,1,2))].">
      <j1 rule="para" parents="5404 1472"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y) = L(x,y,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(730,a,5405,a)].">
      <j1 rule="hyper" parents="730 5405"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y) = L(x,y,y * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1822,a(flip),b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="325 1822 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x,x * R(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ (x * u) = w
    ]]></literal>
    <justification jstring="[para(5407(a,1),538(a,1))].">
      <j1 rule="para" parents="5407 538"/>
    </justification>
  </clause>

  <clause id="5409">
    <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(2658(a,1),4900(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2658 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5410">
    <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(5409(a,2),3356(a,1))].">
      <j1 rule="para" parents="5409 3356"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ u,y,x) / z)) = (x * y) * (z * (((x * y) \ (x * u)) / z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5161,a(flip),b,5177,a),flip(a)].">
      <j1 rule="hyper" parents="65 5161 5177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ u) / z),y,x) = (x * y) * (z * (((x * y) \ (x * u)) / z))
    ]]></literal>
    <justification jstring="[para(1750(a,2),5412(a,1,2))].">
      <j1 rule="para" parents="1750 5412"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ (x * u)) / z)) = x * (y * (z * ((y \ u) / z)))
    ]]></literal>
    <justification jstring="[hyper(298,a,5441,a),flip(a)].">
      <j1 rule="hyper" parents="298 5441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[hyper(325,a,1620,a(flip),b,4876,a),flip(a)].">
      <j1 rule="hyper" parents="325 1620 4876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[para(114(a,1),5443(a,1,1,1))].">
      <j1 rule="para" parents="114 5443"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      T((((x / y) \ 1) \ y) * ((x / y) \ 1),z) = (x / y) \ T(x * K(y,z),(x / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,5147,a,b,5170,a)].">
      <j1 rule="hyper" parents="325 5147 5170"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5161(a,1),5176(a,2,1))].">
      <j1 rule="para" parents="5161 5176"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(5291(a,1),5445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5291 5445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(5447(a,1),2214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5447 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,5142,a(flip),b,5448,a),flip(a)].">
      <j1 rule="hyper" parents="325 5142 5448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3863,a(flip),b,5449,a)].">
      <j1 rule="hyper" parents="65 3863 5449"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(85(a,1),5446(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="85 5446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) = ((x * T(x \ y,z)) * x) / x
    ]]></literal>
    <justification jstring="[para(4276(a,1),4814(a,2,1))].">
      <j1 rule="para" parents="4276 4814"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(5452(a,2),258(a,1)),flip(b)].">
      <j1 rule="para" parents="5452 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,5383,a(flip),b,4908,a),flip(a)].">
      <j1 rule="hyper" parents="325 5383 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      L(x \ 1,y,x) * L(L(x \ 1,y,x) \ 1,z,u) = L(R(x,y,x),z,u) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5003(a,2),5004(a,1,2,1,1))].">
      <j1 rule="para" parents="5003 5004"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,3950,a(flip),b,5015,a),flip(a)].">
      <j1 rule="hyper" parents="325 3950 5015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(3679(a,1),5460(a,1,2,1,2,1))].">
      <j1 rule="para" parents="3679 5460"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      (x * x) * (R(T(x \ 1,x * x),y,z) * u) = (x / (x \ 1)) * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(272(a,1),5276(a,1,2,1,1,2))].">
      <j1 rule="para" parents="272 5276"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      (x / (x \ 1)) * (R(x \ 1,y,z) * u) = (x * x) * (R(1 / x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(597(a,1),5462(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="597 5462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      (x / (x \ 1)) * (R(x \ 1,y,z) * u) = R((x * x) / x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(325,a,1056,a(flip),b,5463,a),flip(a)].">
      <j1 rule="hyper" parents="325 1056 5463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      (x / (x \ 1)) * (R(x \ 1,y,z) * u) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(11(a,1),5464(a,2,1,1))].">
      <j1 rule="para" parents="11 5464"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      L(x \ 1,y,x) \ L(L(x \ 1,y,x),z,u) = L(R(x,y,x),z,u) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1317,a,5459,a)].">
      <j1 rule="hyper" parents="1317 5459"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (R(x,y,x) \ 1) = L((x \ 1) \ L(x \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4459,a,5466,a),flip(a)].">
      <j1 rule="hyper" parents="4459 5466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (R(x,y,x) \ 1) = L(x \ (1 * L(1 \ x,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(1410(a,1),5467(a,2,1))].">
      <j1 rule="para" parents="1410 5467"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (R(x,y,x) \ 1) = L(x \ (1 * L(x,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(67(a,1),5468(a,2,1,2,2,1))].">
      <j1 rule="para" parents="67 5468"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (R(x,y,x) \ 1) = L(x \ L(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),5469(a,2,1,2))].">
      <j1 rule="para" parents="7 5469"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      R(x,y,x) * L(x \ L(x,z,u),y,x) = L(R(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,5470,a(flip),b,946,a(flip))].">
      <j1 rule="hyper" parents="137 5470 946"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(85(a,1),5451(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="85 5451"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(536,a,5487,a)].">
      <j1 rule="hyper" parents="536 5487"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(5488(a,1),4297(a,1,1))].">
      <j1 rule="para" parents="5488 4297"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(4066,a,5491,a)].">
      <j1 rule="hyper" parents="4066 5491"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,4766,a(flip),b,5492,a),flip(a)].">
      <j1 rule="hyper" parents="65 4766 5492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(T(x,y * z),u / (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(113(a,1),5492(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 5492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,4768,a(flip),b,5494,a)].">
      <j1 rule="hyper" parents="65 4768 5494"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(137,a,5497,a(flip),b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 5497 2104"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(3050(a,1),5499(a,1,2))].">
      <j1 rule="para" parents="3050 5499"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(2140,a,5501,a),flip(a)].">
      <j1 rule="hyper" parents="2140 5501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5503">
    <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(5502(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="5502 4273"/>
    </justification>
  </clause>

  <clause id="5504">
    <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),5503(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 5503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(542,a,5504,a),flip(a)].">
      <j1 rule="hyper" parents="542 5504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5506">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,x \ w),y,z) * u) = K(R(x,y,z) \ w,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(5504(a,1),2709(a,1,2,1))].">
      <j1 rule="para" parents="5504 2709"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5505(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[para(114(a,1),5505(a,1,1))].">
      <j1 rule="para" parents="114 5505"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(596(a,1),5505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="596 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[para(678(a,1),5505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="678 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2143(a,1),5505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2143 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) * K(u,R(x,y,z) \ 1) = T(R(x,y,z) \ 1,u) \ 1
    ]]></literal>
    <justification jstring="[para(5508(a,2),3748(a,1,1))].">
      <j1 rule="para" parents="5508 3748"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      x / R(y \ x,z,u) = R(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(202,a,5509,a)].">
      <j1 rule="hyper" parents="202 5509"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      x / (x / R(y \ x,z,u)) = R(x / y,z,u)
    ]]></literal>
    <justification jstring="[para(5509(a,1),196(a,1,2,2))].">
      <j1 rule="para" parents="5509 196"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = T(R(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5511(a,1),4624(a,1,2,1))].">
      <j1 rule="para" parents="5511 4624"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) * T(R(x \ 1,y,z) \ 1,x) = T(R(x \ 1,y,z) \ 1,T(u,1))
    ]]></literal>
    <justification jstring="[para(5514(a,1),3805(a,1,1,1))].">
      <j1 rule="para" parents="5514 3805"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      R(x / (x / y),z,u) = x / (x / R(y,z,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),5515(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="85 5515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      x / (x / R(x * x,y,z)) = R(x / (x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(272(a,1),5515(a,1,2,2,1))].">
      <j1 rule="para" parents="272 5515"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(961(a,1),5507(a,1,1))].">
      <j1 rule="para" parents="961 5507"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) = (R(K(y,x),v5,v6) * z) \ z
    ]]></literal>
    <justification jstring="[para(2911(a,1),5510(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2911 5510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      R(x / (x \ 1),y,z) = x / (x / (x * x))
    ]]></literal>
    <justification jstring="[para(486(a,1),5522(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="486 5522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      R(x / (x \ 1),y,z) = x / (x \ 1)
    ]]></literal>
    <justification jstring="[para(271(a,1),5526(a,2,2))].">
      <j1 rule="para" parents="271 5526"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      (x / (x \ 1)) * y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(136,a,5527,a(flip),b,496,a(flip))].">
      <j1 rule="hyper" parents="136 5527 496"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      (x / (x \ 1)) \ y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(5527(a,1),480(a,1,1))].">
      <j1 rule="para" parents="5527 480"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      x * ((x \ 1) \ (R(x \ 1,y,z) * u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,5465,a(flip),b,5529,a),flip(a)].">
      <j1 rule="hyper" parents="65 5465 5529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      (x / (x \ 1)) \ y = ((x \ 1) / x) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,737,a,b,5530,a),flip(a)].">
      <j1 rule="hyper" parents="325 737 5530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      (x * x) \ a(x,x,x) = (x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,5532,a(flip),b,2947,a),flip(a)].">
      <j1 rule="hyper" parents="134 5532 2947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),5524(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      ((1 / x) * (x * y)) \ ((1 / x) * y) = R(T(1 / x,y),x,y)
    ]]></literal>
    <justification jstring="[para(365(a,1),5524(a,1,1,2))].">
      <j1 rule="para" parents="365 5524"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      R(T(K(x,y),z * u),w,v5) = ((K(y,x) * z) * u) \ (z * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),5525(a,2,1))].">
      <j1 rule="para" parents="109 5525"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = R(T(x,w),z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(27(a,2),5518(a,2,1))].">
      <j1 rule="para" parents="27 5518"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      x * (R(x \ 1,y,z) * ((x \ 1) \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(958(a,1),5531(a,1,2))].">
      <j1 rule="para" parents="958 5531"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      ((x \ 1) * y) \ (R(x \ 1,z,u) * w) = (x * y) \ (R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5531(a,1),1511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5531 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      R(x \ 1,y,z) * ((x \ 1) \ u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(36,a,960,a,b,5539,a),flip(a)].">
      <j1 rule="hyper" parents="36 960 5539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      (x / (y \ 1)) * R(y \ 1,z,u) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3001,a(flip),b,5541,a)].">
      <j1 rule="hyper" parents="65 3001 5541"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      L(x,y,y) \ ((1 / y) * x) = R(T(1 / y,x),y,x)
    ]]></literal>
    <justification jstring="[para(650(a,1),5535(a,1,1))].">
      <j1 rule="para" parents="650 5535"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      R(K(x,T(y,z * u)),w,v5) = ((K(y,x) * z) * u) \ (z * u)
    ]]></literal>
    <justification jstring="[para(3111(a,2),5536(a,1,1))].">
      <j1 rule="para" parents="3111 5536"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),v5,v6) = ((K(y,T(x,z)) * L(y,u,w)) * z) \ (L(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(3802(a,1),5544(a,1,1))].">
      <j1 rule="para" parents="3802 5544"/>
    </justification>
  </clause>

  <clause id="5546">
    <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(325,a,240,a(flip),b,5534,a),flip(a)].">
      <j1 rule="hyper" parents="325 240 5534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = L(R(T(x,u),y,z),u,x)
    ]]></literal>
    <justification jstring="[para(27(a,2),5546(a,2,1))].">
      <j1 rule="para" parents="27 5546"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(44,a,602,a(flip),b,5547,a),flip(a)].">
      <j1 rule="hyper" parents="44 602 5547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5549(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = R(T(x,x * u),w,v5) \ R(x,w,v5)
    ]]></literal>
    <attribute><![CDATA[
      label(flip_matches_hint)
    ]]></attribute>
    <justification jstring="[para(5549(a,1),2527(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5549 2527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = x * K(x,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a(flip),b,5550,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 5550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(2108,a,5553,a)].">
      <j1 rule="hyper" parents="2108 5553"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),5554(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      K(x,R(x,y,z) \ (x * u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(961(a,2),5554(a,1,2))].">
      <j1 rule="para" parents="961 5554"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      K(R(x,y,z),R(x,u,w) * v5) = K(x,x * v5)
    ]]></literal>
    <justification jstring="[hyper(3256,a,5555,a)].">
      <j1 rule="hyper" parents="3256 5555"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5556(a,1,2,2))].">
      <j1 rule="para" parents="10 5556"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x,y,z)) = u * K(x,x \ u)
    ]]></literal>
    <justification jstring="[para(5559(a,1),2996(a,2,2))].">
      <j1 rule="para" parents="5559 2996"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x,y,z)) = x * (u / x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2558,a(flip),b,5562,a),flip(a)].">
      <j1 rule="hyper" parents="325 2558 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,7,a(flip),b,5562,a),flip(a)].">
      <j1 rule="hyper" parents="325 7 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = K(x * u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,2527,a(flip),b,5552,a),flip(a)].">
      <j1 rule="hyper" parents="325 2527 5552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4742,a,5570,a)].">
      <j1 rule="hyper" parents="4742 5570"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(3481,a,5506,a),flip(a)].">
      <j1 rule="hyper" parents="3481 5506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,w,v5)) * (v6 * v7) = (K(x \ u,R(x,v8,v9)) * v6) * v7
    ]]></literal>
    <justification jstring="[para(5576(a,1),3067(a,2,1,1))].">
      <j1 rule="para" parents="5576 3067"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,w,v5)) * (v6 * v7) = (K(x \ u,x) * v6) * v7
    ]]></literal>
    <justification jstring="[para(485(a,1),5582(a,2,1,1,2))].">
      <j1 rule="para" parents="485 5582"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,w,v5)) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,3359,a,b,5583,a),flip(a)].">
      <j1 rule="hyper" parents="37 3359 5583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      K(x \ y,x) * (y / R(x,z,u)) = R(x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(37,a,2591,a(flip),b,5583,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 2591 5583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      (R(x,y,z) \ u) * R(x,y,z) = u * K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,5584,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="137 5584 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      (x / y) \ (x / R(y,z,u)) = (y \ x) \ (R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(132,a,5585,a(flip),b,2593,a),flip(a)].">
      <j1 rule="hyper" parents="132 5585 2593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      (R(x,y,z) \ u) * R(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,313,a(flip),b,5586,a),flip(a)].">
      <j1 rule="hyper" parents="325 313 5586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,T(u / (x * (y * z)),y * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3113,a(flip),b,5495,a),flip(a)].">
      <j1 rule="hyper" parents="325 3113 5495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),v5,v6) = (L(y,u,w) * (K(y,T(x,z)) * z)) \ (L(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(4503(a,1),5545(a,2,1))].">
      <j1 rule="para" parents="4503 5545"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),v5,v6) = (L(y,u,w) * (z * K(y,x))) \ (L(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(3640(a,1),5590(a,2,1,2))].">
      <j1 rule="para" parents="3640 5590"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),v5,v6) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5017,a,5591,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5017 5591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4047,a,5592,a),flip(a)].">
      <j1 rule="hyper" parents="4047 5592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      T(L(L(x * K(y,x),y,x),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(1604(a,1),4994(a,1,1,1,1))].">
      <j1 rule="para" parents="1604 4994"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      T(x * L(L(y,z,u),x,y),y * K(x,y)) = L(y * K(x,y),z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1657(a,1),5594(a,1,1))].">
      <j1 rule="para" parents="1657 5594"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      T(x * L(L(y,z,u),x,y),y * K(x,y)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2538,a(flip),b,5596,a),flip(a)].">
      <j1 rule="hyper" parents="325 2538 5596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y * K(x,y)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(30(a,1),5598(a,1,1,2))].">
      <j1 rule="para" parents="30 5598"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),T(y,x)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3677,a(flip),b,5599,a)].">
      <j1 rule="hyper" parents="65 3677 5599"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3827,a(flip),b,5600,a)].">
      <j1 rule="hyper" parents="65 3827 5600"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      K(x,L(L(x,y,x),z,u) / (y \ 1)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5601(a,1),5098(a,1,2,2))].">
      <j1 rule="para" parents="5601 5098"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      K(x,(y \ 1) \ L(L(x,y,x),z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3188(a,1),5602(a,1,1))].">
      <j1 rule="para" parents="3188 5602"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = (x * (y / x)) \ (K(x,x \ y) * T(y,z))
    ]]></literal>
    <justification jstring="[para(2125(a,1),5114(a,2,2))].">
      <j1 rule="para" parents="2125 5114"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2604,a(flip),b,5604,a),flip(a)].">
      <j1 rule="hyper" parents="325 2604 5604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5252,a,5605,a)].">
      <j1 rule="hyper" parents="5252 5605"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      x * ((T(x,y) \ z) * R((T(x,y) \ z) \ z,u,w)) = R(T(x,y),u,w) * (x * (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(1066,a,4571,a)].">
      <j1 rule="hyper" parents="1066 4571"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x * (T(x,y) \ w)) = x * (R(T(x,y),z,u) * (T(x,y) \ w))
    ]]></literal>
    <justification jstring="[para(594(a,1),5608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="594 5608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      T(x,y) * (x * (R(T(x,y),z,u) * (T(x,y) \ w))) = R(T(x,y),z,u) * (x * w)
    ]]></literal>
    <justification jstring="[para(5609(a,1),4572(a,1,2))].">
      <j1 rule="para" parents="5609 4572"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      x * (T(x,y) * (R(T(x,y),z,u) * (T(x,y) \ w))) = R(T(x,y),z,u) * (x * w)
    ]]></literal>
    <justification jstring="[hyper(4570,a,5610,a)].">
      <j1 rule="hyper" parents="4570 5610"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x * w) = x * (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[para(960(a,1),5611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="960 5611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (x * w) = x * (R(T(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(132,a,156,a(flip),b,5612,a)].">
      <j1 rule="hyper" parents="132 156 5612"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) = T(y / T(x,y),z) * T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(5220(a,1),4749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5220 4749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,y * T(y \ x,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5453,a,5620,a),flip(a)].">
      <j1 rule="hyper" parents="5453 5620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,K(y,y \ x) * w)
    ]]></literal>
    <justification jstring="[para(2993(a,1),5309(a,2,2))].">
      <j1 rule="para" parents="2993 5309"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      (R(x / y,z,u) * w) / R(y \ x,z,u) = (K(y,y \ x) * w) * K(y \ x,w)
    ]]></literal>
    <justification jstring="[para(4709(a,1),5622(a,2,2))].">
      <j1 rule="para" parents="4709 5622"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      (K(x,x \ y) * z) * K(z \ (K(x \ y,x) * ((y / x) * z)),K(x,x \ y) * z) = ((y / x) * z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(2674(a,1),4856(a,1,2,1))].">
      <j1 rule="para" parents="2674 4856"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      (K(x,x \ y) * z) * K(z \ ((x \ y) * z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(2591(a,1),5626(a,1,2,1,2))].">
      <j1 rule="para" parents="2591 5626"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      (K(x,x \ y) * z) * K(T(x \ y,z),K(x,x \ y) * z) = ((y / x) * z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),5627(a,1,2,1))].">
      <j1 rule="para" parents="22 5627"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      (K(x,x \ y) * z) * K(T(x \ y,z),z) = ((y / x) * z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(4722(a,1),5628(a,1,2))].">
      <j1 rule="para" parents="4722 5628"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      (K(x,x \ y) * z) * K(x \ y,z) = ((y / x) * z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(2629(a,1),5629(a,1,2))].">
      <j1 rule="para" parents="2629 5629"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      (R(x / y,z,u) * w) / R(y \ x,z,u) = ((x / y) * w) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5624,a,b,5630,a)].">
      <j1 rule="hyper" parents="65 5624 5630"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      K(x,((1 / (1 / R(y / z,u,w))) * v5) / R(z \ y,u,w)) = K(x,((y / z) * v5) / (z \ y))
    ]]></literal>
    <justification jstring="[para(5632(a,1),3446(a,2,2))].">
      <j1 rule="para" parents="5632 3446"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(x,((1 / y) * w) * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,3422,a(flip),b,5633,a),flip(a)].">
      <j1 rule="hyper" parents="325 3422 5633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      K(x,((1 / (1 / R(1 / y,z,u))) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,4327,a(flip),b,5634,a),flip(a)].">
      <j1 rule="hyper" parents="325 4327 5634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      K(x,(R(1 / (1 / (1 / y)),z,u) * w) / R(y \ 1,z,u)) = K(T(x,y \ 1),w)
    ]]></literal>
    <justification jstring="[para(5521(a,2),5635(a,1,2,1,1))].">
      <j1 rule="para" parents="5521 5635"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(T(x,y \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(3037,a,5636,a)].">
      <j1 rule="hyper" parents="3037 5636"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      K(x,R(1 / (1 / (1 / y)),z,u) / (R(y \ 1,z,u) / w)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3813,a(flip),b,5637,a),flip(a)].">
      <j1 rule="hyper" parents="325 3813 5637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      R(x,y,z) * ((y * z) \ (z * ((x * y) * R((x * y) \ (z \ (y * z)),u,w)))) = R(((x * y) * z) / (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(5392(a,1),4242(a,1,2,2))].">
      <j1 rule="para" parents="5392 4242"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      (K(x,y / z) * K(x,K(u,z \ y))) / T(K(x,z \ y),u) = R(K(x,K(z,y)),K(x,z \ y),K(K(x,z \ y),u))
    ]]></literal>
    <justification jstring="[para(3581(a,1),4868(a,1,1,2))].">
      <j1 rule="para" parents="3581 4868"/>
    </justification>
  </clause>

  <clause id="5642">
    <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(2391(a,1),5218(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2391 5218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5643">
    <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(325,a,4528,a(flip),b,5642,a),flip(a)].">
      <j1 rule="hyper" parents="325 4528 5642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <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(325,a,2114,a(flip),b,5643,a),flip(a)].">
      <j1 rule="hyper" parents="325 2114 5643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <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(2391(a,1),5645(a,1,2))].">
      <j1 rule="para" parents="2391 5645"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      T(x * K(y,z),L(y,u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4680,a(flip),b,5646,a)].">
      <j1 rule="hyper" parents="65 4680 5646"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      (R(T(x,y),z,x) \ T(x,u)) * K(x \ L(T(x,u),z,x),R(x,z,x)) = T(T(x,u) / T(R(x,z,x),y),R(x,z,x))
    ]]></literal>
    <justification jstring="[para(5538(a,1),5381(a,1,1))].">
      <j1 rule="para" parents="5538 5381"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      ((x * R(x \ y,z,u)) * ((y * w) / y)) \ ((x * R(x \ y,z,u)) * w) = K(w,T(x * R(x \ y,z,u),y))
    ]]></literal>
    <justification jstring="[para(5396(a,1),5400(a,1,2))].">
      <j1 rule="para" parents="5396 5400"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      K(x,T(y * R(y \ z,u,w),z)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4016,a(flip),b,5650,a),flip(a)].">
      <j1 rule="hyper" parents="65 4016 5650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      K(x,y * R(y \ z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5044(a,1),5651(a,1,2))].">
      <j1 rule="para" parents="5044 5651"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      K(x,R(y,z,u) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(2935(a,1),5653(a,1,2))].">
      <j1 rule="para" parents="2935 5653"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      K(x,(1 / (1 / (1 / y))) / (R(y \ 1,z,u) / w)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,5638,a(flip),b,5654,a),flip(a)].">
      <j1 rule="hyper" parents="65 5638 5654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      K(x,1 / ((R(y \ 1,z,u) / w) * (1 / (1 / y)))) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2962,a(flip),b,5655,a)].">
      <j1 rule="hyper" parents="65 2962 5655"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      K(x,1 / ((R(y \ 1,z,u) / w) * ((1 / y) \ 1))) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3453,a(flip),b,5657,a)].">
      <j1 rule="hyper" parents="65 3453 5657"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      K(x,1 / ((R(y \ 1,z,u) / w) * y)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[para(85(a,1),5658(a,1,2,2,2))].">
      <j1 rule="para" parents="85 5658"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      K(x,((R(y \ 1,z,u) / w) * y) \ 1) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(2803,a,5659,a)].">
      <j1 rule="hyper" parents="2803 5659"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      R(x,y,z) * ((y * z) \ (z * ((x * y) * R((x * y) \ T(y,z),u,w)))) = R(((x * y) * z) / (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),5639(a,1,2,2,2,2,1,2))].">
      <j1 rule="para" parents="22 5639"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      R(x,y,z) * ((y * z) \ (z * (y * (x * R(x \ (y \ T(y,z)),u,w))))) = R(((x * y) * z) / (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(5392(a,1),5662(a,1,2,2,2))].">
      <j1 rule="para" parents="5392 5662"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      R(x,y,z) * ((y * z) \ (z * (y * (x * R(x \ K(y,z),u,w))))) = R(((x * y) * z) / (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(2104(a,2),5663(a,1,2,2,2,2,2,1,2))].">
      <j1 rule="para" parents="2104 5663"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) / T(K(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(3718(a,1),5641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3718 5641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) / K(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(3111(a,2),5666(a,2,2))].">
      <j1 rule="para" parents="3111 5666"/>
    </justification>
  </clause>

  <clause id="5670">
    <literal><![CDATA[
      R(K(x,K(y,z)),K(x,y \ z),K(K(x,y \ z),u)) = K(x,T(z / y,T(u,y))) * K(y \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3139,a(flip),b,5668,a),flip(a)].">
      <j1 rule="hyper" parents="325 3139 5668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      K(x,T(y / z,T(u,z))) * K(z \ y,T(x,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3606,a(flip),b,5670,a),flip(a)].">
      <j1 rule="hyper" parents="65 3606 5670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      (R(T(x,y),z,x) \ T(x,u)) * K(x \ L(T(x,u),z,x),x) = T(T(x,u) / T(R(x,z,x),y),R(x,z,x))
    ]]></literal>
    <justification jstring="[para(2957(a,1),5649(a,1,2))].">
      <j1 rule="para" parents="2957 5649"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      L((x \ 1) * (x * (L(x,y,z) \ L(x,y,z))),u,w) \ 1 = a(x,x \ 1,L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,719,a(flip),b,4469,a),flip(a)].">
      <j1 rule="hyper" parents="65 719 4469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      a(x,x \ 1,L(L(x,y,z),u,w)) = L((x \ 1) * x,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(177(a,1),5675(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="177 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      a(x,x \ 1,L(L(x,y,z),u,w)) = L(K(x \ 1,x),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(262(a,2),5676(a,2,1,1))].">
      <j1 rule="para" parents="262 5676"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      a(x,x \ 1,L(L(x,y,z),u,w)) = K(x \ 1,x) \ 1
    ]]></literal>
    <justification jstring="[para(1040(a,1),5677(a,2,1))].">
      <j1 rule="para" parents="1040 5677"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      a(x,x \ 1,L(L(x,y,z),u,w)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2608,a(flip),b,5678,a),flip(a)].">
      <j1 rule="hyper" parents="325 2608 5678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = L(y,y,x) * ((y \ 1) * ((x * y) \ R(x,y,y)))
    ]]></literal>
    <justification jstring="[para(1948(a,1),925(a,2,1))].">
      <j1 rule="para" parents="1948 925"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = L(y,y,x) * ((y \ 1) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(573(a,1),5681(a,2,2,2))].">
      <j1 rule="para" parents="573 5681"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = L(y,y,x) * ((y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(420(a,1),5682(a,2,2))].">
      <j1 rule="para" parents="420 5682"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = L(y * ((y \ 1) / y),y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1118,a,b,5683,a),flip(a)].">
      <j1 rule="hyper" parents="325 1118 5683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = L(T(y \ 1,y),y,x)
    ]]></literal>
    <justification jstring="[para(4080(a,1),5685(a,2,1))].">
      <j1 rule="para" parents="4080 5685"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      L(x \ 1,(y * x) \ R(y,x,x),y * x) = L(T(x \ 1,x),x,y)
    ]]></literal>
    <justification jstring="[para(573(a,1),5686(a,1,1))].">
      <j1 rule="para" parents="573 5686"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      L(x \ 1,x \ 1,y * x) = L(T(x \ 1,x),x,y)
    ]]></literal>
    <justification jstring="[para(573(a,1),5687(a,1,2))].">
      <j1 rule="para" parents="573 5687"/>
    </justification>
  </clause>

  <clause id="5691">
    <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),1281(a,2,2,1,1))].">
      <j1 rule="para" parents="20 1281"/>
    </justification>
  </clause>

  <clause id="5692">
    <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(1811(a,1),5691(a,1,1))].">
      <j1 rule="para" parents="1811 5691"/>
    </justification>
  </clause>

  <clause id="5693">
    <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(1457(a,1),5692(a,1,1,1))].">
      <j1 rule="para" parents="1457 5692"/>
    </justification>
  </clause>

  <clause id="5694">
    <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(490,a,5693,a),flip(a)].">
      <j1 rule="hyper" parents="490 5693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R((1 / y) * R((1 / y) \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4437,a,b,5694,a)].">
      <j1 rule="hyper" parents="65 4437 5694"/>
    </justification>
  </clause>

  <clause id="5696">
    <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(65,a,968,a(flip),b,5694,a),flip(a)].">
      <j1 rule="hyper" parents="65 968 5694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <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(1476(a,1),5696(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1476 5696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2044,a,5707,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2044 5707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(5057,a,5708,a)].">
      <j1 rule="hyper" parents="5057 5708"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,5709,a(flip),b,2005,a)].">
      <j1 rule="hyper" parents="132 5709 2005"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      (T(x,y) * R(T(x,y) \ (x * y),z,u)) / (x * y) = R(R(y,z,u) / y,y,x)
    ]]></literal>
    <justification jstring="[para(5200(a,1),5695(a,2,1))].">
      <j1 rule="para" parents="5200 5695"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      (T(x,y) * R(T(y,x),z,u)) / (x * y) = R(R(y,z,u) / y,y,x)
    ]]></literal>
    <justification jstring="[para(2490(a,1),5717(a,1,1,2,1))].">
      <j1 rule="para" parents="2490 5717"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      R(R(x,y,z) / x,x,u) = (u * R(x,y,z)) / (u * x)
    ]]></literal>
    <justification jstring="[para(2981(a,1),5718(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2981 5718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5720">
    <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(109(a,1),1306(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 1306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5721">
    <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(325,a,803,a(flip),b,5720,a),flip(a)].">
      <j1 rule="hyper" parents="325 803 5720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5722">
    <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(325,a,1683,a(flip),b,5721,a),flip(a)].">
      <j1 rule="hyper" parents="325 1683 5721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5723">
    <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(803(a,1),5722(a,1,1))].">
      <j1 rule="para" parents="803 5722"/>
    </justification>
  </clause>

  <clause id="5724">
    <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(1698(a,1),5723(a,2,1))].">
      <j1 rule="para" parents="1698 5723"/>
    </justification>
  </clause>

  <clause id="5725">
    <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(37,a,109,a,b,5724,a),flip(a)].">
      <j1 rule="hyper" parents="37 109 5724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2057,a(flip),b,5725,a),flip(a)].">
      <j1 rule="hyper" parents="65 2057 5725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2057(a,1),5726(a,1,1))].">
      <j1 rule="para" parents="2057 5726"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(638,a,5727,a),flip(a)].">
      <j1 rule="hyper" parents="638 5727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(85(a,1),5727(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="85 5727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(2744(a,1),5727(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2744 5727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) * K(u,x \ 1) = T(R(x,y,z) \ 1,u) \ 1
    ]]></literal>
    <justification jstring="[para(5729(a,1),5513(a,1,2))].">
      <j1 rule="para" parents="5729 5513"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(y,x),w,v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,2910,a(flip),b,5731,a),flip(a)].">
      <j1 rule="hyper" parents="325 2910 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5742">
    <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(5733(a,1),4191(a,1,2))].">
      <j1 rule="para" parents="5733 4191"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(1 / x,w,v5) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,2608,a,b,5736,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 2608 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,w,v5) \ 1,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),5743(a,2,1,1,1))].">
      <j1 rule="para" parents="82 5743"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(4047,a,5744,a)].">
      <j1 rule="hyper" parents="4047 5744"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      K((1 / x) \ 1,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1))
    ]]></literal>
    <justification jstring="[para(5745(a,1),5520(a,1,1))].">
      <j1 rule="para" parents="5745 5520"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      R(((x \ 1) \ 1) * K(y,x \ 1),z,u) = T(R(x,z,u) \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,4229,a,b,5735,a)].">
      <j1 rule="hyper" parents="65 4229 5735"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      R(T(x \ 1,y) \ 1,z,u) = T(R(x,z,u) \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[para(3748(a,1),5749(a,1,1))].">
      <j1 rule="para" parents="3748 5749"/>
    </justification>
  </clause>

  <clause id="5758">
    <literal><![CDATA[
      K(x,K(a(y,z,u),T(w,y * (z * u)))) = K(x,K(R(y,z,u) \ y,R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(3694,a,5742,a),flip(a)].">
      <j1 rule="hyper" parents="3694 5742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      K(x,K(a(y,z,u),T(w,y * (z * u)))) = a(K(v5,v6),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(325,a,5067,a(flip),b,5758,a),flip(a)].">
      <j1 rule="hyper" parents="325 5067 5758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      K(x,y) * T(R(x \ 1,z,u) \ 1,x) = T(R(x \ 1,z,u) \ 1,T(y,1))
    ]]></literal>
    <justification jstring="[para(85(a,1),5747(a,1,1,1))].">
      <j1 rule="para" parents="85 5747"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      T(R(x \ 1,y,z) \ 1,T(u,1)) = K(x,u) * (R(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3292(a,1),5763(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3292 5763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      K(x,y) * (R(x \ 1,z,u) \ 1) = T(R(x \ 1,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(203(a,1),5766(a,1,2)),flip(a)].">
      <j1 rule="para" parents="203 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      ((x \ 1) * (R((x \ 1) \ 1,y,z) \ 1)) / (1 / x) = T(R((x \ 1) \ 1,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3470,a,b,5767,a)].">
      <j1 rule="hyper" parents="65 3470 5767"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      K(x,(T(R((y \ 1) \ 1,z,u) \ 1,y) \ 1) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(5768(a,1),3551(a,1,2,1,1))].">
      <j1 rule="para" parents="5768 3551"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,((R((y \ 1) \ 1,z,u) \ 1) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(5751(a,2),5769(a,1,2,1))].">
      <j1 rule="para" parents="5751 5769"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R((y \ 1) \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,3405,a(flip),b,5771,a),flip(a)].">
      <j1 rule="hyper" parents="325 3405 5771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      K(x,R(T(((y \ 1) \ 1) \ 1,y) \ 1,z,u) \ w) = K(x,R(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,3473,a(flip),b,5772,a),flip(a)].">
      <j1 rule="hyper" parents="325 3473 5772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5774">
    <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),1409(a,1,1))].">
      <j1 rule="para" parents="18 1409"/>
    </justification>
  </clause>

  <clause id="5775">
    <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),5774(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="18 5774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      L(R(x,y,(x * y) \ 1),z,u) \ R(x,y,(x * y) \ 1) = L(y * ((x * y) \ 1),z,u) \ (y * ((x * y) \ 1))
    ]]></literal>
    <justification jstring="[para(483(a,1),1521(a,2,2))].">
      <j1 rule="para" parents="483 1521"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      L(R(x,y,x * y),z,u) \ R(x,y,(x * y) \ 1) = L(y * ((x * y) \ 1),z,u) \ (y * ((x * y) \ 1))
    ]]></literal>
    <justification jstring="[para(1005(a,1),5776(a,1,1,1))].">
      <j1 rule="para" parents="1005 5776"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      L(R(x,y,x * y),z,u) \ R(x,y,x * y) = L(y * ((x * y) \ 1),z,u) \ (y * ((x * y) \ 1))
    ]]></literal>
    <justification jstring="[para(1005(a,1),5777(a,1,2))].">
      <j1 rule="para" parents="1005 5777"/>
    </justification>
  </clause>

  <clause id="5779">
    <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),1939(a,2,2,1,1))].">
      <j1 rule="para" parents="20 1939"/>
    </justification>
  </clause>

  <clause id="5780">
    <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(1705(a,1),5779(a,1,1))].">
      <j1 rule="para" parents="1705 5779"/>
    </justification>
  </clause>

  <clause id="5781">
    <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(1432(a,1),5780(a,1,1,1))].">
      <j1 rule="para" parents="1432 5780"/>
    </justification>
  </clause>

  <clause id="5782">
    <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(490,a,5781,a),flip(a)].">
      <j1 rule="hyper" parents="490 5781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5783">
    <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(731(a,1),5782(a,2,1,2))].">
      <j1 rule="para" parents="731 5782"/>
    </justification>
  </clause>

  <clause id="5784">
    <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(970(a,1),5783(a,1,2))].">
      <j1 rule="para" parents="970 5783"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(203(a,1),5784(a,2,1,2))].">
      <j1 rule="para" parents="203 5784"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1366(a,2),5785(a,2,1))].">
      <j1 rule="para" parents="1366 5785"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,625,a(flip),b,5786,a),flip(a)].">
      <j1 rule="hyper" parents="325 625 5786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5566,a,b,5787,a),flip(a)].">
      <j1 rule="hyper" parents="36 5566 5787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(5789(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5789 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(5790,a,5587,a),flip(a)].">
      <j1 rule="hyper" parents="5790 5587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,5710,a(flip),b,5791,a)].">
      <j1 rule="hyper" parents="65 5710 5791"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      1 / (R(x,y,z) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,5791,a(flip),b,5710,a(flip))].">
      <j1 rule="hyper" parents="201 5791 5710"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      1 / (x \ R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,5052,a,b,5794,a)].">
      <j1 rule="hyper" parents="65 5052 5794"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) \ 1 = R(L(x,y,z),u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),5794(a,1,1,2))].">
      <j1 rule="para" parents="29 5794"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      R(x,y,y) \ x = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(1896(a,1),5794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1896 5794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ L(x \ R(x,y,z),x,z * y) = a(x,y,z) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(5794(a,1),2348(a,2,2))].">
      <j1 rule="para" parents="5794 2348"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      (R(x,y,y) \ x) \ L(a(x,y,y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y) \ (x * L(x \ R(x,y,y),z,u)) = w
    ]]></literal>
    <justification jstring="[para(5798(a,1),1416(a,1,2,1))].">
      <j1 rule="para" parents="5798 1416"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) \ 1 = L(R(x,u,w),y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),5797(a,2,1))].">
      <j1 rule="para" parents="29 5797"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(x,y,z) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2326(a,2),5799(a,1,2))].">
      <j1 rule="para" parents="2326 5799"/>
    </justification>
  </clause>

  <clause id="5806">
    <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),1966(a,1,2,1,2,1))].">
      <j1 rule="para" parents="100 1966"/>
    </justification>
  </clause>

  <clause id="5807">
    <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(992,a,5806,a),flip(a)].">
      <j1 rule="hyper" parents="992 5806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5808">
    <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(1964(a,1),5807(a,2,2))].">
      <j1 rule="para" parents="1964 5807"/>
    </justification>
  </clause>

  <clause id="5809">
    <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(455,a,5808,a),flip(a)].">
      <j1 rule="hyper" parents="455 5808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,2139,a(flip),b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="65 2139 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2139(a,1),5810(a,1,1))].">
      <j1 rule="para" parents="2139 5810"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a,b,5811,a),flip(a)].">
      <j1 rule="hyper" parents="325 2104 5811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2104(a,2),5812(a,1,1))].">
      <j1 rule="para" parents="2104 5812"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(85(a,1),5813(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="85 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2054(a,1),5813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2054 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ 1) = L(K(x,K(z,y)),u,w)
    ]]></literal>
    <justification jstring="[para(2608(a,1),5813(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2608 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(2744(a,1),5813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2744 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5814(a,1),4647(a,1,1,2))].">
      <j1 rule="para" parents="5814 4647"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5814(a,1),4674(a,1,2,2))].">
      <j1 rule="para" parents="5814 4674"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      K(x \ L(K(y,z),u,w),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(5814(a,1),4910(a,1,1,2))].">
      <j1 rule="para" parents="5814 4910"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(100(a,1),5818(a,1,1))].">
      <j1 rule="para" parents="100 5818"/>
    </justification>
  </clause>

  <clause id="5822">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3546(a,1),5818(a,1,1,2))].">
      <j1 rule="para" parents="3546 5818"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3546(a,1),5819(a,1,2,2))].">
      <j1 rule="para" parents="3546 5819"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(93(a,1),5822(a,1,1))].">
      <j1 rule="para" parents="93 5822"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(312(a,1),5822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="312 5822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = K(x \ L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(5325(a,1),5822(a,1,1))].">
      <j1 rule="para" parents="5325 5822"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = T(x,u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(93(a,1),5823(a,1,2))].">
      <j1 rule="para" parents="93 5823"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),5821(a,1,1,2))].">
      <j1 rule="para" parents="3106 5821"/>
    </justification>
  </clause>

  <clause id="5830">
    <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(5828(a,1),2547(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5828 2547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(2993(a,1),5828(a,1,1,2,1))].">
      <j1 rule="para" parents="2993 5828"/>
    </justification>
  </clause>

  <clause id="5832">
    <literal><![CDATA[
      K(L(x,y,z),u \ L(K(x,w),v5,v6)) = L(x * K(u \ 1,x),y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5820(a,1),2808(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5820 2808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2849,a,b,5815,a)].">
      <j1 rule="hyper" parents="65 2849 5815"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) * w = L(K(u,x),y,z) \ w
    ]]></literal>
    <justification jstring="[para(5815(a,1),2618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5815 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5827(a,2),2970(a,1,2))].">
      <j1 rule="para" parents="5827 2970"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),5835(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 5835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(2799,a,5817,a),flip(a)].">
      <j1 rule="hyper" parents="2799 5817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(914(a,1),5817(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="914 5817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2248,a(flip),b,5837,a),flip(a)].">
      <j1 rule="hyper" parents="65 2248 5837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),5837(a,2,2,1))].">
      <j1 rule="para" parents="10 5837"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5837(a,2,2,2))].">
      <j1 rule="para" parents="10 5837"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(102(a,2),5837(a,2,2))].">
      <j1 rule="para" parents="102 5837"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      T(x,(y * z) \ (y * x)) = x * K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(137,a,5839,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 5839 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),5839(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),5839(a,1,2,2))].">
      <j1 rule="para" parents="10 5839"/>
    </justification>
  </clause>

  <clause id="5847">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3468,a(flip),b,5845,a),flip(a)].">
      <j1 rule="hyper" parents="65 3468 5845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(1 / y) * z)
    ]]></literal>
    <justification jstring="[para(914(a,1),5842(a,2,2))].">
      <j1 rule="para" parents="914 5842"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      T(x,(y * z) \ (y * x)) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,5844,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 5844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),5849(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(5850(a,1),3060(a,1,2))].">
      <j1 rule="para" parents="5850 3060"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3818,a,b,5851,a),flip(a)].">
      <j1 rule="hyper" parents="325 3818 5851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5853">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),5851(a,1,2,2,2))].">
      <j1 rule="para" parents="10 5851"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      K(x,T(y,(z * (u * y)) \ (z * u))) = K(x,T(y,a(z,u,y)))
    ]]></literal>
    <justification jstring="[para(14(a,2),5851(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14 5851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      K(x,T(y,z \ (y * u))) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(4967(a,1),5852(a,1,2))].">
      <j1 rule="para" parents="4967 5852"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(3828,a,5855,a)].">
      <j1 rule="hyper" parents="3828 5855"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),5856(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) != K(x,y) * w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(5857(a,2),3709(a,1))].">
      <j1 rule="para" parents="5857 3709"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(4808,a,5840,a)].">
      <j1 rule="hyper" parents="4808 5840"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(3949,a,5840,a)].">
      <j1 rule="hyper" parents="3949 5840"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3540,a(flip),b,5840,a),flip(a)].">
      <j1 rule="hyper" parents="65 3540 5840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(325,a,4955,a,b,5859,a),flip(a)].">
      <j1 rule="hyper" parents="325 4955 5859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      K(x,(x \ y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5859(a,2,2,2))].">
      <j1 rule="para" parents="10 5859"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      K(x,(x \ 1) \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(67(a,1),5859(a,2,2))].">
      <j1 rule="para" parents="67 5859"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,4736,a,b,5863,a)].">
      <j1 rule="hyper" parents="65 4736 5863"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5863(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5863(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ (u * y))) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5863(a,1),3571(a,1,2,2))].">
      <j1 rule="para" parents="5863 3571"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),5865(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,L(y,x \ 1,x) \ z)
    ]]></literal>
    <justification jstring="[para(389(a,1),5865(a,1,2,1))].">
      <j1 rule="para" parents="389 5865"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,z \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,4961,a(flip),b,5868,a)].">
      <j1 rule="hyper" parents="65 4961 5868"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4944,a,b,5871,a)].">
      <j1 rule="hyper" parents="65 4944 5871"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3189,a,b,5871,a)].">
      <j1 rule="hyper" parents="65 3189 5871"/>
    </justification>
  </clause>

  <clause id="5876">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2891,a,b,5871,a)].">
      <j1 rule="hyper" parents="65 2891 5871"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5871(a,1),2918(a,2,2))].">
      <j1 rule="para" parents="5871 2918"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,5837,a,b,5874,a)].">
      <j1 rule="hyper" parents="65 5837 5874"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (x * z)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),5874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 5874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[para(102(a,2),5874(a,1,2))].">
      <j1 rule="para" parents="102 5874"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(240(a,1),5874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="240 5874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,5589,a,b,5875,a)].">
      <j1 rule="hyper" parents="65 5589 5875"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3401,a(flip),b,5848,a),flip(a)].">
      <j1 rule="hyper" parents="325 3401 5848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,z \ ((x \ z) * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,5865,a(flip),b,5878,a),flip(a)].">
      <j1 rule="hyper" parents="325 5865 5878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5885">
    <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(1737(a,1),5879(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1737 5879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5886">
    <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(2796(a,1),5880(a,2,2,2,2))].">
      <j1 rule="para" parents="2796 5880"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,1759,a(flip),b,5826,a),flip(a)].">
      <j1 rule="hyper" parents="325 1759 5826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (R(T(x,u),z,x) \ T(x,y)) * 1
    ]]></literal>
    <justification jstring="[para(5887(a,1),5673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5887 5673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(5846(a,1),3192(a,1,1))].">
      <j1 rule="para" parents="5846 3192"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(3826,a,5853,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3826 5853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      K(x,y \ (z \ (x * y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(3903,a,5873,a),flip(a)].">
      <j1 rule="hyper" parents="3903 5873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(5030(a,1),5876(a,1,1))].">
      <j1 rule="para" parents="5030 5876"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(65,a,5161,a(flip),b,5877,a),flip(a)].">
      <j1 rule="hyper" parents="65 5161 5877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4223,a(flip),b,5893,a)].">
      <j1 rule="hyper" parents="65 4223 5893"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(41,a,2849,a,b,5893,a)].">
      <j1 rule="hyper" parents="41 2849 5893"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(9(a,1),5894(a,2,2,2,1))].">
      <j1 rule="para" parents="9 5894"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),5895(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 5895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(5895(a,1),2849(a,1,1,2))].">
      <j1 rule="para" parents="5895 2849"/>
    </justification>
  </clause>

  <clause id="5900">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,5896,a,b,5286,a(flip))].">
      <j1 rule="hyper" parents="136 5896 5286"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2394,a,b,5896,a)].">
      <j1 rule="hyper" parents="36 2394 5896"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      (x * y) * K(x \ (z \ (x * y)),z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5896(a,2,2,1,2))].">
      <j1 rule="para" parents="9 5896"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4929,a(flip),b,5901,a)].">
      <j1 rule="hyper" parents="65 4929 5901"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5901(a,2),5119(a,1))].">
      <j1 rule="para" parents="5901 5119"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4054,a,b,5903,a)].">
      <j1 rule="hyper" parents="65 4054 5903"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[para(5903(a,1),3638(a,1,1))].">
      <j1 rule="para" parents="5903 3638"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(5290,a,5905,a)].">
      <j1 rule="hyper" parents="5290 5905"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3440,a(flip),b,5910,a),flip(a)].">
      <j1 rule="hyper" parents="65 3440 5910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(5119,a,5911,a),flip(a)].">
      <j1 rule="hyper" parents="5119 5911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(5912(a,1),2626(a,2,2,2))].">
      <j1 rule="para" parents="5912 2626"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(4938(a,1),5904(a,1))].">
      <j1 rule="para" parents="4938 5904"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4948,a(flip),b,5898,a)].">
      <j1 rule="hyper" parents="65 4948 5898"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(y / (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3804,a(flip),b,5907,a(flip))].">
      <j1 rule="hyper" parents="36 3804 5907"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,3057,a(flip),b,5917,a),flip(a)].">
      <j1 rule="hyper" parents="325 3057 5917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(5918(a,1),3108(a,1,1))].">
      <j1 rule="para" parents="5918 3108"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(3156,a,5919,a)].">
      <j1 rule="hyper" parents="3156 5919"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,3945,a(flip),b,5920,a)].">
      <j1 rule="hyper" parents="65 3945 5920"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(5921(a,1),2849(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5921 2849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,3442,a(flip),b,5838,a),flip(a)].">
      <j1 rule="hyper" parents="325 3442 5838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4799,a(flip),b,5841,a),flip(a)].">
      <j1 rule="hyper" parents="65 4799 5841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(2618(a,1),5841(a,1,1,2))].">
      <j1 rule="para" parents="2618 5841"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(5841(a,1),4808(a,1))].">
      <j1 rule="para" parents="5841 4808"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(5866(a,1),5841(a,1,1))].">
      <j1 rule="para" parents="5866 5841"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(5863(a,1),5841(a,1,1))].">
      <j1 rule="para" parents="5863 5841"/>
    </justification>
  </clause>

  <clause id="5930">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(5867(a,1),5841(a,1,1))].">
      <j1 rule="para" parents="5867 5841"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(4944(a,2),5927(a,1))].">
      <j1 rule="para" parents="4944 5927"/>
    </justification>
  </clause>

  <clause id="5932">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ (z * y))) = u
    ]]></literal>
    <justification jstring="[para(5837(a,2),5931(a,1))].">
      <j1 rule="para" parents="5837 5931"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,4959,a(flip),b,5925,a),flip(a)].">
      <j1 rule="hyper" parents="325 4959 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2531,a(flip),b,5881,a),flip(a)].">
      <j1 rule="hyper" parents="325 2531 5881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      (1 / x) \ K(y,((x \ 1) * z) \ 1) = x * K(y,z \ x)
    ]]></literal>
    <justification jstring="[hyper(132,a,5924,a(flip),b,911,a)].">
      <j1 rule="hyper" parents="132 5924 911"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(85(a,1),5924(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="85 5924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2121(a,1),5831(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2121 5831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,5572,a,b,5942,a)].">
      <j1 rule="hyper" parents="325 5572 5942"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(2310(a,1),5833(a,1,1,2))].">
      <j1 rule="para" parents="2310 5833"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,394,a(flip),b,5947,a)].">
      <j1 rule="hyper" parents="65 394 5947"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,273,a(flip),b,5947,a)].">
      <j1 rule="hyper" parents="65 273 5947"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(41,a,18,a(flip),b,5947,a),flip(a)].">
      <j1 rule="hyper" parents="41 18 5947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      x * L(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 * L(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(5947(a,1),143(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5947 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),5947(a,1,1))].">
      <j1 rule="para" parents="100 5947"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3547,a,b,5949,a)].">
      <j1 rule="hyper" parents="65 3547 5949"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(5949(a,1),294(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5949 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5949(a,1),3573(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5949 3573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5949(a,1),5816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5949 5816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(5950(a,1),270(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5950 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4806,a,5954,a),flip(a)].">
      <j1 rule="hyper" parents="4806 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      L(K(T(x,y),T(z,y)),u,w) = K(x,L(z,u / T(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(3705,a,5954,a),flip(a)].">
      <j1 rule="hyper" parents="3705 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5593,a(flip),b,5954,a),flip(a)].">
      <j1 rule="hyper" parents="65 5593 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),5954(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(3949,a,5959,a)].">
      <j1 rule="hyper" parents="3949 5959"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,5959,a(flip),b,4391,a(flip))].">
      <j1 rule="hyper" parents="137 5959 4391"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(30(a,1),5963(a,1,1))].">
      <j1 rule="para" parents="30 5963"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x)
    ]]></literal>
    <justification jstring="[para(1548(a,1),5963(a,1,1))].">
      <j1 rule="para" parents="1548 5963"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      T(x,L(y,z,x)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(5963(a,1),2634(a,2,1))].">
      <j1 rule="para" parents="5963 2634"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2634,a,b,5968,a),flip(a)].">
      <j1 rule="hyper" parents="325 2634 5968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      T(x,(x * y) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(308(a,1),5969(a,1,2))].">
      <j1 rule="para" parents="308 5969"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(3949,a,5961,a)].">
      <j1 rule="hyper" parents="3949 5961"/>
    </justification>
  </clause>

  <clause id="5972">
    <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(2598(a,1),5971(a,1,1))].">
      <j1 rule="para" parents="2598 5971"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4808,a,5962,a),flip(a)].">
      <j1 rule="hyper" parents="4808 5962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      L(L(K(x,y),z * y,u),y,w) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4024,a,5962,a)].">
      <j1 rule="hyper" parents="4024 5962"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(5962(a,1),4735(a,1,2,2))].">
      <j1 rule="para" parents="5962 4735"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),5973(a,1,2))].">
      <j1 rule="para" parents="30 5973"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(5973(a,1),3546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5973 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      T((x * y) / T(x,z),x) = y * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(2887,a,5964,a)].">
      <j1 rule="hyper" parents="2887 5964"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      T(x,T(y,x) \ (x \ z)) = T(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(113(a,1),5970(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 5970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5978(a,1,1,1))].">
      <j1 rule="para" parents="10 5978"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (x \ L(T(x,y),z,x)) * K(u,R(x,z,x))
    ]]></literal>
    <justification jstring="[para(5380(a,1),5980(a,2,1))].">
      <j1 rule="para" parents="5380 5980"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5198,a,b,5965,a)].">
      <j1 rule="hyper" parents="65 5198 5965"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      K(x,(T(L(x,y,z),u) \ w) \ 1) = K(x,w \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,5008,a(flip),b,5975,a),flip(a)].">
      <j1 rule="hyper" parents="65 5008 5975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(3906,a,5956,a),flip(a)].">
      <j1 rule="hyper" parents="3906 5956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(3905,a,5957,a),flip(a)].">
      <j1 rule="hyper" parents="3905 5957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      T(x,(y * x) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4685,a(flip),b,5979,a),flip(a)].">
      <j1 rule="hyper" parents="65 4685 5979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      T(x,L(x \ y,x,z)) = T(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[para(102(a,2),5986(a,1,2))].">
      <j1 rule="para" parents="102 5986"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,3580,a,b,5984,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 5984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(5950(a,2),5985(a,1,2))].">
      <j1 rule="para" parents="5950 5985"/>
    </justification>
  </clause>

  <clause id="5990">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,L(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,5985,a,b,5988,a),flip(a)].">
      <j1 rule="hyper" parents="325 5985 5988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      x * K(L(K(y,z),u,w),x) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,5990,a,b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 5990 2104"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      (x * (y * T(z,u))) * L(K(u,z),y * z,x) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(2093(a,1),5951(a,1,1,2))].">
      <j1 rule="para" parents="2093 5951"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,T(y,u)),u,x) = x * u
    ]]></literal>
    <justification jstring="[para(3075(a,1),5951(a,1,1,2))].">
      <j1 rule="para" parents="3075 5951"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x)
    ]]></literal>
    <justification jstring="[para(3075(a,1),5953(a,1,1,2))].">
      <j1 rule="para" parents="3075 5953"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(3547(a,2),5958(a,1))].">
      <j1 rule="para" parents="3547 5958"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      L(K(x,L(y,z,u)),y,w) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5962(a,1),5974(a,1,1))].">
      <j1 rule="para" parents="5962 5974"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      K((x \ y) \ z,L(z,u,w)) = K(y \ (x * z),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3540,a(flip),b,5996,a),flip(a)].">
      <j1 rule="hyper" parents="65 3540 5996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,3546,a(flip),b,5977,a),flip(a)].">
      <j1 rule="hyper" parents="325 3546 5977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      K(L(x,y,z),(x \ u) \ w) = K(L(x,y,z),u \ (x * w))
    ]]></literal>
    <justification jstring="[para(469(a,1),5998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="469 5998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),z,y) = w
    ]]></literal>
    <justification jstring="[para(104(a,1),5995(a,1,2))].">
      <j1 rule="para" parents="104 5995"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,4939,a(flip),b,5967,a),flip(a)].">
      <j1 rule="hyper" parents="325 4939 5967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(6001(a,1),3582(a,2,2))].">
      <j1 rule="para" parents="6001 3582"/>
    </justification>
  </clause>

  <clause id="6004">
    <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(1617,a,5991,a),flip(a)].">
      <j1 rule="hyper" parents="1617 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * (K(y,x) * z))),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(5993(a,1),3669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5993 3669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6006">
    <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(65,a,4086,a,b,5994,a)].">
      <j1 rule="hyper" parents="65 4086 5994"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(2310(a,1),5834(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2310 5834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(332,a,6007,a),flip(a)].">
      <j1 rule="hyper" parents="332 6007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6010">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) * (v5 \ (x * L(K(z,y),u,w)))) = K(x,T(v5 \ x,L(K(z,y),u,w)))
    ]]></literal>
    <justification jstring="[para(6007(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="6007 5892"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1256(a,1),5847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1256 5847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6012">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(5911(a,1),5900(a,1,1,2))].">
      <j1 rule="para" parents="5911 5900"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2626,a,b,5913,a),flip(a)].">
      <j1 rule="hyper" parents="325 2626 5913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4973,a,6013,a),flip(a)].">
      <j1 rule="hyper" parents="4973 6013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6015">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(2108,a,6014,a)].">
      <j1 rule="hyper" parents="2108 6014"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      K(x,(y \ x) \ (x * z)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6015(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      K(x,(y \ x) \ (z * x)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4955,a,b,6016,a)].">
      <j1 rule="hyper" parents="65 4955 6016"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2849,a(flip),b,5922,a),flip(a)].">
      <j1 rule="hyper" parents="325 2849 5922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(3205,a,6018,a)].">
      <j1 rule="hyper" parents="3205 6018"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),6019(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 6019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(3645(a,1),5960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3645 5960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(194(a,1),6021(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="194 6021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(268(a,1),6021(a,1,2,2))].">
      <j1 rule="para" parents="268 6021"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(2165(a,1),6021(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2165 6021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,6022,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 6022 18"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,5954,a(flip),b,6024,a),flip(a)].">
      <j1 rule="hyper" parents="325 5954 6024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6027(a,1),4282(a,1,2))].">
      <j1 rule="para" parents="6027 4282"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      K(L(K(x,y),z * K(y,u),w),v5) = L(K(x,K(y,v5)),z,w)
    ]]></literal>
    <justification jstring="[para(6027(a,2),5956(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6027 5956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(5952,a,6029,a)].">
      <j1 rule="hyper" parents="5952 6029"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(3091,a,6029,a)].">
      <j1 rule="hyper" parents="3091 6029"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      T(x,y) * L(K(y,x),z,u) = x * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,6029,a(flip),b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="137 6029 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6034">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[hyper(136,a,6029,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 6029 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(3546(a,1),6029(a,1,2))].">
      <j1 rule="para" parents="3546 6029"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,K(z,y)) = x * L(K(y,z),w,u)
    ]]></literal>
    <justification jstring="[para(6029(a,1),4129(a,1,2))].">
      <j1 rule="para" parents="6029 4129"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3932,a,b,6032,a)].">
      <j1 rule="hyper" parents="65 3932 6032"/>
    </justification>
  </clause>

  <clause id="6040">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,6008,a,b,6032,a)].">
      <j1 rule="hyper" parents="36 6008 6032"/>
    </justification>
  </clause>

  <clause id="6041">
    <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(3544(a,1),6040(a,1,1))].">
      <j1 rule="para" parents="3544 6040"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      T(x * L(K(y,x),z,u),y) = x * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,4205,a,b,6033,a)].">
      <j1 rule="hyper" parents="65 4205 6033"/>
    </justification>
  </clause>

  <clause id="6043">
    <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(137,a,6035,a(flip),b,4864,a),flip(a)].">
      <j1 rule="hyper" parents="137 6035 4864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      (x * K(y * L(K(z,y),u,w),z)) * (y * L(K(z,y),u,w)) = x * (y * a(w,u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6042(a,1),2082(a,2,2))].">
      <j1 rule="para" parents="6042 2082"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      K(x,(L(T(x,y),z,u) \ w) \ 1) = K(x,w \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),5983(a,1,2,1,1))].">
      <j1 rule="para" parents="25 5983"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),(x \ u) \ L(K(x,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(2253(a,2),5999(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2253 5999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,z),y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(5302(a,1),6000(a,1))].">
      <j1 rule="para" parents="5302 6000"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,3582,a(flip),b,6003,a),flip(a)].">
      <j1 rule="hyper" parents="325 3582 6003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      K(L(K(x,y),z * K(y,u),w),v5) = K(L(K(y,x),z,w) \ 1,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,3573,a,b,6030,a),flip(a)].">
      <j1 rule="hyper" parents="325 3573 6030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      K(L(K(x,y),z * K(y,u),w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(v5,L(y,z,w))) = v6
    ]]></literal>
    <justification jstring="[para(6030(a,2),3905(a,1))].">
      <j1 rule="para" parents="6030 3905"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(65,a,4224,a,b,6034,a)].">
      <j1 rule="hyper" parents="65 4224 6034"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(6008(a,1),6034(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6008 6034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(z,y),u,w) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(2851(a,1),6036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2851 6036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(2745,a,6045,a)].">
      <j1 rule="hyper" parents="2745 6045"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K((x \ y) \ T(y,x),z \ L(T(x,x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(2781(a,1),6054(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2781 6054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L(L(T(x,x \ y),y,x),u,w)) = K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(2816(a,1),6054(a,1,2,2,1))].">
      <j1 rule="para" parents="2816 6054"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(132,a,2619,a(flip),b,6052,a),flip(a)].">
      <j1 rule="hyper" parents="132 2619 6052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(65,a,6051,a(flip),b,6057,a),flip(a)].">
      <j1 rule="hyper" parents="65 6051 6057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(201,a,6051,a(flip),b,6057,a(flip))].">
      <j1 rule="hyper" parents="201 6051 6057"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) = K(x,T(y,a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(2769(a,1),5854(a,1,2))].">
      <j1 rule="para" parents="2769 5854"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      K(x,T(y,a(z,u,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3185,a(flip),b,6060,a),flip(a)].">
      <j1 rule="hyper" parents="65 3185 6060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      T(x,T(y,a(z,u,y))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,6061,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 6061 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      T(x,T(y,a(z,u,y))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,6063,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 6063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      (x * T(y,a(z,u,y))) / T(x,y) = T(y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(201,a,6064,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="201 6064 22"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      T(x,T(a(y,z,x),u)) = T(x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,3737,a(flip),b,6065,a)].">
      <j1 rule="hyper" parents="65 3737 6065"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      T(T(x,y),T(a(z,u,x),w)) = T(T(x,a(z,u,x)),y)
    ]]></literal>
    <justification jstring="[para(6066(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6066 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      K(x,a(y,z,x)) * T(x,u) = T(T(x,a(y,z,x)),u)
    ]]></literal>
    <justification jstring="[hyper(3734,a,6067,a)].">
      <j1 rule="hyper" parents="3734 6067"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      T(x,T(y,a(z,u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3219,a,b,6068,a)].">
      <j1 rule="hyper" parents="36 3219 6068"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      T(x,T(y,a(z,u,x))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a(flip),b,6069,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 6069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      K(x,T(y,a(z,u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2108,a,6070,a)].">
      <j1 rule="hyper" parents="2108 6070"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      K(x,y) * a(z,u,x) = a(z,u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,6071,a(flip),b,3647,a)].">
      <j1 rule="hyper" parents="136 6071 3647"/>
    </justification>
  </clause>

  <clause id="6073">
    <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(451(a,1),5860(a,2,2))].">
      <j1 rule="para" parents="451 5860"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      (x * (y * T(z,u))) * K(u,L(z,y,x)) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(5962(a,1),5992(a,1,2))].">
      <j1 rule="para" parents="5962 5992"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      (x * (y * T(T(z,y),u))) \ (x * (z * y)) = K(u,L(T(z,y),y,x))
    ]]></literal>
    <justification jstring="[hyper(132,a,233,a(flip),b,6075,a)].">
      <j1 rule="hyper" parents="132 233 6075"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(113(a,1),6075(a,1,1,2))].">
      <j1 rule="para" parents="113 6075"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(z,L(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(140,a,6078,a)].">
      <j1 rule="hyper" parents="140 6078"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6078(a,1),4674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6078 4674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6078(a,1),4927(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6078 4927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6082">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6078(a,1),4963(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6078 4963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6080(a,1),3065(a,1,2))].">
      <j1 rule="para" parents="6080 3065"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(4846,a,6083,a),flip(a)].">
      <j1 rule="hyper" parents="4846 6083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u * z)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4764,a,b,6084,a)].">
      <j1 rule="hyper" parents="65 4764 6084"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6079(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6079 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(5964(a,1),6026(a,2,2))].">
      <j1 rule="para" parents="5964 6026"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = ((x / y) * y) \ (((x / y) * (y * K(x,z))) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,1601,a,b,6039,a)].">
      <j1 rule="hyper" parents="325 1601 6039"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      (x * (y * (K(z,y) \ (y \ u)))) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(5030(a,2),6087(a,2,2))].">
      <j1 rule="para" parents="5030 6087"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(67(a,1),5861(a,2,1))].">
      <j1 rule="para" parents="67 5861"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(6090(a,1),3761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6090 3761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z)
    ]]></literal>
    <justification jstring="[hyper(2859,a,5899,a),flip(a)].">
      <j1 rule="hyper" parents="2859 5899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6081,a(flip),b,6093,a)].">
      <j1 rule="hyper" parents="65 6081 6093"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      1 / (x \ K((y * z) \ (x \ u),x)) = T(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6094(a,1),2626(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6094 2626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      K(L(K(x,y \ 1),z * K(y \ 1,u),w),v5) = K(K(L(y,z,w) \ 1,x) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(2307(a,1),6049(a,2,1,1))].">
      <j1 rule="para" parents="2307 6049"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      x * (T(y,z) * L(K(z,y),u,w)) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4013,a(flip),b,6053,a)].">
      <j1 rule="hyper" parents="65 4013 6053"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      T(x,(y * (x * z)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(2636,a,6095,a),flip(a)].">
      <j1 rule="hyper" parents="2636 6095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6082,a,b,6098,a)].">
      <j1 rule="hyper" parents="65 6082 6098"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * (y * a(z,u,K(y,w)))
    ]]></literal>
    <justification jstring="[para(6033(a,1),6097(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6033 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      a(x,y,a(z,u,K(y,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,6100,a(flip),b,89,a),flip(a)].">
      <j1 rule="hyper" parents="131 6100 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) = 1
    ]]></literal>
    <justification jstring="[para(3645(a,1),6101(a,1,3,3))].">
      <j1 rule="para" parents="3645 6101"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(5858,a,5870,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5858 5870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3580,a,b,6103,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 6103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(3585,a,6104,a)].">
      <j1 rule="hyper" parents="3585 6104"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3946,a,b,6105,a)].">
      <j1 rule="hyper" parents="65 3946 6105"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4883,a(flip),b,6106,a)].">
      <j1 rule="hyper" parents="65 4883 6106"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(3777,a,6107,a)].">
      <j1 rule="hyper" parents="3777 6107"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6048,a,b,6108,a)].">
      <j1 rule="hyper" parents="65 6048 6108"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(3595,a,6109,a)].">
      <j1 rule="hyper" parents="3595 6109"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      K(x * y,K(z,L(a(x,y,u),x * (y * u),K(x * y,w)))) = K(x * y,K(z,(T(x * y,w) * u) \ L(u,y,x)))
    ]]></literal>
    <justification jstring="[para(4436(a,1),6110(a,1,2,2))].">
      <j1 rule="para" parents="4436 6110"/>
    </justification>
  </clause>

  <clause id="6112">
    <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(3362(a,2),5926(a,2,2,1))].">
      <j1 rule="para" parents="3362 5926"/>
    </justification>
  </clause>

  <clause id="6113">
    <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(3469(a,2),5926(a,2,2,1))].">
      <j1 rule="para" parents="3469 5926"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2211,a,b,5930,a),flip(a)].">
      <j1 rule="hyper" parents="325 2211 5930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      L(K(x,(y \ x) \ ((z \ u) * x)),z \ u,z) = K(x,(z * ((((y \ x) / x) * y) * (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(1479(a,2),5930(a,2,2,1,2))].">
      <j1 rule="para" parents="1479 5930"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6094,a(flip),b,5982,a)].">
      <j1 rule="hyper" parents="65 6094 5982"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      (x * (T(y,z) * u)) \ (x * (y * u)) = K(z,L(T(y,u),u,x))
    ]]></literal>
    <justification jstring="[para(241(a,1),6077(a,1,1,2))].">
      <j1 rule="para" parents="241 6077"/>
    </justification>
  </clause>

  <clause id="6119">
    <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),6118(a,2,2))].">
      <j1 rule="para" parents="25 6118"/>
    </justification>
  </clause>

  <clause id="6120">
    <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(5890(a,1),3193(a,1))].">
      <j1 rule="para" parents="5890 3193"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(6120,a,5280,a)].">
      <j1 rule="hyper" parents="6120 5280"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(3205,a,5882,a)].">
      <j1 rule="hyper" parents="3205 5882"/>
    </justification>
  </clause>

  <clause id="6126">
    <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(3195,a,6043,a)].">
      <j1 rule="hyper" parents="3195 6043"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(187(a,1),6126(a,1,2,2))].">
      <j1 rule="para" parents="187 6126"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,5461,a(flip),b,6125,a)].">
      <j1 rule="hyper" parents="65 5461 6125"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3500,a(flip),b,6128,a)].">
      <j1 rule="hyper" parents="65 3500 6128"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4951,a(flip),b,6130,a),flip(a)].">
      <j1 rule="hyper" parents="65 4951 6130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6131(a,2,2,1))].">
      <j1 rule="para" parents="7 6131"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(69(a,1),6131(a,1,2,2))].">
      <j1 rule="para" parents="69 6131"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      K(x,L(y,x \ 1,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5872,a(flip),b,6132,a)].">
      <j1 rule="hyper" parents="65 5872 6132"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,2547,a(flip),b,5830,a),flip(a)].">
      <j1 rule="hyper" parents="325 2547 5830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      K(L(x,y,z),K(u,x) * w) = K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(2619(a,1),6135(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2619 6135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      K(L(x,y,z),L(K(u,x),w,v5) * v6) = K(L(x,y,z),v6)
    ]]></literal>
    <justification jstring="[para(2310(a,1),6136(a,1,2,1))].">
      <j1 rule="para" parents="2310 6136"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = R(T(x,u),z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,8,a(flip),b,5889,a),flip(a)].">
      <j1 rule="hyper" parents="325 8 5889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(3510(a,1),6005(a,1,1))].">
      <j1 rule="para" parents="3510 6005"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / (x * u) = (x * u) / (x * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3952,a(flip),b,6140,a)].">
      <j1 rule="hyper" parents="65 3952 6140"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3505,a,b,6142,a)].">
      <j1 rule="hyper" parents="325 3505 6142"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = (x * (T(K(w,z),u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(2375(a,1),6142(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2375 6142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6147">
    <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(6145(a,2),4271(a,1))].">
      <j1 rule="para" parents="6145 4271"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(6147,a,5494,a),flip(a)].">
      <j1 rule="hyper" parents="6147 5494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6148(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 6148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),6149(a,2,2))].">
      <j1 rule="para" parents="20 6149"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2957,a(flip),b,6150,a),flip(a)].">
      <j1 rule="hyper" parents="325 2957 6150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,6152,a(flip),b,4270,a)].">
      <j1 rule="hyper" parents="136 6152 4270"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,2488,a(flip),b,6154,a),flip(a)].">
      <j1 rule="hyper" parents="65 2488 6154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(132,a,2488,a(flip),b,6154,a(flip))].">
      <j1 rule="hyper" parents="132 2488 6154"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(771,a,6155,a)].">
      <j1 rule="hyper" parents="771 6155"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      x * (K(y \ x,y) * z) = ((y \ x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(528,a,6155,a)].">
      <j1 rule="hyper" parents="528 6155"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,2093,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="132 2093 6155"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      (x * y) \ ((y * z) * (z \ x)) = K(y,x) * a(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(132,a,706,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="132 706 6155"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(132,a,10,a(flip),b,6155,a),flip(a)].">
      <j1 rule="hyper" parents="132 10 6155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      (x * y) * (T(x,y) \ z) = (y * x) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4526(a,1),6155(a,1,2))].">
      <j1 rule="para" parents="4526 6155"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[hyper(2350,a,6158,a)].">
      <j1 rule="hyper" parents="2350 6158"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      x * (K(y,y \ x) * z) = (y * (x / y)) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,6165,a(flip),b,2595,a),flip(a)].">
      <j1 rule="hyper" parents="137 6165 2595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      K(x,x \ y) * (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),6163(a,1,2,1))].">
      <j1 rule="para" parents="10 6163"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ v5)) = L(x,y,z * ((w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(6163(a,1),3507(a,1,3,2))].">
      <j1 rule="para" parents="6163 3507"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      a(x * ((y * z) \ u),w,v5) = a(x * ((z * y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(6163(a,1),3508(a,1,1,2))].">
      <j1 rule="para" parents="6163 3508"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      K(x \ y,x) * L(T(x,x \ y),z,u) = y \ ((L(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(132,a,987,a(flip),b,6159,a),flip(a)].">
      <j1 rule="hyper" parents="132 987 6159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(36,a,2919,a(flip),b,6159,a),flip(a)].">
      <j1 rule="hyper" parents="36 2919 6159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6173">
    <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(325,a,3934,a(flip),b,6161,a),flip(a)].">
      <j1 rule="hyper" parents="325 3934 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6174">
    <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(325,a,3933,a(flip),b,6161,a),flip(a)].">
      <j1 rule="hyper" parents="325 3933 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2543,a(flip),b,6161,a),flip(a)].">
      <j1 rule="hyper" parents="65 2543 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(6161(a,2),3089(a,1))].">
      <j1 rule="para" parents="6161 3089"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4842,a,b,6175,a)].">
      <j1 rule="hyper" parents="65 4842 6175"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),6177(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(236(a,1),6178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="236 6178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4837(a,1),6179(a,1,2))].">
      <j1 rule="para" parents="4837 6179"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(6179(a,1),5050(a,1,2))].">
      <j1 rule="para" parents="6179 5050"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      K(a(x,y,x),z) = 1
    ]]></literal>
    <justification jstring="[para(6179(a,1),5053(a,1,1))].">
      <j1 rule="para" parents="6179 5053"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[para(6179(a,1),5054(a,1,2))].">
      <j1 rule="para" parents="6179 5054"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1998,a,6181,a),flip(a)].">
      <j1 rule="hyper" parents="1998 6181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(1996,a,6181,a)].">
      <j1 rule="hyper" parents="1996 6181"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,2973,a,b,6181,a)].">
      <j1 rule="hyper" parents="65 2973 6181"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(6181(a,1),292(a,1,2))].">
      <j1 rule="para" parents="6181 292"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,6183,a,b,69,a)].">
      <j1 rule="hyper" parents="137 6183 69"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(6188(a,1),1602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6188 1602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4844,a,6180,a)].">
      <j1 rule="hyper" parents="4844 6180"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1473,a,6180,a)].">
      <j1 rule="hyper" parents="1473 6180"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(148,a,6180,a)].">
      <j1 rule="hyper" parents="148 6180"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5314,a(flip),b,6180,a),flip(a)].">
      <j1 rule="hyper" parents="65 5314 6180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,6180,a(flip),b,2228,a)].">
      <j1 rule="hyper" parents="137 6180 2228"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,6180,a(flip),b,1464,a)].">
      <j1 rule="hyper" parents="136 6180 1464"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(6180(a,1),4843(a,1,1))].">
      <j1 rule="para" parents="6180 4843"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      x \ R(T(x,y),z,x) = K(x,y) * a(x,z,x)
    ]]></literal>
    <justification jstring="[para(6180(a,1),4542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6180 4542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(6180(a,1),4907(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6180 4907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(6180(a,1),5454(a,1,3))].">
      <j1 rule="para" parents="6180 5454"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(6192(a,1),5719(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6192 5719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      R(x,y,x) \ (x * (z * a(x,y,x))) = L(T(z,a(x,y,x)),a(x,y,x),x)
    ]]></literal>
    <justification jstring="[para(6193(a,1),240(a,1,1))].">
      <j1 rule="para" parents="6193 240"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(6200(a,1),379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6200 379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2857,a,6190,a)].">
      <j1 rule="hyper" parents="2857 6190"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(2676,a,6190,a)].">
      <j1 rule="hyper" parents="2676 6190"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(6190(a,1),1544(a,1,3))].">
      <j1 rule="para" parents="6190 1544"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(6190(a,1),4902(a,1,2))].">
      <j1 rule="para" parents="6190 4902"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(6190(a,1),5078(a,1,1))].">
      <j1 rule="para" parents="6190 5078"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(989,a,6207,a),flip(a)].">
      <j1 rule="hyper" parents="989 6207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = z \ (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(538,a,6207,a),flip(a)].">
      <j1 rule="hyper" parents="538 6207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      (a(x,y,x) \ 1) \ z = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(537,a,6207,a),flip(a)].">
      <j1 rule="hyper" parents="537 6207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(526,a,6207,a),flip(a)].">
      <j1 rule="hyper" parents="526 6207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      a(x,y,x) * (1 / z) = a(x,y,x) / z
    ]]></literal>
    <justification jstring="[hyper(201,a,6207,a(flip),b,229,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 6207 229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(201,a,6207,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="201 6207 104"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6207(a,1),52(a,2))].">
      <j1 rule="para" parents="6207 52"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ (x * (a(y,z,y) * (u * w))) = L(w,a(y,z,y) * u,x)
    ]]></literal>
    <justification jstring="[para(6207(a,1),451(a,2,1))].">
      <j1 rule="para" parents="6207 451"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = ((a(x,y,x) * (z * u)) * w) / (u * w)
    ]]></literal>
    <justification jstring="[para(6207(a,1),452(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6207 452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      ((a(x,y,x) * z) * (u * w)) \ ((a(x,y,x) * (z * u)) * w) = a(a(x,y,x) * z,L(u,z,a(x,y,x)),w)
    ]]></literal>
    <justification jstring="[para(6207(a,1),449(a,1,1,2,1))].">
      <j1 rule="para" parents="6207 449"/>
    </justification>
  </clause>

  <clause id="6221">
    <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="[hyper(137,a,3164,a(flip),b,6197,a)].">
      <j1 rule="hyper" parents="137 3164 6197"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),6199(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(6199(a,1),115(a,1,1))].">
      <j1 rule="para" parents="6199 115"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      (x * y) \ (y * (T(z * T(x,y),z) / z)) = L(a(z,T(x,y),z),T(x,y),y)
    ]]></literal>
    <justification jstring="[para(6199(a,2),239(a,1,2,2))].">
      <j1 rule="para" parents="6199 239"/>
    </justification>
  </clause>

  <clause id="6225">
    <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(6199(a,2),450(a,1,2,2))].">
      <j1 rule="para" parents="6199 450"/>
    </justification>
  </clause>

  <clause id="6226">
    <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(6199(a,2),774(a,1,2,2,2))].">
      <j1 rule="para" parents="6199 774"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,6180,a(flip),b,6194,a),flip(a)].">
      <j1 rule="hyper" parents="325 6180 6194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      x * a(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,5227,a(flip),b,6194,a(flip))].">
      <j1 rule="hyper" parents="137 5227 6194"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      a(x,y,T(x,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5227,a(flip),b,6228,a)].">
      <j1 rule="hyper" parents="65 5227 6228"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      a(T(x,y),z,T(x,u)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1868,a,b,6230,a)].">
      <j1 rule="hyper" parents="65 1868 6230"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      x * (y * a(y,x,T(y,z))) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,6229,a,b,4774,a)].">
      <j1 rule="hyper" parents="137 6229 4774"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),6208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      (1 / x) * a(y,z,y) = a(y,z,y) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,6184,a(flip),b,6214,a)].">
      <j1 rule="hyper" parents="65 6184 6214"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(195,a,6234,a)].">
      <j1 rule="hyper" parents="195 6234"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1707,a(flip),b,6234,a)].">
      <j1 rule="hyper" parents="65 1707 6234"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,470,a(flip),b,6236,a)].">
      <j1 rule="hyper" parents="65 470 6236"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      a(x,y,x) * L(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,6236,a(flip),b,470,a(flip))].">
      <j1 rule="hyper" parents="137 6236 470"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(6199(a,2),6236(a,1,1))].">
      <j1 rule="para" parents="6199 6236"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      L(x,y,x) * a(x,y,x) = x
    ]]></literal>
    <justification jstring="[para(6238(a,1),6185(a,1,1))].">
      <j1 rule="para" parents="6238 6185"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4819,a(flip),b,6237,a)].">
      <j1 rule="hyper" parents="65 4819 6237"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      L(x,y,x) \ (x * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1269,a,6243,a)].">
      <j1 rule="hyper" parents="1269 6243"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      x * (a(x,y,x) \ z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,6185,a(flip),b,6245,a),flip(a)].">
      <j1 rule="hyper" parents="137 6185 6245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      a(x,y,x) \ 1 = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,8,a(flip),b,6247,a),flip(a)].">
      <j1 rule="hyper" parents="132 8 6247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(6248(a,1),6212(a,1,1))].">
      <j1 rule="para" parents="6248 6212"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,6184,a(flip),b,6249,a),flip(a)].">
      <j1 rule="hyper" parents="325 6184 6249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = x * K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4615,a(flip),b,6223,a),flip(a)].">
      <j1 rule="hyper" parents="325 4615 6223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      x * ((y * a(y,x,T(y,z))) * L((y * a(y,x,T(y,z))) \ (x \ u),w,v5)) = T(y * x,y) * L((x * (y * a(y,x,T(y,z)))) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(6233(a,1),908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6233 908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6253">
    <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(3638(a,1),6241(a,1,2))].">
      <j1 rule="para" parents="3638 6241"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      (x * y) * (y \ (x \ T(y,x))) = (y * x) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(4599(a,1),6164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4599 6164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      L((K(x,x \ y) * z) \ 1,K(x,x \ y) * z,y) = ((x * (y / x)) * z) \ y
    ]]></literal>
    <justification jstring="[para(6166(a,1),225(a,2,1))].">
      <j1 rule="para" parents="6166 225"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      a(((x \ y) * x) \ z,u,w) = a(y \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6168(a,1),1865(a,1,1))].">
      <j1 rule="para" parents="6168 1865"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(520,a,6172,a),flip(a)].">
      <j1 rule="hyper" parents="520 6172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      T(x,x \ y) * ((x * (y / x)) \ z) = x * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(137,a,6172,a(flip),b,4507,a)].">
      <j1 rule="hyper" parents="137 6172 4507"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (x * ((K(x,y) * a(x,z,x)) * u)) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(6198(a,1),101(a,1,2,2,1))].">
      <j1 rule="para" parents="6198 101"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      L((K(x,y) * a(x,z,x)) \ u,x \ R(T(x,y),z,x),T(x,R(T(x,y),z,x))) = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u)
    ]]></literal>
    <justification jstring="[para(6198(a,1),2579(a,1,1,1))].">
      <j1 rule="para" parents="6198 2579"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1062,a,6210,a)].">
      <j1 rule="hyper" parents="1062 6210"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      (a(x,y,x) * (1 / z)) * (z \ u) = a(x,y,x) * ((z * z) \ u)
    ]]></literal>
    <justification jstring="[para(653(a,1),6210(a,2,2))].">
      <j1 rule="para" parents="653 6210"/>
    </justification>
  </clause>

  <clause id="6263">
    <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(6210(a,1),709(a,1,1,2))].">
      <j1 rule="para" parents="6210 709"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      (a(x,y,x) * ((z \ 1) * (z \ u))) * w = a(x,y,x) * ((z \ 1) * (z \ (u * w)))
    ]]></literal>
    <justification jstring="[para(901(a,1),6210(a,2,2))].">
      <j1 rule="para" parents="901 6210"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      a(a(x,y,x) * (z * u),w,v5) = a(u * (a(x,y,x) * z),w,v5)
    ]]></literal>
    <justification jstring="[para(6210(a,1),2337(a,1,1))].">
      <j1 rule="para" parents="6210 2337"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      a(x * (a(y,z,y) * (u * w)),v5,v6) = a(x * (w * (a(y,z,y) * u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(6210(a,1),3512(a,1,1,2))].">
      <j1 rule="para" parents="6210 3512"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(6196(a,1),6210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6196 6210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(6184(a,1),6210(a,1,1))].">
      <j1 rule="para" parents="6184 6210"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      ((a(x,y,x) * (z * u)) * L(w,u,z)) / (z * (u * w)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,453,a,b,6261,a)].">
      <j1 rule="hyper" parents="65 453 6261"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      x * R(a(y,z,y),u,w) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[para(6261(a,2),6184(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6261 6184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(6187,a,6267,a)].">
      <j1 rule="hyper" parents="6187 6267"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      R(x,y,x) \ (a(x,y,x) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(548,a,6267,a)].">
      <j1 rule="hyper" parents="548 6267"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(331,a,6267,a),flip(a)].">
      <j1 rule="hyper" parents="331 6267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,6267,a(flip),b,6184,a(flip))].">
      <j1 rule="hyper" parents="132 6267 6184"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(528,a,6272,a),flip(a)].">
      <j1 rule="hyper" parents="528 6272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      x * (a(x,y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,6274,a(flip),b,958,a)].">
      <j1 rule="hyper" parents="137 6274 958"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,6276,a(flip),b,958,a)].">
      <j1 rule="hyper" parents="137 6276 958"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      L(a(x,z,x),y,x) = u
    ]]></literal>
    <justification jstring="[para(6278(a,1),456(a,1,2))].">
      <j1 rule="para" parents="6278 456"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      R(x,y,x) * (z / x) = x * (z / L(x,y,x))
    ]]></literal>
    <justification jstring="[para(6208(a,1),6278(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6208 6278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[para(6257(a,1),5293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6257 5293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = (w * v5) \ ((w * a(x,y,x)) * v5)
    ]]></literal>
    <justification jstring="[hyper(132,a,6268,a,b,6271,a),flip(a)].">
      <j1 rule="hyper" parents="132 6268 6271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      R(1 / x,y,x) = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1668,a(flip),b,6280,a(flip))].">
      <j1 rule="hyper" parents="36 1668 6280"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      R(T(R(1 / x,y,x),L(x,y,x) * z),L(x,y,x),z) = (L(x,y,x) * z) \ (1 * z)
    ]]></literal>
    <justification jstring="[para(6283(a,2),825(a,1,1,1))].">
      <j1 rule="para" parents="6283 825"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3793,a,6285,a)].">
      <j1 rule="hyper" parents="3793 6285"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,6261,a(flip),b,6201,a)].">
      <j1 rule="hyper" parents="136 6261 6201"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(6187,a,6288,a)].">
      <j1 rule="hyper" parents="6187 6288"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      (a(x,y,x) * z) * x = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6210,a,b,6288,a)].">
      <j1 rule="hyper" parents="65 6210 6288"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,6288,a(flip),b,6184,a(flip))].">
      <j1 rule="hyper" parents="132 6288 6184"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,12,a(flip),b,6289,a),flip(a)].">
      <j1 rule="hyper" parents="135 12 6289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) = (u * x) \ (u * R(x,z,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,6275,a,b,6291,a)].">
      <j1 rule="hyper" parents="325 6275 6291"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5000,a(flip),b,6292,a)].">
      <j1 rule="hyper" parents="65 5000 6292"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      x * (a(y,z,y) \ 1) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[para(6248(a,2),6294(a,1,2))].">
      <j1 rule="para" parents="6248 6294"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      x / (a(y,z,y) \ 1) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,11,a(flip),b,6295,a)].">
      <j1 rule="hyper" parents="135 11 6295"/>
    </justification>
  </clause>

  <clause id="6297">
    <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(6295(a,1),488(a,1,1,1))].">
      <j1 rule="para" parents="6295 488"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      R(x,a(y,z,y),a(y,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(519,a,6296,a)].">
      <j1 rule="hyper" parents="519 6296"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      R(x,a(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(6248(a,1),6298(a,1,3))].">
      <j1 rule="para" parents="6248 6298"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      R(x,y \ R(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(6180(a,2),6299(a,1,2))].">
      <j1 rule="para" parents="6180 6299"/>
    </justification>
  </clause>

  <clause id="6301">
    <literal><![CDATA[
      R(x,y \ R(y,z,y),y \ L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6300(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="6300 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(6203(a,1),6223(a,1,1))].">
      <j1 rule="para" parents="6203 6223"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      T(x,x \ y) * L(z,y / x,x) = x * (y \ (x * ((y / x) * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),6258(a,1,2))].">
      <j1 rule="para" parents="18 6258"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(6289(a,1),6189(a,1,1,2))].">
      <j1 rule="para" parents="6289 6189"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = (y * w) \ ((T(x * y,x) / x) * w)
    ]]></literal>
    <justification jstring="[para(6199(a,2),6282(a,2,2,1))].">
      <j1 rule="para" parents="6199 6282"/>
    </justification>
  </clause>

  <clause id="6309">
    <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(6304(a,1),1917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6304 1917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      L(x,y,((z * u) \ w) * v5) = L(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(2349,a,6169,a)].">
      <j1 rule="hyper" parents="2349 6169"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      L(a(x,y,x),z,x) = (u * x) \ (u * R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(6279,a,6293,a)].">
      <j1 rule="hyper" parents="6279 6293"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      L(a(x \ y,z,x \ y),u,x \ y) = y \ (x * R(x \ y,z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,159,a(flip),b,6311,a),flip(a)].">
      <j1 rule="hyper" parents="325 159 6311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      L(x,y,z * L(z,z,u)) = L(x,y,z * ((z * u) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2344,a(flip),b,6310,a)].">
      <j1 rule="hyper" parents="65 2344 6310"/>
    </justification>
  </clause>

  <clause id="6314">
    <literal><![CDATA[
      (a(x,y,x) / z) * (z \ u) = a(x,y,x) * ((z * z) \ u)
    ]]></literal>
    <justification jstring="[para(6214(a,1),6262(a,1,1))].">
      <j1 rule="para" parents="6214 6262"/>
    </justification>
  </clause>

  <clause id="6315">
    <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(6290(a,1),6270(a,1,1))].">
      <j1 rule="para" parents="6290 6270"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      T(x,x \ y) * L(z,x \ y,x) = x * (y \ (x * ((y / x) * z)))
    ]]></literal>
    <justification jstring="[para(5240(a,1),6305(a,1,2))].">
      <j1 rule="para" parents="5240 6305"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      x * (1 \ (x * ((1 / x) * y))) = L(x * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1399,a(flip),b,6316,a),flip(a)].">
      <j1 rule="hyper" parents="65 1399 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6318">
    <literal><![CDATA[
      x * (x * ((1 / x) * y)) = L(x * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(67(a,1),6317(a,1,2))].">
      <j1 rule="para" parents="67 6317"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      x * (x * ((1 / x) * y)) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a(flip),b,6318,a),flip(a)].">
      <j1 rule="hyper" parents="325 1499 6318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      L(T(x,a(y,z,y)),a(y,z,y),y) = R(y,z,y) \ (R(y,z,y) * x)
    ]]></literal>
    <justification jstring="[para(6278(a,1),6202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6278 6202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      L(T(x,a(y,z,y)),a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,9,a(flip),b,6320,a),flip(a)].">
      <j1 rule="hyper" parents="325 9 6320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      L(x,a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[para(6181(a,1),6321(a,1,1))].">
      <j1 rule="para" parents="6181 6321"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      (T(x,y) * a(x,z,x)) * u = T(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[para(6323(a,1),1549(a,1,2))].">
      <j1 rule="para" parents="6323 1549"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      T(x,y) * (a(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(6195(a,1),6325(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6195 6325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,(x \ y) \ y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(594(a,1),6312(a,2,2))].">
      <j1 rule="para" parents="594 6312"/>
    </justification>
  </clause>

  <clause id="6334">
    <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(65,a,4594,a,b,6171,a)].">
      <j1 rule="hyper" parents="65 4594 6171"/>
    </justification>
  </clause>

  <clause id="6335">
    <literal><![CDATA[
      (x * y) \ (y * T(T(z * x,z) / z,y)) = L(a(z,T(x,y),z),T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1182(a,1),6224(a,1,2,2))].">
      <j1 rule="para" parents="1182 6224"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,2821,a(flip),b,6334,a)].">
      <j1 rule="hyper" parents="65 2821 6334"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = (y * z) \ ((T(x * y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,232,a(flip),b,6335,a),flip(a)].">
      <j1 rule="hyper" parents="65 232 6335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = L(a(x,T(y,w),x),T(y,w),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,6307,a,b,6341,a)].">
      <j1 rule="hyper" parents="325 6307 6341"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      R(a(x,y * K(z,y),x),u,w) = L(a(x,y,x),T(y * K(z,y),z),z)
    ]]></literal>
    <justification jstring="[para(1589(a,1),6342(a,2,1,2))].">
      <j1 rule="para" parents="1589 6342"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      R(a(x,y * K(z,y),x),u,w) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[para(1589(a,1),6344(a,2,2))].">
      <j1 rule="para" parents="1589 6344"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(6301,a,6345,a),flip(a)].">
      <j1 rule="hyper" parents="6301 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      L(a(x,y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y * K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(6345(a,1),494(a,1)),flip(b)].">
      <j1 rule="para" parents="6345 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      L(a(x,L(y,z,u),x),L(y,z,u),w) = a(x,L(y * K(w,y),z,u),x)
    ]]></literal>
    <justification jstring="[para(1628(a,1),6346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1628 6346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (L(y,x \ 1,x) / x)) \ u)
    ]]></literal>
    <justification jstring="[para(6134(a,1),6114(a,1,1))].">
      <j1 rule="para" parents="6134 6114"/>
    </justification>
  </clause>

  <clause id="6350">
    <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(5160(a,1),6253(a,1,1))].">
      <j1 rule="para" parents="5160 6253"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      L(x \ K(y \ z,y),K(y,y \ z) * x,z) = ((y * (z / y)) * x) \ z
    ]]></literal>
    <justification jstring="[para(2616(a,1),6255(a,1,1))].">
      <j1 rule="para" parents="2616 6255"/>
    </justification>
  </clause>

  <clause id="6352">
    <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(3638(a,1),6350(a,1,1,2,1))].">
      <j1 rule="para" parents="3638 6350"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      K(L(x,y,z),u \ L(K(x,w),v5,v6)) = K(L(x,y,z),u \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2808,a(flip),b,5832,a),flip(a)].">
      <j1 rule="hyper" parents="325 2808 5832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      K(K(L(x,y,z) \ 1,u) \ 1,w) = K(u,K(w,L(x \ 1,y,z)))
    ]]></literal>
    <justification jstring="[hyper(6050,a,6096,a),flip(a)].">
      <j1 rule="hyper" parents="6050 6096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      K(K(L(x,y,z) \ 1,u) \ 1,w) = K(w,K(x,L(u,y,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,3873,a(flip),b,6354,a),flip(a)].">
      <j1 rule="hyper" parents="325 3873 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) = K(K(T(z * y,z) \ 1,u) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4176(a,1),6355(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4176 6355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) = K(K(u,T(z * y,z) \ 1),x)
    ]]></literal>
    <justification jstring="[para(2608(a,1),6356(a,2,1))].">
      <j1 rule="para" parents="2608 6356"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) = K(u,K(T(z * y,z) \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,3563,a(flip),b,6357,a),flip(a)].">
      <j1 rule="hyper" parents="325 3563 6357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(x,T(z * y,z))) = w
    ]]></literal>
    <justification jstring="[para(6358(a,2),3770(a,1))].">
      <j1 rule="para" parents="6358 3770"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z \ 1,z))) = K(u,K(x,T(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(6359,a,3799,a),flip(a)].">
      <j1 rule="hyper" parents="6359 3799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(y,K(u,L(x,z \ 1,z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),6360(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 6360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(x,K(u,L(y,z \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(3585,a,6361,a)].">
      <j1 rule="hyper" parents="3585 6361"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(z,L(y,u \ 1,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,3457,a(flip),b,6362,a)].">
      <j1 rule="hyper" parents="65 3457 6362"/>
    </justification>
  </clause>

  <clause id="6364">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(x,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(6363(a,1),5179(a,2,2))].">
      <j1 rule="para" parents="6363 5179"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(3580(a,1),6364(a,2,2))].">
      <j1 rule="para" parents="3580 6364"/>
    </justification>
  </clause>

  <clause id="6366">
    <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(1732(a,1),6173(a,1,2))].">
      <j1 rule="para" parents="1732 6173"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(709,a,6366,a),flip(a)].">
      <j1 rule="hyper" parents="709 6366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3956,a,6367,a)].">
      <j1 rule="hyper" parents="3956 6367"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(6367(a,1),3955(a,1,2))].">
      <j1 rule="para" parents="6367 3955"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(6368(a,1),2699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6368 2699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5824(a,2),6368(a,1,1))].">
      <j1 rule="para" parents="5824 6368"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      K(x * L(y,z,u),y) != K(x,y) * w
    ]]></literal>
    <literal><![CDATA[
      a(y,x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(6369(a,1),45(a,1))].">
      <j1 rule="para" parents="6369 45"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,5268,a(flip),b,6371,a)].">
      <j1 rule="hyper" parents="65 5268 6371"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) \ x = L(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(6373(a,1),1779(a,1,1))].">
      <j1 rule="para" parents="6373 1779"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      (a(x,y,L(x,z,u)) * K(L(x,y,L(x,z,u)),w)) \ (x * K(L(x,y,L(x,z,u)),w)) = T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(6373(a,1),4098(a,1,1,1))].">
      <j1 rule="para" parents="6373 4098"/>
    </justification>
  </clause>

  <clause id="6376">
    <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(1825(a,1),6174(a,1,2))].">
      <j1 rule="para" parents="1825 6174"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,14,a,b,6376,a(flip))].">
      <j1 rule="hyper" parents="137 14 6376"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = (a(x,y,x) * ((z * u) * w)) / (u * w)
    ]]></literal>
    <justification jstring="[para(6210(a,1),6218(a,2,1))].">
      <j1 rule="para" parents="6210 6218"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * (((z * u) * w) / (u * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,6215,a(flip),b,6378,a),flip(a)].">
      <j1 rule="hyper" parents="325 6215 6378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      R(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),6380(a,2,2))].">
      <j1 rule="para" parents="20 6380"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(6207(a,1),6381(a,1,2))].">
      <j1 rule="para" parents="6207 6381"/>
    </justification>
  </clause>

  <clause id="6383">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (x \ L(T(x,y),z,x)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(2957(a,1),5981(a,2,2))].">
      <j1 rule="para" parents="2957 5981"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = T(x,u) \ L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,4600,a(flip),b,6383,a),flip(a)].">
      <j1 rule="hyper" parents="325 4600 6383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(x,u) = T(x,y) \ L(T(x,u),z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6138,a(flip),b,6384,a)].">
      <j1 rule="hyper" parents="65 6138 6384"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * (K(w,z) * y)) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1656,a(flip),b,6146,a),flip(a)].">
      <j1 rule="hyper" parents="325 1656 6146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (x * (K(x,y) * (a(x,z,x) * u))) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(287(a,1),6259(a,1,2,2))].">
      <j1 rule="para" parents="287 6259"/>
    </justification>
  </clause>

  <clause id="6389">
    <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(413(a,1),6315(a,1,1))].">
      <j1 rule="para" parents="413 6315"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * y) / (x * (K(z,w) * y)),u)
    ]]></literal>
    <justification jstring="[para(6142(a,1),6387(a,2,1))].">
      <j1 rule="para" parents="6142 6387"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (T(x,y) * (a(x,z,x) * u)) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(4517(a,1),6388(a,1,2))].">
      <j1 rule="para" parents="4517 6388"/>
    </justification>
  </clause>

  <clause id="6392">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (R(T(x,y),z,x) * u) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(6326(a,1),6391(a,1,2))].">
      <j1 rule="para" parents="6326 6391"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      L(x,y \ R(T(y,z),u,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(332,a,6392,a),flip(a)].">
      <j1 rule="hyper" parents="332 6392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      L(x,K(y,z) * a(y,u,y),y) = x
    ]]></literal>
    <justification jstring="[para(6198(a,1),6393(a,1,2))].">
      <j1 rule="para" parents="6198 6393"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      (x * y) / (x * (T(K(z,u),w) * y)) = T((x * y) / (x * (K(z,u) * y)),w)
    ]]></literal>
    <justification jstring="[para(2290(a,1),6390(a,1,2,2,1))].">
      <j1 rule="para" parents="2290 6390"/>
    </justification>
  </clause>

  <clause id="6397">
    <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),5885(a,2,2,2))].">
      <j1 rule="para" parents="22 5885"/>
    </justification>
  </clause>

  <clause id="6398">
    <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(5091,a,6397,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5091 6397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      K(x,L((y * x) \ (z * x),u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(525(a,1),6398(a,1,2))].">
      <j1 rule="para" parents="525 6398"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      K(x,L((y / x) \ z,u,w)) = K(x,L(y \ (z * x),u,w))
    ]]></literal>
    <justification jstring="[para(12(a,1),6399(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 6399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6401">
    <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),6400(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6402">
    <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(65,a,5842,a,b,6401,a)].">
      <j1 rule="hyper" parents="65 5842 6401"/>
    </justification>
  </clause>

  <clause id="6403">
    <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(4956(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="4956 6402"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      L(K(x,y),((z / x) * y) * x,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5869(a,1),6403(a,1,1))].">
      <j1 rule="para" parents="5869 6403"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      K(L(x,(y / x) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3546,a(flip),b,6404,a)].">
      <j1 rule="hyper" parents="65 3546 6404"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(6405(a,1),5975(a,1,2,2))].">
      <j1 rule="para" parents="6405 5975"/>
    </justification>
  </clause>

  <clause id="6408">
    <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(3205,a,5972,a),flip(a)].">
      <j1 rule="hyper" parents="3205 5972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6409">
    <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(184(a,1),6006(a,2,1,2))].">
      <j1 rule="para" parents="184 6006"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1715(a,1),6409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1715 6409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3540,a(flip),b,6410,a),flip(a)].">
      <j1 rule="hyper" parents="65 3540 6410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),u \ (L(x,y,z) * L(K(x,w),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6137,a(flip),b,6010,a),flip(a)].">
      <j1 rule="hyper" parents="65 6137 6010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      (x * K(y,z)) * (y * L(K(z,y),u,w)) = x * (y * a(w,u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(5818(a,1),6044(a,1,1,2))].">
      <j1 rule="para" parents="5818 6044"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      (x * (y * a(z,u,K(y,w)))) / y = (x * K(y,w)) * L((x * K(y,w)) \ x,u,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,6413,a(flip),b,4414,a)].">
      <j1 rule="hyper" parents="135 6413 4414"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      (x * (y * a(z,u,K(y,w)))) / y = (x * K(y,w)) * L(K(w,y),u,z)
    ]]></literal>
    <justification jstring="[para(2849(a,1),6414(a,2,2,1))].">
      <j1 rule="para" parents="2849 6414"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      (x * (y * a(z,u,K(y,w)))) / y = x * (L(K(w,y),u,z) * K(y,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,4124,a(flip),b,6416,a),flip(a)].">
      <j1 rule="hyper" parents="325 4124 6416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      (x * (y * a(z,u,K(y,w)))) / y = x * a(z,u,K(y,w))
    ]]></literal>
    <justification jstring="[para(6032(a,1),6417(a,2,2))].">
      <j1 rule="para" parents="6032 6417"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      (x * a(y,z,K(x,u))) / x = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(701,a,6419,a)].">
      <j1 rule="hyper" parents="701 6419"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,194,a,b,6420,a)].">
      <j1 rule="hyper" parents="38 194 6420"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6421(a,1),3106(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6421 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,6058,a,b,6422,a)].">
      <j1 rule="hyper" parents="325 6058 6422"/>
    </justification>
  </clause>

  <clause id="6424">
    <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(6423(a,2),45(a,1))].">
      <j1 rule="para" parents="6423 45"/>
    </justification>
  </clause>

  <clause id="6425">
    <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),6073(a,1,2,1))].">
      <j1 rule="para" parents="9 6073"/>
    </justification>
  </clause>

  <clause id="6427">
    <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),6425(a,1,2))].">
      <j1 rule="para" parents="18 6425"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,5998,a(flip),b,6427,a)].">
      <j1 rule="hyper" parents="65 5998 6427"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,5976,a(flip),b,6428,a),flip(a)].">
      <j1 rule="hyper" parents="325 5976 6428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),6429(a,2,2,2))].">
      <j1 rule="para" parents="10 6429"/>
    </justification>
  </clause>

  <clause id="6433">
    <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(4773(a,1),6432(a,1,1,2))].">
      <j1 rule="para" parents="4773 6432"/>
    </justification>
  </clause>

  <clause id="6435">
    <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(3002,a,6433,a)].">
      <j1 rule="hyper" parents="3002 6433"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5324,a(flip),b,6435,a),flip(a)].">
      <j1 rule="hyper" parents="65 5324 6435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6437">
    <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(6436(a,1),3036(a,1))].">
      <j1 rule="para" parents="6436 3036"/>
    </justification>
  </clause>

  <clause id="6438">
    <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(6232(a,1),6221(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6232 6221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6085,a(flip),b,6438,a),flip(a)].">
      <j1 rule="hyper" parents="65 6085 6438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3152,a,6439,a)].">
      <j1 rule="hyper" parents="3152 6439"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) * K(x,T(T(y,u),z)) = a(x,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(23(a,1),6441(a,1,2,2))].">
      <j1 rule="para" parents="23 6441"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u)) = a((x \ y) \ y,z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4760(a,1),6441(a,1,1))].">
      <j1 rule="para" parents="4760 6441"/>
    </justification>
  </clause>

  <clause id="6445">
    <literal><![CDATA[
      a(x,T(y,z),x) != u * K(x,T(T(y,w),z))
    ]]></literal>
    <literal><![CDATA[
      K(x * T(y,z),T(x,w)) = u
    ]]></literal>
    <justification jstring="[para(6443(a,1),46(a,1))].">
      <j1 rule="para" parents="6443 46"/>
    </justification>
  </clause>

  <clause id="6446">
    <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(325,a,5836,a(flip),b,6408,a),flip(a)].">
      <j1 rule="hyper" parents="325 5836 6408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,3649,a(flip),b,6446,a),flip(a)].">
      <j1 rule="hyper" parents="325 3649 6446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,3276,a(flip),b,6448,a),flip(a)].">
      <j1 rule="hyper" parents="325 3276 6448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6450">
    <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(6449(a,1),3797(a,1))].">
      <j1 rule="para" parents="6449 3797"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),(x \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,6353,a(flip),b,6046,a),flip(a)].">
      <j1 rule="hyper" parents="325 6353 6046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      K(L(x,y,z),u \ ((1 / x) \ L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2744,a(flip),b,6451,a),flip(a)].">
      <j1 rule="hyper" parents="325 2744 6451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x * L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(2253(a,1),6453(a,1,2,2))].">
      <j1 rule="para" parents="2253 6453"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      K((x \ 1) \ 1,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5929,a(flip),b,6349,a),flip(a)].">
      <j1 rule="hyper" parents="65 5929 6349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      K(x,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(2224,a,6455,a)].">
      <j1 rule="hyper" parents="2224 6455"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      K(x,(y * (x \ L(z,x \ 1,x))) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4948,a(flip),b,6456,a)].">
      <j1 rule="hyper" parents="65 4948 6456"/>
    </justification>
  </clause>

  <clause id="6458">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(389(a,1),6457(a,1,2,1,2))].">
      <j1 rule="para" parents="389 6457"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,5916,a(flip),b,6458,a),flip(a)].">
      <j1 rule="hyper" parents="325 5916 6458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ T(u,x)) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[para(22(a,2),6459(a,1,2,2))].">
      <j1 rule="para" parents="22 6459"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(5094,a,6460,a)].">
      <j1 rule="hyper" parents="5094 6460"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6458,a(flip),b,6461,a)].">
      <j1 rule="hyper" parents="65 6458 6461"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5929,a,b,6462,a)].">
      <j1 rule="hyper" parents="65 5929 6462"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,4948,a,b,6462,a)].">
      <j1 rule="hyper" parents="65 4948 6462"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(8(a,1),6462(a,2,2,1))].">
      <j1 rule="para" parents="8 6462"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(1585(a,1),6462(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1585 6462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(6462(a,1),4976(a,1,2,2))].">
      <j1 rule="para" parents="6462 4976"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5928,a,b,6465,a)].">
      <j1 rule="hyper" parents="65 5928 6465"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(6464(a,1),5841(a,1,1))].">
      <j1 rule="para" parents="6464 5841"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(2605(a,2),6466(a,1,2,1,1))].">
      <j1 rule="para" parents="2605 6466"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(4123,a,6467,a),flip(a)].">
      <j1 rule="hyper" parents="4123 6467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(5281,a,6471,a)].">
      <j1 rule="hyper" parents="5281 6471"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      K((x * y) \ (z * u),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (u \ y)) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(6471(a,1),5281(a,1))].">
      <j1 rule="para" parents="6471 5281"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(8(a,1),6472(a,2,1,1))].">
      <j1 rule="para" parents="8 6472"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5093,a,b,6474,a)].">
      <j1 rule="hyper" parents="65 5093 6474"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5092,a,b,6474,a)].">
      <j1 rule="hyper" parents="65 5092 6474"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      K(x,x * y) * K(z \ ((z * y) * x),x) = a(z,y,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(6476(a,1),6029(a,1,2))].">
      <j1 rule="para" parents="6476 6029"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * a(y,z,K(x,x * z)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(6478(a,1),3087(a,1,2))].">
      <j1 rule="para" parents="6478 3087"/>
    </justification>
  </clause>

  <clause id="6480">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(37,a,6040,a,b,6479,a)].">
      <j1 rule="hyper" parents="37 6040 6479"/>
    </justification>
  </clause>

  <clause id="6481">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(4705(a,2),6480(a,1,1))].">
      <j1 rule="para" parents="4705 6480"/>
    </justification>
  </clause>

  <clause id="6482">
    <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(307(a,1),6481(a,2,2))].">
      <j1 rule="para" parents="307 6481"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4713,a(flip),b,6482,a),flip(a)].">
      <j1 rule="hyper" parents="325 4713 6482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3442,a,b,6470,a)].">
      <j1 rule="hyper" parents="65 3442 6470"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6463,a(flip),b,6469,a),flip(a)].">
      <j1 rule="hyper" parents="65 6463 6469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,4979,a(flip),b,6486,a)].">
      <j1 rule="hyper" parents="65 4979 6486"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,3286,a,b,6487,a),flip(a)].">
      <j1 rule="hyper" parents="65 3286 6487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,5026,a(flip),b,6488,a),flip(a)].">
      <j1 rule="hyper" parents="325 5026 6488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6490">
    <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),6489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 6489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,((z * u) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3217,a(flip),b,6490,a),flip(a)].">
      <j1 rule="hyper" parents="65 3217 6490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2744,a(flip),b,6491,a),flip(a)].">
      <j1 rule="hyper" parents="325 2744 6491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5869,a(flip),b,6492,a),flip(a)].">
      <j1 rule="hyper" parents="65 5869 6492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5884,a,b,6493,a)].">
      <j1 rule="hyper" parents="65 5884 6493"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(1575,a,6494,a)].">
      <j1 rule="hyper" parents="1575 6494"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(5932,a,6495,a)].">
      <j1 rule="hyper" parents="5932 6495"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      a(x,y,K(z,z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,6495,a,b,6031,a),flip(a)].">
      <j1 rule="hyper" parents="133 6495 6031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      a(x,y * z,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),6499(a,1,3,2))].">
      <j1 rule="para" parents="9 6499"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      L(K(x,y),x * y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,6500,a)].">
      <j1 rule="hyper" parents="54 6500"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3949,a,6502,a)].">
      <j1 rule="hyper" parents="3949 6502"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5962,a(flip),b,6502,a)].">
      <j1 rule="hyper" parents="65 5962 6502"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,6504,a,b,6505,a)].">
      <j1 rule="hyper" parents="325 6504 6505"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,6152,a,b,6505,a)].">
      <j1 rule="hyper" parents="325 6152 6505"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,6505,a(flip),b,6079,a)].">
      <j1 rule="hyper" parents="137 6505 6079"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      T(x,L(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,6505,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 6505 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,6511,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 6511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      T(x,y \ (x \ (y * z))) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5987,a(flip),b,6512,a)].">
      <j1 rule="hyper" parents="65 5987 6512"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,6512,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 6512 22"/>
    </justification>
  </clause>

  <clause id="6515">
    <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(477(a,1),6512(a,1,2))].">
      <j1 rule="para" parents="477 6512"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6507(a,1),4807(a,1))].">
      <j1 rule="para" parents="6507 4807"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(5977(a,1),6517(a,1))].">
      <j1 rule="para" parents="5977 6517"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6497(a,1,2,2,2))].">
      <j1 rule="para" parents="10 6497"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(6497(a,1),5897(a,1,2))].">
      <j1 rule="para" parents="6497 5897"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,u \ (x \ (u * (y * x))))
    ]]></literal>
    <justification jstring="[hyper(325,a,5935,a,b,6508,a),flip(a)].">
      <j1 rule="hyper" parents="325 5935 6508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      K(x,y) / (x * y) = 1 / (y * x)
    ]]></literal>
    <justification jstring="[hyper(371,a,6510,a)].">
      <j1 rule="hyper" parents="371 6510"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      (x * (y * z)) / T(y,z) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,6510,a(flip),b,2870,a),flip(a)].">
      <j1 rule="hyper" parents="135 6510 2870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      L(x,y,(y * x) \ K(y,x)) = ((1 / (x * y)) * y) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(6525(a,1),1634(a,2,1,1))].">
      <j1 rule="para" parents="6525 1634"/>
    </justification>
  </clause>

  <clause id="6531">
    <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(6514(a,1),1258(a,1,2,2))].">
      <j1 rule="para" parents="6514 1258"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      K(x,x \ ((y * (x \ z)) \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5916,a(flip),b,6522,a),flip(a)].">
      <j1 rule="hyper" parents="65 5916 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(6522(a,2),3691(a,1,2))].">
      <j1 rule="para" parents="6522 3691"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,309,a(flip),b,6526,a),flip(a)].">
      <j1 rule="hyper" parents="136 309 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,4042,a,b,6538,a)].">
      <j1 rule="hyper" parents="37 4042 6538"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(776,a,6538,a(flip))].">
      <j1 rule="hyper" parents="776 6538"/>
    </justification>
  </clause>

  <clause id="6541">
    <literal><![CDATA[
      (x * y) \ ((z * y) * T(x,y)) = R(T(z,x * y),y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,6538,a(flip),b,243,a)].">
      <j1 rule="hyper" parents="132 6538 243"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      (x * y) \ (((z / (x * y)) * y) * T(x,y)) = R((x * y) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,6538,a(flip),b,592,a(flip))].">
      <j1 rule="hyper" parents="132 6538 592"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      R(x,y,T(z,z * y)) = R(x,y,L(z,y,z))
    ]]></literal>
    <justification jstring="[para(601(a,1),6540(a,1,3))].">
      <j1 rule="para" parents="601 6540"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,497,a(flip),b,6539,a),flip(a)].">
      <j1 rule="hyper" parents="65 497 6539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      (x / y) \ R(x / y,y \ x,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(6539(a,1),1086(a,1,2))].">
      <j1 rule="para" parents="6539 1086"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      R(x,y,T(z,y * z)) = R(x,y,L(z,y,z))
    ]]></literal>
    <justification jstring="[para(4675(a,2),6545(a,1,3))].">
      <j1 rule="para" parents="4675 6545"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      R(x,y,L(z,y,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4202,a(flip),b,6552,a),flip(a)].">
      <j1 rule="hyper" parents="65 4202 6552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      R(L(x,y,x),y,L(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,4782,a(flip),b,6553,a),flip(a)].">
      <j1 rule="hyper" parents="325 4782 6553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6554(a,1),4236(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6554 4236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      K(L(x,y,z),x \ ((u * (x \ w)) \ v5)) = L(K(x,(u * w) \ v5),y * x,z)
    ]]></literal>
    <justification jstring="[para(6535(a,1),3546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6535 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ ((u * (x \ (1 / L(x,y,z)))) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[para(4173(a,1),6535(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4173 6535"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((u / w) * w) \ (x \ (u * (y * x))))
    ]]></literal>
    <justification jstring="[para(154(a,1),6524(a,2,2,2,2))].">
      <j1 rule="para" parents="154 6524"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      R(T(x / y,z * y),y,z) = (z * y) \ (x * T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),6541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 6541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,x \ y,x) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(4245,a,6551,a)].">
      <j1 rule="hyper" parents="4245 6551"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      ((1 / (x * y)) * y) \ K(y,x) = L(x,y,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(2491(a,1),6529(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2491 6529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      ((1 / (x * y)) * y) \ K(y,x) = L(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a(flip),b,6564,a),flip(a)].">
      <j1 rule="hyper" parents="325 1499 6564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      ((1 / (x * y)) * y) \ (K(y,x) * R(K(y,x) \ ((1 / (x * y)) * y),z,u)) = L(x,y,x * y) \ R(((1 / (x * y)) * y) \ K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6565(a,1),1403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6565 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((u / w) * (w * x)) \ (u * (y * x)))
    ]]></literal>
    <justification jstring="[hyper(325,a,5895,a,b,6561,a),flip(a)].">
      <j1 rule="hyper" parents="325 5895 6561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = (u * (y * x)) \ ((u * K(x,y)) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(325,a,4199,a(flip),b,6567,a),flip(a)].">
      <j1 rule="hyper" parents="325 4199 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      (x * (y * z)) * L(K(z,y),u,y * z) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,6568,a,b,232,a)].">
      <j1 rule="hyper" parents="137 6568 232"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      K(L(x,y,z),x \ ((u * (x \ w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(6558(a,2),6518(a,1))].">
      <j1 rule="para" parents="6558 6518"/>
    </justification>
  </clause>

  <clause id="6571">
    <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(1578,a,6515,a)].">
      <j1 rule="hyper" parents="1578 6515"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,u)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(6508(a,1),6569(a,1,2))].">
      <j1 rule="para" parents="6508 6569"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(6086,a,6572,a),flip(a)].">
      <j1 rule="hyper" parents="6086 6572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,6573,a(flip),b,113,a(flip))].">
      <j1 rule="hyper" parents="135 6573 113"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(375,a,6574,a),flip(a)].">
      <j1 rule="hyper" parents="375 6574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      (x / (y * z)) * T(y,z) = (x / (z * y)) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,6576,a(flip),b,2877,a)].">
      <j1 rule="hyper" parents="136 6576 2877"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      ((x / (y * z)) * z) * T(y,z) = ((x / (z * y)) * z) * y
    ]]></literal>
    <justification jstring="[para(6578(a,1),2871(a,1,1))].">
      <j1 rule="para" parents="6578 2871"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      (x * y) \ (((z / (y * x)) * y) * x) = R((x * y) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(6579(a,1),6542(a,1,2))].">
      <j1 rule="para" parents="6579 6542"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      R((x * y) \ (y * (z * x)),y,x) = (x * y) \ (y * (R(z,y,x) * x))
    ]]></literal>
    <justification jstring="[para(1300(a,1),6580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1300 6580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      a((x * y) \ (((z / ((y \ 1) * x)) * (y \ 1)) * x),u,w) = a(R((x * (y \ 1)) \ z,y \ 1,x),u,w)
    ]]></literal>
    <justification jstring="[para(6580(a,1),5204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6580 5204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6583">
    <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(6099(a,1),6571(a,1,1))].">
      <j1 rule="para" parents="6099 6571"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(6513(a,1),6583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6513 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      x / L(T(y,y \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(201,a,6584,a(flip),b,114,a(flip))].">
      <j1 rule="hyper" parents="201 6584 114"/>
    </justification>
  </clause>

  <clause id="6586">
    <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(6584(a,1),4551(a,1,2,1))].">
      <j1 rule="para" parents="6584 4551"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(596(a,1),6585(a,1,2,1))].">
      <j1 rule="para" parents="596 6585"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ x = x / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(609(a,1),6585(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="609 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) \ x = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(195,a,6588,a)].">
      <j1 rule="hyper" parents="195 6588"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      L((x * y) / x,z,u) \ (x * y) = (x * y) / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),6588(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      L(K(x,1 / y),z,u) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6589(a,1),5814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6589 5814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[para(82(a,1),6590(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 6590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4168(a,1),6590(a,1,1))].">
      <j1 rule="para" parents="4168 6590"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      (x * (L(x,x,x \ y) \ x)) \ 1 = y \ ((y / x) * 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,1559,a(flip),b,6594,a),flip(a)].">
      <j1 rule="hyper" parents="325 1559 6594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x \ y,x) \ (x \ y)) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(201,a,359,a(flip),b,6594,a),flip(a)].">
      <j1 rule="hyper" parents="201 359 6594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      1 / ((x * y) \ x) = y * (L(y,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(201,a,225,a(flip),b,6594,a)].">
      <j1 rule="hyper" parents="201 225 6594"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      (x * x) * (y * (L(y,z,u) \ y)) = (x * x) / L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(201,a,6594,a(flip),b,394,a),flip(a)].">
      <j1 rule="hyper" parents="201 6594 394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      (x * a(y,y \ 1,x)) \ 1 = L(x \ 1,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(719(a,1),6594(a,1,1,2))].">
      <j1 rule="para" parents="719 6594"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      (x * a(y,y,x)) \ 1 = L(x \ 1,y,y)
    ]]></literal>
    <justification jstring="[para(824(a,1),6594(a,1,1,2))].">
      <j1 rule="para" parents="824 6594"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ 1,x * (L(x,y,z) \ x)) = (L(x \ 1,y,z) \ 1) \ (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(6594(a,1),1021(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6594 1021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      R(x,y,z * (u * (L(u,w,v5) \ u))) = R(x,y,z * L(u \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(6594(a,1),1017(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6594 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(201,a,6597,a,b,4168,a),flip(a)].">
      <j1 rule="hyper" parents="201 6597 4168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      x / L(1 / y,y,x) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(6603(a,2),1397(a,1,2))].">
      <j1 rule="para" parents="6603 1397"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(82(a,1),6604(a,1,2,1))].">
      <j1 rule="para" parents="82 6604"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),6605(a,2,2,2))].">
      <j1 rule="para" parents="82 6605"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      L(x,x \ 1,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(195,a,6606,a),flip(a)].">
      <j1 rule="hyper" parents="195 6606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      (x * (L(x,x,x * y) \ x)) \ 1 = y \ ((y / x) * 1)
    ]]></literal>
    <justification jstring="[para(2368(a,1),6595(a,1,1,2,1))].">
      <j1 rule="para" parents="2368 6595"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      L(x \ 1,x,x * y) = y \ ((y / x) * 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6594,a(flip),b,6609,a)].">
      <j1 rule="hyper" parents="65 6594 6609"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      L(x \ 1,x,x \ y) = L(x \ 1,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1559,a,b,6610,a)].">
      <j1 rule="hyper" parents="325 1559 6610"/>
    </justification>
  </clause>

  <clause id="6612">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = L(x \ 1,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(475,a,6611,a)].">
      <j1 rule="hyper" parents="475 6611"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ (x \ y)) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1525,a(flip),b,6596,a)].">
      <j1 rule="hyper" parents="65 1525 6596"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      R(x \ y,(x \ y) \ 1,(y \ x) \ (x \ y)) \ (1 * ((y \ x) \ (x \ y))) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,481,a,b,6613,a)].">
      <j1 rule="hyper" parents="65 481 6613"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      R(x,y,z * L(u \ 1,w,v5)) = R(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,1267,a(flip),b,6602,a),flip(a)].">
      <j1 rule="hyper" parents="65 1267 6602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4569,a(flip),b,6586,a),flip(a)].">
      <j1 rule="hyper" parents="65 4569 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6617">
    <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(113(a,1),6531(a,1,1,1))].">
      <j1 rule="para" parents="113 6531"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1719,a,6617,a),flip(a)].">
      <j1 rule="hyper" parents="1719 6617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(113(a,1),6618(a,1,2))].">
      <j1 rule="para" parents="113 6618"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4762,a,6619,a),flip(a)].">
      <j1 rule="hyper" parents="4762 6619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(6620(a,1),3546(a,1,1))].">
      <j1 rule="para" parents="6620 3546"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(6518,a,6622,a),flip(a)].">
      <j1 rule="hyper" parents="6518 6622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(6623(a,1),6483(a,1,1))].">
      <j1 rule="para" parents="6623 6483"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4007(a,1),6624(a,1,1))].">
      <j1 rule="para" parents="4007 6624"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,6625,a,b,2608,a)].">
      <j1 rule="hyper" parents="201 6625 2608"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6468,a(flip),b,6625,a)].">
      <j1 rule="hyper" parents="65 6468 6625"/>
    </justification>
  </clause>

  <clause id="6631">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,x * ((y * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6464,a,b,6628,a)].">
      <j1 rule="hyper" parents="65 6464 6628"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      K(x,y \ (x * z)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4955,a(flip),b,6628,a)].">
      <j1 rule="hyper" parents="65 4955 6628"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = K(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(1256(a,1),6628(a,1,2))].">
      <j1 rule="para" parents="1256 6628"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),u * x,w) = K(L(x,u,w),y \ (z * x))
    ]]></literal>
    <justification jstring="[para(6628(a,1),3546(a,1,1))].">
      <j1 rule="para" parents="6628 3546"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5955,a,6627,a)].">
      <j1 rule="hyper" parents="5955 6627"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6477,a(flip),b,6635,a)].">
      <j1 rule="hyper" parents="65 6477 6635"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K(y * ((x * z) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(6473,a,6636,a)].">
      <j1 rule="hyper" parents="6473 6636"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(4026,a,6636,a)].">
      <j1 rule="hyper" parents="4026 6636"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4938,a(flip),b,6636,a),flip(a)].">
      <j1 rule="hyper" parents="65 4938 6636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      L(x * K(x * (y \ z),x),u,w) / L(x,u,w) = K(y \ (z * x),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(6636(a,1),2459(a,1,1,1,2))].">
      <j1 rule="para" parents="6636 2459"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,x) = u
    ]]></literal>
    <justification jstring="[para(6636(a,1),5904(a,1))].">
      <j1 rule="para" parents="6636 5904"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      L(x * K(x * ((y * z) \ u),x),w,v5) \ L(x,w,v5) = K(L(x,w,v5),(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(6637(a,1),2808(a,1,1,1,2))].">
      <j1 rule="para" parents="6637 2808"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      K(L(x,y,z),u \ (w * x)) = K(L(x,y,z),x * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(6518,a,6634,a),flip(a)].">
      <j1 rule="hyper" parents="6518 6634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x * w)) = K(L(x,y,z),x * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(5317,a,6644,a)].">
      <j1 rule="hyper" parents="5317 6644"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      K(L(x,y,z),x * (u \ L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6454,a(flip),b,6645,a),flip(a)].">
      <j1 rule="hyper" parents="65 6454 6645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K(z * (x \ y),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,2459,a(flip),b,6641,a),flip(a)].">
      <j1 rule="hyper" parents="65 2459 6641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      K((x \ y) \ z,L(z,u,w)) = K(z * (y \ x),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,5997,a,b,6647,a)].">
      <j1 rule="hyper" parents="65 5997 6647"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      R(x \ y,(x \ y) \ 1,(x \ y) * (y \ x)) \ (1 * ((y \ x) \ (x \ y))) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[para(1833(a,1),6614(a,1,1))].">
      <j1 rule="para" parents="1833 6614"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      K(L(x,y,z),(u * (x \ w)) \ v5) = K(L(x,y,z),x * ((u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(2889,a,6643,a),flip(a)].">
      <j1 rule="hyper" parents="2889 6643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      (x \ y) \ (1 * ((y \ x) \ (x \ y))) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[para(1830(a,1),6649(a,1,1))].">
      <j1 rule="para" parents="1830 6649"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) \ (x \ y)) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(305,a,6651,a)].">
      <j1 rule="hyper" parents="305 6651"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      (x \ y) * (1 / (y \ x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ x) \ (x \ y) = z
    ]]></literal>
    <justification jstring="[para(6652(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6652 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      (1 / (x \ y)) * (y \ x) = (x \ y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(6652(a,1),3464(a,1,1))].">
      <j1 rule="para" parents="6652 3464"/>
    </justification>
  </clause>

  <clause id="6655">
    <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(325,a,6020,a(flip),b,5886,a),flip(a)].">
      <j1 rule="hyper" parents="325 6020 5886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <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(3368(a,1),6655(a,2,2))].">
      <j1 rule="para" parents="3368 6655"/>
    </justification>
  </clause>

  <clause id="6657">
    <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(325,a,5891,a(flip),b,6656,a),flip(a)].">
      <j1 rule="hyper" parents="325 5891 6656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,3812,a(flip),b,6657,a),flip(a)].">
      <j1 rule="hyper" parents="325 3812 6657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6659">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6517,a,6658,a),flip(a)].">
      <j1 rule="hyper" parents="6517 6658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6661">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,5450,a,b,6659,a)].">
      <j1 rule="hyper" parents="325 5450 6659"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(136,a,6661,a(flip),b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 6661 2117"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4258,a(flip),b,6662,a),flip(a)].">
      <j1 rule="hyper" parents="65 4258 6662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(6663(a,2),4854(a,1,2))].">
      <j1 rule="para" parents="6663 4854"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(292,a,6664,a)].">
      <j1 rule="hyper" parents="292 6664"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(6665(a,1),4299(a,1,1))].">
      <j1 rule="para" parents="6665 4299"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,178,a(flip),b,6666,a),flip(a)].">
      <j1 rule="hyper" parents="39 178 6666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,6668,a)].">
      <j1 rule="hyper" parents="140 6668"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,6668,a(flip),b,191,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 6668 191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),6668(a,1,1))].">
      <j1 rule="para" parents="11 6668"/>
    </justification>
  </clause>

  <clause id="6673">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ 1,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,6365,a(flip),b,6669,a(flip))].">
      <j1 rule="hyper" parents="36 6365 6669"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),6669(a,1,1))].">
      <j1 rule="para" parents="11 6669"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(194(a,1),6669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="194 6669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2857,a,6670,a)].">
      <j1 rule="hyper" parents="2857 6670"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      L(x,x,y) * K(y / (x \ 1),z) = y \ T(y / (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(1721(a,2),6670(a,1,1))].">
      <j1 rule="para" parents="1721 6670"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(546,a,6676,a),flip(a)].">
      <j1 rule="hyper" parents="546 6676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6676(a,1),6286(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6676 6286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      T(x,y) * (z * K(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(4649(a,1),6671(a,1,2,2))].">
      <j1 rule="para" parents="4649 6671"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5086,a(flip),b,6674,a(flip))].">
      <j1 rule="hyper" parents="36 5086 6674"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(6674(a,1),467(a,1,1))].">
      <j1 rule="para" parents="6674 467"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(3491,a,6686,a),flip(a)].">
      <j1 rule="hyper" parents="3491 6686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(6686(a,1),3491(a,1))].">
      <j1 rule="para" parents="6686 3491"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K((y \ 1) * x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3145,a,b,6690,a)].">
      <j1 rule="hyper" parents="325 3145 6690"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(85(a,1),6690(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="85 6690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      K(L((x \ 1) \ 1,y,z) * u,w) = K((L(x,y,z) \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(6593(a,2),6690(a,1,1,1))].">
      <j1 rule="para" parents="6593 6690"/>
    </justification>
  </clause>

  <clause id="6699">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(114(a,1),6683(a,1,2,2))].">
      <j1 rule="para" parents="114 6683"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      K(x * (y \ 1),T(z,y)) = K((y \ 1) * x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2998,a,b,6695,a)].">
      <j1 rule="hyper" parents="65 2998 6695"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      K(x,L(y,((z \ x) \ x) \ 1,(z \ x) \ x) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2952,a,6699,a),flip(a)].">
      <j1 rule="hyper" parents="2952 6699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(468(a,1),6673(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="468 6673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(3683,a,6700,a),flip(a)].">
      <j1 rule="hyper" parents="3683 6700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6705">
    <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="[para(423(a,1),6700(a,1,1))].">
      <j1 rule="para" parents="423 6700"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(3777,a,6702,a)].">
      <j1 rule="hyper" parents="3777 6702"/>
    </justification>
  </clause>

  <clause id="6707">
    <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(1687(a,1),6704(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1687 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6091,a(flip),b,6706,a),flip(a)].">
      <j1 rule="hyper" parents="65 6091 6706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(4615(a,2),6684(a,1,2))].">
      <j1 rule="para" parents="4615 6684"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      T(T(x,y) * L(x \ z,u,w),x) = T(x,y) * L(x \ T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(1743(a,1),6709(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1743 6709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      L(x * K(y * x,y),y,y) = ((y * y) \ (y * x)) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,391,a(flip),b,6687,a),flip(a)].">
      <j1 rule="hyper" parents="325 391 6687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) = ((y * y) \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(4651(a,2),6711(a,1,1,2))].">
      <j1 rule="para" parents="4651 6711"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) = ((1 / y) * x) * y
    ]]></literal>
    <justification jstring="[para(647(a,1),6712(a,2,1))].">
      <j1 rule="para" parents="647 6712"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      L(T(x,y) * K(x * y,y),y,y) = ((1 / y) * T(x,y)) * y
    ]]></literal>
    <justification jstring="[para(4653(a,1),6713(a,1,1,2))].">
      <j1 rule="para" parents="4653 6713"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      L(x,x,y) * K(y * x,z) = y \ T(y / (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(3416(a,1),6681(a,1,2))].">
      <j1 rule="para" parents="3416 6681"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      L(x \ T(y * x,x),x,x) = ((1 / x) * T(y,x)) * x
    ]]></literal>
    <justification jstring="[para(6675(a,1),6714(a,1,1))].">
      <j1 rule="para" parents="6675 6714"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      ((1 / x) * T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(6716(a,1),660(a,1))].">
      <j1 rule="para" parents="6716 660"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x) = (1 / x) * T(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(6717,a,1223,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6717 1223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      K(L((x \ 1) \ 1,y,z) * u,w) = K(L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,6686,a(flip),b,6697,a),flip(a)].">
      <j1 rule="hyper" parents="325 6686 6697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3753,a(flip),b,6708,a),flip(a)].">
      <j1 rule="hyper" parents="65 3753 6708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(3777,a,6720,a)].">
      <j1 rule="hyper" parents="3777 6720"/>
    </justification>
  </clause>

  <clause id="6722">
    <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(4714(a,2),6721(a,2,2))].">
      <j1 rule="para" parents="4714 6721"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,5389,a(flip),b,6710,a),flip(a)].">
      <j1 rule="hyper" parents="325 5389 6710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6724">
    <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),6723(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6725">
    <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),6724(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(5085(a,1),6705(a,1,1))].">
      <j1 rule="para" parents="5085 6705"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(5154,a,6726,a),flip(a)].">
      <j1 rule="hyper" parents="5154 6726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4993(a,1),6701(a,1,2,1))].">
      <j1 rule="para" parents="4993 6701"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2952,a,6728,a),flip(a)].">
      <j1 rule="hyper" parents="2952 6728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6731">
    <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(67(a,1),6707(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="67 6707"/>
    </justification>
  </clause>

  <clause id="6732">
    <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),6731(a,2,1,2))].">
      <j1 rule="para" parents="7 6731"/>
    </justification>
  </clause>

  <clause id="6733">
    <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(6732(a,2),3701(a,1))].">
      <j1 rule="para" parents="6732 3701"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      L(K(x,(y \ 1) \ (z \ u)),z \ u,z) = K(x,(z * ((((y \ x) / x) * y) * (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(6017(a,1),6115(a,1,1))].">
      <j1 rule="para" parents="6017 6115"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      K(x,(y * ((((z \ x) / x) * z) * (1 / z))) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5841,a(flip),b,6734,a),flip(a)].">
      <j1 rule="hyper" parents="65 5841 6734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      K(x,(y * ((z \ x) / x)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(1479(a,1),6735(a,1,2,1,2))].">
      <j1 rule="para" parents="1479 6735"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6464,a(flip),b,6736,a)].">
      <j1 rule="hyper" parents="65 6464 6736"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5294,a(flip),b,6737,a),flip(a)].">
      <j1 rule="hyper" parents="65 5294 6737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K(x,((1 / (K(y,(z \ x) \ 1) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * (1 / (1 / y))) \ u)
    ]]></literal>
    <justification jstring="[para(3911(a,1),6738(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3911 6738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (R(x,z,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(4834(a,1),6328(a,2,2,1))].">
      <j1 rule="para" parents="4834 6328"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      L(a((x \ y) \ y,z,(x \ y) \ y),u,(x \ y) \ y) = y \ (y * a(x,z,x))
    ]]></literal>
    <justification jstring="[para(6276(a,1),6740(a,2,2))].">
      <j1 rule="para" parents="6276 6740"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(43,a,3998,a,b,6742,a),flip(a)].">
      <j1 rule="hyper" parents="43 3998 6742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = x \ (((x / y) * (y * K(x,z))) * K(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),6088(a,2,1))].">
      <j1 rule="para" parents="12 6088"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      T(((x / y) * (y * K(x,z))) / T(x,z),x) = ((x / y) * (y * K(z,x))) \ ((z * x) / z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2882,a,b,6744,a)].">
      <j1 rule="hyper" parents="325 2882 6744"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(6666(a,1),6745(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6666 6745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      K(L(x,y,z),x \ ((u * (x \ (1 / L(x,y,z)))) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6616,a(flip),b,6559,a)].">
      <j1 rule="hyper" parents="65 6616 6559"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      K(L(x,y,z),(u * (1 / L(x,y,z))) \ w) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[hyper(6570,a,6748,a)].">
      <j1 rule="hyper" parents="6570 6748"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * ((u * 1) \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6631,a(flip),b,6749,a)].">
      <j1 rule="hyper" parents="65 6631 6749"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),(u * (1 / x)) \ w)
    ]]></literal>
    <justification jstring="[para(8(a,1),6750(a,1,2,2,1))].">
      <j1 rule="para" parents="8 6750"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),(u * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,3449,a(flip),b,6751,a),flip(a)].">
      <j1 rule="hyper" parents="325 3449 6751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),x * ((u * 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,6650,a(flip),b,6752,a),flip(a)].">
      <j1 rule="hyper" parents="325 6650 6752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) * (u \ w)) = K(L(x,y,z),x * (u \ w))
    ]]></literal>
    <justification jstring="[para(8(a,1),6753(a,2,2,2,1))].">
      <j1 rule="para" parents="8 6753"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      K(x,((1 / (K(y,(z \ x) \ 1) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * (1 / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,3471,a(flip),b,6739,a),flip(a)].">
      <j1 rule="hyper" parents="325 3471 6739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      K(x,((1 / (K(y,(z \ x) \ 1) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(82(a,1),6755(a,2,2,1,2))].">
      <j1 rule="para" parents="82 6755"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(2744(a,1),6756(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="2744 6756"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6485,a(flip),b,6758,a),flip(a)].">
      <j1 rule="hyper" parents="65 6485 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,6729,a(flip),b,6759,a),flip(a)].">
      <j1 rule="hyper" parents="65 6729 6759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6133,a(flip),b,6760,a),flip(a)].">
      <j1 rule="hyper" parents="65 6133 6760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,5940,a(flip),b,6761,a),flip(a)].">
      <j1 rule="hyper" parents="65 5940 6761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6047,a,6762,a),flip(a)].">
      <j1 rule="hyper" parents="6047 6762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6764">
    <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(1746(a,2),6225(a,1,2,2))].">
      <j1 rule="para" parents="1746 6225"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K((x \ y) \ y,T(z,u))
    ]]></literal>
    <justification jstring="[para(5444(a,1),6444(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5444 6444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = K(x * z,T(T(x,y),u)) * K(x,T(T(z,u),y))
    ]]></literal>
    <justification jstring="[para(3117(a,1),6765(a,2,2))].">
      <j1 rule="para" parents="3117 6765"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      K(x * y,T(T(x,z),u)) * K(x,T(T(y,u),z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6743,a(flip),b,6766,a),flip(a)].">
      <j1 rule="hyper" parents="65 6743 6766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      K(x * y,T(T(x,z),u)) * K(x,T(T(y,z),u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(23(a,1),6768(a,1,1,2))].">
      <j1 rule="para" parents="23 6768"/>
    </justification>
  </clause>

  <clause id="6771">
    <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),6764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 6764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,L(z * K(x * y,z),y,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6348,a(flip),b,6771,a),flip(a)].">
      <j1 rule="hyper" parents="65 6348 6771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(1602(a,1),6772(a,2,2))].">
      <j1 rule="para" parents="1602 6772"/>
    </justification>
  </clause>

  <clause id="6774">
    <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(6226,a,6773,a)].">
      <j1 rule="hyper" parents="6226 6773"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ ((a(x,y,x) * (z * u)) * w) = a(a(x,y,x) * z,L(u,z,a(x,y,x)),w)
    ]]></literal>
    <justification jstring="[para(6210(a,1),6219(a,1,1))].">
      <j1 rule="para" parents="6210 6219"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),L(x,y,z) * (u \ L(K(x,w),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(325,a,6632,a(flip),b,6412,a),flip(a)].">
      <j1 rule="hyper" parents="325 6632 6412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ (a(x,y,x) * ((z * u) * w)) = a(a(x,y,x) * z,L(u,z,a(x,y,x)),w)
    ]]></literal>
    <justification jstring="[para(6210(a,1),6775(a,1,2))].">
      <j1 rule="para" parents="6210 6775"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),x * (u \ L(K(x,w),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(325,a,6754,a(flip),b,6776,a),flip(a)].">
      <j1 rule="hyper" parents="325 6754 6776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      K(L(x,y,z),T(u \ L(x,y,z),L(K(x,w),v5,v6))) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,6646,a(flip),b,6778,a),flip(a)].">
      <j1 rule="hyper" parents="325 6646 6778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      K(L(x,y,z),u \ L(x,y,z)) = K(L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(2469(a,1),6779(a,1,2))].">
      <j1 rule="para" parents="2469 6779"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      K(x \ L(y,z,u),L(y,z,u)) = (w * K(L(y,z,u),x \ y)) \ w
    ]]></literal>
    <justification jstring="[para(6781(a,1),2849(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6781 2849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      K(x \ L(y,z,u),L(y,z,u)) = K(x \ y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2849,a(flip),b,6782,a),flip(a)].">
      <j1 rule="hyper" parents="325 2849 6782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      T(L(x,y,z) * K((u \ 1) \ x,L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6783(a,1),5163(a,1,1,2))].">
      <j1 rule="para" parents="6783 5163"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      T(L(x,y,z) * K(x * (1 \ u),L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6648(a,1),6784(a,1,1,2))].">
      <j1 rule="para" parents="6648 6784"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      T(L(x,y,z) * K(x * u,L(x,y,z)),u) = u \ T(L(x,y,z) * u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(67(a,1),6785(a,1,1,2,1,2))].">
      <j1 rule="para" parents="67 6785"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      T(L(x * K(x * y,x),z,u),y) = y \ T(L(x,z,u) * y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(1628(a,1),6786(a,1,1))].">
      <j1 rule="para" parents="1628 6786"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      L(T(x * K(x * y,x),y),z,u) = y \ T(L(x,z,u) * y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1578,a,6787,a)].">
      <j1 rule="hyper" parents="1578 6787"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,L(y,z,u)) = L(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4667(a,1),6788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4667 6788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(4777,a,6789,a)].">
      <j1 rule="hyper" parents="4777 6789"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(43,a,29,a(flip),b,6790,a(flip))].">
      <j1 rule="hyper" parents="43 29 6790"/>
    </justification>
  </clause>

  <clause id="6792">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1597,a,b,6791,a)].">
      <j1 rule="hyper" parents="325 1597 6791"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(6791(a,1),4283(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6791 4283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6795">
    <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(6791(a,1),6389(a,1,1,2,2))].">
      <j1 rule="para" parents="6791 6389"/>
    </justification>
  </clause>

  <clause id="6796">
    <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(5944(a,1),6792(a,1,1,2))].">
      <j1 rule="para" parents="5944 6792"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,5193,a(flip),b,6794,a),flip(a)].">
      <j1 rule="hyper" parents="325 5193 6794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6799">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(6693,a,6797,a)].">
      <j1 rule="hyper" parents="6693 6797"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,6205,a,b,6797,a),flip(a)].">
      <j1 rule="hyper" parents="325 6205 6797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5825,a(flip),b,6797,a),flip(a)].">
      <j1 rule="hyper" parents="65 5825 6797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6640,a(flip),b,6801,a)].">
      <j1 rule="hyper" parents="65 6640 6801"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(3791,a,6803,a)].">
      <j1 rule="hyper" parents="3791 6803"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,3035,a(flip),b,6799,a),flip(a)].">
      <j1 rule="hyper" parents="325 3035 6799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(6450,a,6805,a)].">
      <j1 rule="hyper" parents="6450 6805"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6411,a(flip),b,6805,a)].">
      <j1 rule="hyper" parents="65 6411 6805"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(6805(a,1),6012(a,1,1,2))].">
      <j1 rule="para" parents="6805 6012"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6372,a,6800,a)].">
      <j1 rule="hyper" parents="6372 6800"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,6638,a(flip),b,6807,a),flip(a)].">
      <j1 rule="hyper" parents="325 6638 6807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6813">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(100(a,1),6812(a,1,1,2))].">
      <j1 rule="para" parents="100 6812"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(5914,a,6813,a)].">
      <j1 rule="hyper" parents="5914 6813"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (z * u),y) = w
    ]]></literal>
    <justification jstring="[para(6814(a,2),6642(a,1))].">
      <j1 rule="para" parents="6814 6642"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(6815,a,6117,a),flip(a)].">
      <j1 rule="hyper" parents="6815 6117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(18(a,2),6816(a,2,1))].">
      <j1 rule="para" parents="18 6816"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6437,a,6817,a),flip(a)].">
      <j1 rule="hyper" parents="6437 6817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3914,a(flip),b,6818,a)].">
      <j1 rule="hyper" parents="65 3914 6818"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      x * L(K(x,y),z,u) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,6819,a,b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 6819 2104"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,6763,a(flip),b,6819,a)].">
      <j1 rule="hyper" parents="65 6763 6819"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5606,a(flip),b,6819,a),flip(a)].">
      <j1 rule="hyper" parents="65 5606 6819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3539,a(flip),b,6819,a),flip(a)].">
      <j1 rule="hyper" parents="65 3539 6819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,6819,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 6819 18"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(308(a,1),6819(a,2,2))].">
      <j1 rule="para" parents="308 6819"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(469(a,1),6819(a,2,2))].">
      <j1 rule="para" parents="469 6819"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6819(a,1),6029(a,1,2))].">
      <j1 rule="para" parents="6819 6029"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(6819(a,1),6031(a,1,2))].">
      <j1 rule="para" parents="6819 6031"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(6819(a,1),6032(a,1,1))].">
      <j1 rule="para" parents="6819 6032"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6819,a(flip),b,6821,a),flip(a)].">
      <j1 rule="hyper" parents="65 6819 6821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(6827(a,1),3927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6827 3927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      ((x * y) / x) * K(y,L(x,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6827(a,1),4580(a,2,2))].">
      <j1 rule="para" parents="6827 4580"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(2857,a,6828,a)].">
      <j1 rule="hyper" parents="2857 6828"/>
    </justification>
  </clause>

  <clause id="6835">
    <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(4482(a,1),6828(a,1,2,2))].">
      <j1 rule="para" parents="4482 6828"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(1553(a,1),6830(a,2,2))].">
      <j1 rule="para" parents="1553 6830"/>
    </justification>
  </clause>

  <clause id="6837">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6035,a(flip),b,6833,a)].">
      <j1 rule="hyper" parents="65 6035 6833"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,6827,a,b,6833,a),flip(a)].">
      <j1 rule="hyper" parents="36 6827 6833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(36,a,6029,a,b,6833,a)].">
      <j1 rule="hyper" parents="36 6029 6833"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(6838(a,1),2090(a,1,1,2))].">
      <j1 rule="para" parents="6838 2090"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      (x / y) * K(z,L(y,u,w)) = x / T(y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6838(a,1),2852(a,1,2))].">
      <j1 rule="para" parents="6838 2852"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),x,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(308(a,1),6839(a,2,1))].">
      <j1 rule="para" parents="308 6839"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(6837(a,1),6127(a,2,2))].">
      <j1 rule="para" parents="6837 6127"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,5647,a,b,6831,a)].">
      <j1 rule="hyper" parents="65 5647 6831"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(6846(a,1),1592(a,1,1))].">
      <j1 rule="para" parents="6846 1592"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6841,a(flip),b,6832,a)].">
      <j1 rule="hyper" parents="65 6841 6832"/>
    </justification>
  </clause>

  <clause id="6849">
    <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(6845(a,1),5201(a,2,2))].">
      <j1 rule="para" parents="6845 5201"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(6824(a,1),6840(a,1,1))].">
      <j1 rule="para" parents="6824 6840"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(2098,a,6850,a)].">
      <j1 rule="hyper" parents="2098 6850"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(1588(a,1),6851(a,1,2))].">
      <j1 rule="para" parents="1588 6851"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ ((x * y) / z) = L(z,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1733,a,b,6852,a)].">
      <j1 rule="hyper" parents="65 1733 6852"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      L(x,x \ y,x \ y) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,1558,a(flip),b,6852,a),flip(a)].">
      <j1 rule="hyper" parents="65 1558 6852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,527,a(flip),b,6852,a),flip(a)].">
      <j1 rule="hyper" parents="65 527 6852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,104,a(flip),b,6852,a),flip(a)].">
      <j1 rule="hyper" parents="65 104 6852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      (x * y) / L(z,z \ y,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[hyper(201,a,6852,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="201 6852 104"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      L(x,x \ y,y \ z) = ((z / y) * (y / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(325,a,3459,a(flip),b,6856,a),flip(a)].">
      <j1 rule="hyper" parents="325 3459 6856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      L((x \ y) / z,((x \ y) / z) \ (x \ y),x) = (x * (z * K(z \ (x \ y),z))) \ y
    ]]></literal>
    <justification jstring="[para(2691(a,1),6855(a,2,1,2))].">
      <j1 rule="para" parents="2691 6855"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ u != L(z,z \ y,x)
    ]]></literal>
    <literal><![CDATA[
      (x * y) / z = u
    ]]></literal>
    <justification jstring="[para(6853(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="6853 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6306,a(flip),b,6795,a)].">
      <j1 rule="hyper" parents="65 6306 6795"/>
    </justification>
  </clause>

  <clause id="6863">
    <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),6861(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 6861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(2470(a,1),6808(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2470 6808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2082,a(flip),b,6864,a),flip(a)].">
      <j1 rule="hyper" parents="325 2082 6864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ u,x) = (x \ u) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),6865(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 6865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1246(a,1),6865(a,1,1))].">
      <j1 rule="para" parents="1246 6865"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      (x \ ((1 / L(x,y,z)) \ u)) * x = (1 / L(x,y,z)) \ T(u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,891,a(flip),b,6866,a),flip(a)].">
      <j1 rule="hyper" parents="65 891 6866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(6867(a,1),6340(a,2,2))].">
      <j1 rule="para" parents="6867 6340"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2086,a,b,6869,a),flip(a)].">
      <j1 rule="hyper" parents="325 2086 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6871">
    <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(1630(a,1),6796(a,1,1))].">
      <j1 rule="para" parents="1630 6796"/>
    </justification>
  </clause>

  <clause id="6872">
    <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(4651(a,1),6871(a,1,1,1,2))].">
      <j1 rule="para" parents="4651 6871"/>
    </justification>
  </clause>

  <clause id="6873">
    <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(65,a,27,a,b,6872,a)].">
      <j1 rule="hyper" parents="65 27 6872"/>
    </justification>
  </clause>

  <clause id="6874">
    <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(4667(a,1),6873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4667 6873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6791,a(flip),b,6874,a)].">
      <j1 rule="hyper" parents="65 6791 6874"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(44,a,31,a,b,6875,a(flip))].">
      <j1 rule="hyper" parents="44 31 6875"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,6193,a,b,6876,a),flip(a)].">
      <j1 rule="hyper" parents="325 6193 6876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,6377,a,b,6877,a(flip))].">
      <j1 rule="hyper" parents="36 6377 6877"/>
    </justification>
  </clause>

  <clause id="6881">
    <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(6870(a,1),6849(a,1,2))].">
      <j1 rule="para" parents="6870 6849"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4620,a(flip),b,6881,a),flip(a)].">
      <j1 rule="hyper" parents="65 4620 6881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(6838(a,1),6882(a,2,1))].">
      <j1 rule="para" parents="6838 6882"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,6829,a(flip),b,6883,a),flip(a)].">
      <j1 rule="hyper" parents="325 6829 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(332,a,6884,a)].">
      <j1 rule="hyper" parents="332 6884"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6885(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 6885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6888">
    <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(6887(a,2),6423(a,1,1))].">
      <j1 rule="para" parents="6887 6423"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6424,a,6888,a)].">
      <j1 rule="hyper" parents="6424 6888"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      (x * (y * K(y \ (x \ z),y))) \ z = L((x \ z) / y,y,x)
    ]]></literal>
    <justification jstring="[para(85(a,1),6859(a,1,2)),flip(a)].">
      <j1 rule="para" parents="85 6859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(u,w,u)) = a(a(u,w,u) * x,L(y,x,a(u,w,u)),z)
    ]]></literal>
    <justification jstring="[hyper(775,a,6777,a)].">
      <j1 rule="hyper" parents="775 6777"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      a(a(x,y,x) * z,L(u,z,a(x,y,x)),w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(6216,a,6891,a),flip(a)].">
      <j1 rule="hyper" parents="6216 6891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(6207(a,1),6892(a,1,2))].">
      <j1 rule="para" parents="6207 6892"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      a(x * (a(y,z,y) * u),w,v5) = a(u * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,6265,a(flip),b,6894,a)].">
      <j1 rule="hyper" parents="65 6265 6894"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),6894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(6239(a,1),6894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6239 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      a(L(((x \ 1) * y) * z,u,(x * y) * z),w,v5) = a(((x \ 1) * y) * z,w,v5)
    ]]></literal>
    <justification jstring="[para(2380(a,1),6897(a,1,1))].">
      <j1 rule="para" parents="2380 6897"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      a(x / a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1870,a,b,6896,a)].">
      <j1 rule="hyper" parents="65 1870 6896"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      a(x * (y * (a(z,u,z) * w)),v5,v6) = a((w * y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,6266,a(flip),b,6895,a)].">
      <j1 rule="hyper" parents="65 6266 6895"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      a(L((x * y) * z,u,(x * y) * z),w,v5) = a(((x \ 1) * y) * z,w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,2010,a(flip),b,6898,a)].">
      <j1 rule="hyper" parents="65 2010 6898"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      a(((x \ 1) * y) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6897,a(flip),b,6903,a),flip(a)].">
      <j1 rule="hyper" parents="65 6897 6903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6905">
    <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),6722(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 6722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(T(x,x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,4810,a(flip),b,6055,a),flip(a)].">
      <j1 rule="hyper" parents="325 4810 6055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,6054,a(flip),b,6906,a),flip(a)].">
      <j1 rule="hyper" parents="325 6054 6906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      (x * (y * (K(y,z) * (y \ u)))) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(2618(a,1),6089(a,1,1,2,2))].">
      <j1 rule="para" parents="2618 6089"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      K(x * y,K(z,(T(x * y,u) * w) \ L(w,y,x))) = K(z,K(x * y,a(x,y,w)))
    ]]></literal>
    <justification jstring="[hyper(4803,a,6111,a),flip(a)].">
      <j1 rule="hyper" parents="4803 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      K(x,K(y * z,(T(y * z,u) * w) \ L(w,z,y))) = K(x,K(y * z,a(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(3585,a,6947,a)].">
      <j1 rule="hyper" parents="3585 6947"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      K(x,K(y * z,u \ ((y * z) \ L(u,z,y)))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(5933(a,1),6948(a,1,2))].">
      <j1 rule="para" parents="5933 6948"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      K(x,K(y * z,u \ L(u,z,y))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(6536,a,6949,a)].">
      <j1 rule="hyper" parents="6536 6949"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,L(y,K(z,y) \ (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(4539(a,1),6946(a,1,1,2))].">
      <j1 rule="para" parents="4539 6946"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,L(y,K(y,z) * (y \ u),x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(2618(a,1),6951(a,1,2,2,2))].">
      <j1 rule="para" parents="2618 6951"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,L(y,y \ u,x)) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(5321(a,1),6952(a,1,2))].">
      <j1 rule="para" parents="5321 6952"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (((K(z,y) \ (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(6023(a,1),6953(a,1,2))].">
      <j1 rule="para" parents="6023 6953"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (((K(y,z) * (u / y)) * K(z,y)) * y)
    ]]></literal>
    <justification jstring="[para(2618(a,1),6955(a,2,2,1,1))].">
      <j1 rule="para" parents="2618 6955"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * (T(u / y,K(y,z)) * y)
    ]]></literal>
    <justification jstring="[para(3620(a,1),6956(a,2,2,1))].">
      <j1 rule="para" parents="3620 6956"/>
    </justification>
  </clause>

  <clause id="6958">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T((u / y) * y,K(y,z))
    ]]></literal>
    <justification jstring="[para(3857(a,2),6957(a,2,2))].">
      <j1 rule="para" parents="3857 6957"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6958(a,2,2,1))].">
      <j1 rule="para" parents="12 6958"/>
    </justification>
  </clause>

  <clause id="6960">
    <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(4558(a,1),5376(a,1,1,1))].">
      <j1 rule="para" parents="4558 5376"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(2643(a,1),6960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2643 6960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4740,a(flip),b,6961,a),flip(a)].">
      <j1 rule="hyper" parents="325 4740 6961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(T(x,x \ y),y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(4811,a,6056,a),flip(a)].">
      <j1 rule="hyper" parents="4811 6056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6967">
    <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(3563(a,1),3808(a,1,2,1,2))].">
      <j1 rule="para" parents="3563 3808"/>
    </justification>
  </clause>

  <clause id="6968">
    <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(3756(a,1),6967(a,1,2,1,2))].">
      <j1 rule="para" parents="3756 6967"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(x,K(y,x * z)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(4715(a,1),6968(a,1,2,1,2))].">
      <j1 rule="para" parents="4715 6968"/>
    </justification>
  </clause>

  <clause id="6970">
    <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(3901(a,1),6969(a,1,2,1,2))].">
      <j1 rule="para" parents="3901 6969"/>
    </justification>
  </clause>

  <clause id="6971">
    <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(2152(a,2),6970(a,1,2,1))].">
      <j1 rule="para" parents="2152 6970"/>
    </justification>
  </clause>

  <clause id="6972">
    <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(65,a,2189,a,b,6971,a)].">
      <j1 rule="hyper" parents="65 2189 6971"/>
    </justification>
  </clause>

  <clause id="6973">
    <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(3771(a,1),6972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3771 6972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6974">
    <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(5212(a,1),6973(a,2,2))].">
      <j1 rule="para" parents="5212 6973"/>
    </justification>
  </clause>

  <clause id="6975">
    <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(325,a,4553,a(flip),b,6974,a),flip(a)].">
      <j1 rule="hyper" parents="325 4553 6974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(u,K(z,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3135(a,2),4438(a,1,1,3))].">
      <j1 rule="para" parents="3135 4438"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ ((K(z,K(u,w)) * K(y,z)) * x) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3580(a,1),6976(a,1,2,1,1))].">
      <j1 rule="para" parents="3580 6976"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(u,K(z,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3210(a,1),6977(a,1,2))].">
      <j1 rule="para" parents="3210 6977"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3580(a,1),6978(a,2,2,1))].">
      <j1 rule="para" parents="3580 6978"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * T(K(z,K(u,w)),x)
    ]]></literal>
    <justification jstring="[para(3377(a,1),6979(a,2,2))].">
      <j1 rule="para" parents="3377 6979"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      R(x,T(K(y,z),x),K(z,K(u,T(w,x)))) \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x)))
    ]]></literal>
    <justification jstring="[para(3135(a,2),6980(a,2,2))].">
      <j1 rule="para" parents="3135 6980"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      x \ (K(y,z) * (K(z,K(u,w)) * x)) = T(K(y,z),x) * K(z,K(u,T(w,x)))
    ]]></literal>
    <justification jstring="[para(3929(a,1),6981(a,1,1))].">
      <j1 rule="para" parents="3929 6981"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,K(u,T(w,z))) = T(K(x,y) * K(y,K(u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(631,a,6983,a),flip(a)].">
      <j1 rule="hyper" parents="631 6983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * T(K(w,x),u) = T(K(w,x) * K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3096,a(flip),b,6984,a)].">
      <j1 rule="hyper" parents="65 3096 6984"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(w,T(x,u)) = T(K(w,x) * K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[para(3111(a,2),6985(a,1,2))].">
      <j1 rule="para" parents="3111 6985"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ (x / x) = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),3897(a,1,2,1))].">
      <j1 rule="para" parents="12 3897"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ 1 = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),6987(a,1,2))].">
      <j1 rule="para" parents="79 6987"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(270,a,6988,a)].">
      <j1 rule="hyper" parents="270 6988"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3533(a,1),6990(a,1,1))].">
      <j1 rule="para" parents="3533 6990"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5372,a(flip),b,6993,a),flip(a)].">
      <j1 rule="hyper" parents="65 5372 6993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,4166,a(flip),b,6994,a),flip(a)].">
      <j1 rule="hyper" parents="325 4166 6994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,1519,a(flip),b,6995,a),flip(a)].">
      <j1 rule="hyper" parents="325 1519 6995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(944(a,1),6996(a,1,2))].">
      <j1 rule="para" parents="944 6996"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(195,a,6997,a)].">
      <j1 rule="hyper" parents="195 6997"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      (1 / (x \ L(x,y,z))) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(136,a,6997,a,b,1778,a)].">
      <j1 rule="hyper" parents="136 6997 1778"/>
    </justification>
  </clause>

  <clause id="7000">
    <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(137,a,6997,a(flip),b,6652,a),flip(a)].">
      <j1 rule="hyper" parents="137 6997 6652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7001">
    <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(6997(a,1),2144(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6997 2144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      (((x * y) \ (x * z)) \ (y \ z)) \ 1 = (y \ z) \ L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),6998(a,1,1,1))].">
      <j1 rule="para" parents="102 6998"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      x / ((L(y,z,u) \ y) * (L(y,z,u) \ y)) = x * ((L(y,z,u) \ y) \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(6998(a,1),582(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6998 582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      a(x,x,y) \ 1 = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(824(a,1),6998(a,1,1))].">
      <j1 rule="para" parents="824 6998"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      x \ (y * L(y \ x,z,z)) = a(z,z,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,1410,a(flip),b,7004,a)].">
      <j1 rule="hyper" parents="325 1410 7004"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * y = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,7004,a,b,1752,a)].">
      <j1 rule="hyper" parents="136 7004 1752"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      R(x,a(y,y,z),a(y,y,z)) / (z \ L(z,y,y)) = x * a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,7004,a(flip),b,573,a)].">
      <j1 rule="hyper" parents="201 7004 573"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      (x * L(y,z,z)) / L(a(z,z,y) \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(7004(a,2),444(a,1,2,1))].">
      <j1 rule="para" parents="7004 444"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      a(a(x,x,y) * y,z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(7006(a,1),1850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7006 1850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      L(x,y,z * a(u,u,z)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(7006(a,1),2327(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7006 2327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      (1 / (L(x,y,z) / x)) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[para(1752(a,2),6999(a,1,1,2))].">
      <j1 rule="para" parents="1752 6999"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,6854,a,b,7011,a)].">
      <j1 rule="hyper" parents="65 6854 7011"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(x \ R(x,y,y),z,z)) = a(z,z,a(x,y,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5798(a,1),7005(a,2,1,3))].">
      <j1 rule="para" parents="5798 7005"/>
    </justification>
  </clause>

  <clause id="7014">
    <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(325,a,3594,a,b,7001,a),flip(a)].">
      <j1 rule="hyper" parents="325 3594 7001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7015">
    <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(7001(a,2),3605(a,1))].">
      <j1 rule="para" parents="7001 3605"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      (((x * y) \ (x * z)) \ (y \ z)) \ 1 = y \ (z * L(z \ y,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,1410,a(flip),b,7002,a),flip(a)].">
      <j1 rule="hyper" parents="325 1410 7002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      x \ (y * L(y \ x,x,z)) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      ((z * x) \ (z * y)) \ (x \ y) = u
    ]]></literal>
    <justification jstring="[para(7016(a,1),50(a,1))].">
      <j1 rule="para" parents="7016 50"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      L(x,y,z) \ (x * ((x \ L(x,y,z)) \ 1)) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2020,a,b,7000,a)].">
      <j1 rule="hyper" parents="65 2020 7000"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ u = ((L(x,y,z) \ x) * (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(7000(a,1),2019(a,2,1))].">
      <j1 rule="para" parents="7000 2019"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(a(x,y,y),z,z)) = a(z,z,a(x,y,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1896(a,1),7013(a,1,2,2,1))].">
      <j1 rule="para" parents="1896 7013"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) \ x)) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2015(a,1),7018(a,1,2,2))].">
      <j1 rule="para" parents="2015 7018"/>
    </justification>
  </clause>

  <clause id="7022">
    <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="[hyper(1265,a,7021,a),flip(a)].">
      <j1 rule="hyper" parents="1265 7021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x * K(y,z * x)))
    ]]></literal>
    <justification jstring="[para(3111(a,2),5226(a,2,2))].">
      <j1 rule="para" parents="3111 5226"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      (a(x,y,L(x,z,u)) * K(x,w)) \ (x * K(L(x,y,L(x,z,u)),w)) = T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(5018(a,1),6375(a,1,1,2))].">
      <j1 rule="para" parents="5018 6375"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x) = (a(x,y,L(x,z,u)) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(5019(a,1),7024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5019 7024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      (a(x,y,L(x,z,u)) * K(x,w)) \ T(x,w) = L(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1777,a(flip),b,7026,a),flip(a)].">
      <j1 rule="hyper" parents="65 1777 7026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = (a(x,y,x) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(6809(a,1),7027(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6809 7027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(3432(a,1),7023(a,2,2))].">
      <j1 rule="para" parents="3432 7023"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,3139,a(flip),b,7031,a),flip(a)].">
      <j1 rule="hyper" parents="325 3139 7031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (x * K(z,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(325,a,287,a(flip),b,7032,a),flip(a)].">
      <j1 rule="hyper" parents="325 287 7032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(3106(a,1),7034(a,2,2))].">
      <j1 rule="para" parents="3106 7034"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(3634(a,1),7035(a,1,2))].">
      <j1 rule="para" parents="3634 7035"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(2858,a,7036,a)].">
      <j1 rule="hyper" parents="2858 7036"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      K(x,y * z) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z * (K(x,y * z) * K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7037(a,1),4093(a,1))].">
      <j1 rule="para" parents="7037 4093"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      x * ((y * a(y,x,T(y,z))) * L((y * a(y,x,T(y,z))) \ (x \ u),w,v5)) = T(y * x,y) * L(T(y * x,y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(6233(a,1),6252(a,2,2,1,1))].">
      <j1 rule="para" parents="6233 6252"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      x * (R(y,x,y) * L((y * a(y,x,T(y,z))) \ (x \ u),w,v5)) = T(y * x,y) * L(T(y * x,y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(6229(a,1),7040(a,1,2,1))].">
      <j1 rule="para" parents="6229 7040"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      x * (R(y,x,y) * L(R(y,x,y) \ (x \ z),u,w)) = T(y * x,y) * L(T(y * x,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6229(a,1),7041(a,1,2,2,1,1))].">
      <j1 rule="para" parents="6229 7041"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      ((1 / (x * y)) * y) \ (K(y,x) * R(K(y,x) \ ((1 / (x * y)) * y),z,u)) = L(x,y,x * y) \ R(L(x,y,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(6565(a,1),6566(a,2,2,1))].">
      <j1 rule="para" parents="6565 6566"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      ((1 / (x * y)) * y) \ (K(y,x) * R(K(y,x) \ ((1 / (x * y)) * y),z,u)) = L(x,y,x * y) \ L(R(x,z,u),y,x * y)
    ]]></literal>
    <justification jstring="[para(29(a,1),7045(a,2,2))].">
      <j1 rule="para" parents="29 7045"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = K(u,u * x) * T(u * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5557(a,1),4778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5557 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(K(u,u * x) * (u * L(x,y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,4541,a,b,7048,a),flip(a)].">
      <j1 rule="hyper" parents="325 4541 7048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,L(x,y,z),u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2114(a,1),7049(a,2,1))].">
      <j1 rule="para" parents="2114 7049"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      L((K(x,y) * a(x,z,x)) \ u,K(x,y) * a(x,z,x),T(x,R(T(x,y),z,x))) = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u)
    ]]></literal>
    <justification jstring="[para(6198(a,1),6260(a,1,2))].">
      <j1 rule="para" parents="6198 6260"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u) = L((K(x,y) * a(x,z,x)) \ u,K(x,y) * a(x,z,x),x)
    ]]></literal>
    <justification jstring="[hyper(1574,a,7052,a),flip(a)].">
      <j1 rule="hyper" parents="1574 7052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7055">
    <literal><![CDATA[
      ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u) = (K(x,y) * a(x,z,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(325,a,6395,a(flip),b,7053,a),flip(a)].">
      <j1 rule="hyper" parents="325 6395 7053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = R(T(x,y),z,x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2607,a(flip),b,7055,a),flip(a)].">
      <j1 rule="hyper" parents="65 2607 7055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = x * (R(T(x,y),z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,5613,a(flip),b,7057,a),flip(a)].">
      <j1 rule="hyper" parents="325 5613 7057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      (a(x,y,x) * K(x,z)) \ u = x * (R(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(6072(a,1),7058(a,1,1))].">
      <j1 rule="para" parents="6072 7058"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (R(T(x,w),y,x) \ T(x,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7029,a,b,7059,a)].">
      <j1 rule="hyper" parents="65 7029 7059"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (T(x,w) \ L(T(x,w),y,x))
    ]]></literal>
    <justification jstring="[para(6386(a,1),7060(a,2,2))].">
      <j1 rule="para" parents="6386 7060"/>
    </justification>
  </clause>

  <clause id="7062">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (x \ L(x,y,x))
    ]]></literal>
    <justification jstring="[para(4822(a,1),7061(a,2,2))].">
      <j1 rule="para" parents="4822 7061"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,10,a(flip),b,7062,a),flip(a)].">
      <j1 rule="hyper" parents="325 10 7062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      L(R(x,y,z),u,L(x,w,v5)) = R(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7063(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7063 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7063(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7063 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      L(x,y,x) \ L(L(x,z,u),y,L(x,w,v5)) = L(x \ L(x,z,u),y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(7063(a,1),4460(a,1,1))].">
      <j1 rule="para" parents="7063 4460"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      L(R(x,y,z),u,L(x,w,v5)) = L(R(x,y,z),u,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,29,a(flip),b,7065,a),flip(a)].">
      <j1 rule="hyper" parents="325 29 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      (L(x,y,z) \ L(L(x,u,x),y,z)) \ w = w * a(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7066(a,1),6250(a,1,1,2))].">
      <j1 rule="para" parents="7066 6250"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = L(x,u,x) \ L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7066(a,1),7067(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7066 7067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = L(x \ L(x,y,z),u,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,4458,a(flip),b,7070,a),flip(a)].">
      <j1 rule="hyper" parents="325 4458 7070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7073">
    <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(6304(a,1),6309(a,2,2,1,1))].">
      <j1 rule="para" parents="6304 6309"/>
    </justification>
  </clause>

  <clause id="7074">
    <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(325,a,1401,a(flip),b,7073,a),flip(a)].">
      <j1 rule="hyper" parents="325 1401 7073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7075">
    <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(1829(a,1),7074(a,2,2))].">
      <j1 rule="para" parents="1829 7074"/>
    </justification>
  </clause>

  <clause id="7076">
    <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(909(a,1),7075(a,2,2,1))].">
      <j1 rule="para" parents="909 7075"/>
    </justification>
  </clause>

  <clause id="7077">
    <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(966(a,1),7076(a,2,2,1,2))].">
      <j1 rule="para" parents="966 7076"/>
    </justification>
  </clause>

  <clause id="7078">
    <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(1401(a,1),7077(a,1,1))].">
      <j1 rule="para" parents="1401 7077"/>
    </justification>
  </clause>

  <clause id="7079">
    <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(6382(a,2),7078(a,1,1,2))].">
      <j1 rule="para" parents="6382 7078"/>
    </justification>
  </clause>

  <clause id="7080">
    <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),7079(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,4775,a,b,7080,a)].">
      <j1 rule="hyper" parents="41 4775 7080"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,7081,a(flip),b,6196,a),flip(a)].">
      <j1 rule="hyper" parents="133 7081 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7083">
    <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(325,a,5192,a(flip),b,4083,a),flip(a)].">
      <j1 rule="hyper" parents="325 5192 4083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <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(325,a,3582,a(flip),b,7083,a),flip(a)].">
      <j1 rule="hyper" parents="325 3582 7083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((1 / y) * (w / (1 / y))) * (R(1 / y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(5565(a,1),3474(a,2,2,1))].">
      <j1 rule="para" parents="5565 3474"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) * (R(1 / y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(3287(a,1),7112(a,2,2,1))].">
      <j1 rule="para" parents="3287 7112"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(1 / y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2963,a(flip),b,7113,a),flip(a)].">
      <j1 rule="hyper" parents="325 2963 7113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((y \ 1) * (w / (y \ 1))) / R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3452,a(flip),b,7115,a),flip(a)].">
      <j1 rule="hyper" parents="325 3452 7115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,(y \ 1) / (R(y \ 1,z,u) / (w / (y \ 1))))
    ]]></literal>
    <justification jstring="[hyper(325,a,2965,a(flip),b,7116,a),flip(a)].">
      <j1 rule="hyper" parents="325 2965 7116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7118">
    <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(1999(a,1),5228(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="1999 5228"/>
    </justification>
  </clause>

  <clause id="7119">
    <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(3383(a,1),7118(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3383 7118"/>
    </justification>
  </clause>

  <clause id="7120">
    <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(3580(a,1),7119(a,1,2,1))].">
      <j1 rule="para" parents="3580 7119"/>
    </justification>
  </clause>

  <clause id="7121">
    <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(3867(a,1),7120(a,1,2,1,2))].">
      <j1 rule="para" parents="3867 7120"/>
    </justification>
  </clause>

  <clause id="7122">
    <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(3243(a,1),7121(a,1,2,1,2))].">
      <j1 rule="para" parents="3243 7121"/>
    </justification>
  </clause>

  <clause id="7124">
    <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(3767(a,1),7122(a,1,2,1))].">
      <j1 rule="para" parents="3767 7122"/>
    </justification>
  </clause>

  <clause id="7125">
    <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(1999(a,1),7124(a,1,2,2,1,2,1,2,2))].">
      <j1 rule="para" parents="1999 7124"/>
    </justification>
  </clause>

  <clause id="7126">
    <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(3383(a,1),7125(a,1,2,2,1,2,1,2))].">
      <j1 rule="para" parents="3383 7125"/>
    </justification>
  </clause>

  <clause id="7127">
    <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(3563(a,1),7126(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3563 7126"/>
    </justification>
  </clause>

  <clause id="7128">
    <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(4367(a,1),7127(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="4367 7127"/>
    </justification>
  </clause>

  <clause id="7129">
    <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(3107(a,1),7128(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="3107 7128"/>
    </justification>
  </clause>

  <clause id="7131">
    <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(3759(a,1),7129(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3759 7129"/>
    </justification>
  </clause>

  <clause id="7132">
    <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(2152(a,2),7131(a,1,2,2,1))].">
      <j1 rule="para" parents="2152 7131"/>
    </justification>
  </clause>

  <clause id="7133">
    <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(4217(a,2),7132(a,1,2))].">
      <j1 rule="para" parents="4217 7132"/>
    </justification>
  </clause>

  <clause id="7134">
    <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(798,a,7133,a)].">
      <j1 rule="hyper" parents="798 7133"/>
    </justification>
  </clause>

  <clause id="7135">
    <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(5212(a,1),7134(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5212 7134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7136">
    <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(325,a,4553,a(flip),b,7135,a),flip(a)].">
      <j1 rule="hyper" parents="325 4553 7135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7137">
    <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(944(a,1),7136(a,1,1)),flip(a)].">
      <j1 rule="para" parents="944 7136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7138">
    <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(65,a,6975,a,b,7137,a)].">
      <j1 rule="hyper" parents="65 6975 7137"/>
    </justification>
  </clause>

  <clause id="7139">
    <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(944(a,1),7138(a,1,1))].">
      <j1 rule="para" parents="944 7138"/>
    </justification>
  </clause>

  <clause id="7140">
    <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(7139(a,1),7014(a,1,2))].">
      <j1 rule="para" parents="7139 7014"/>
    </justification>
  </clause>

  <clause id="7141">
    <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(7015,a,7140,a),flip(a)].">
      <j1 rule="hyper" parents="7015 7140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) = K(u,K(w,x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,3582,a,b,7141,a),flip(a)].">
      <j1 rule="hyper" parents="325 3582 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7143">
    <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(65,a,4425,a(flip),b,7142,a)].">
      <j1 rule="hyper" parents="65 4425 7142"/>
    </justification>
  </clause>

  <clause id="7144">
    <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(325,a,3580,a,b,7143,a),flip(a)].">
      <j1 rule="hyper" parents="325 3580 7143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7145">
    <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(4426,a,7144,a)].">
      <j1 rule="hyper" parents="4426 7144"/>
    </justification>
  </clause>

  <clause id="7146">
    <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(65,a,6905,a,b,7145,a)].">
      <j1 rule="hyper" parents="65 6905 7145"/>
    </justification>
  </clause>

  <clause id="7147">
    <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(325,a,6950,a(flip),b,7146,a),flip(a)].">
      <j1 rule="hyper" parents="325 6950 7146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7148">
    <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(3698,a,7147,a)].">
      <j1 rule="hyper" parents="3698 7147"/>
    </justification>
  </clause>

  <clause id="7149">
    <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(7147(a,1),3698(a,1))].">
      <j1 rule="para" parents="7147 3698"/>
    </justification>
  </clause>

  <clause id="7150">
    <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(65,a,3575,a,b,7148,a)].">
      <j1 rule="hyper" parents="65 3575 7148"/>
    </justification>
  </clause>

  <clause id="7151">
    <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(65,a,7084,a,b,7150,a)].">
      <j1 rule="hyper" parents="65 7084 7150"/>
    </justification>
  </clause>

  <clause id="7152">
    <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(5359,a,7151,a)].">
      <j1 rule="hyper" parents="5359 7151"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(65,a,5760,a(flip),b,7152,a),flip(a)].">
      <j1 rule="hyper" parents="65 5760 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,7082,a(flip),b,7153,a),flip(a)].">
      <j1 rule="hyper" parents="325 7082 7153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(7149,a,7155,a)].">
      <j1 rule="hyper" parents="7149 7155"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(7156(a,1),4175(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7156 4175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),w,v5) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,7158,a(flip),b,3007,a),flip(a)].">
      <j1 rule="hyper" parents="134 7158 3007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      R(a(K(x,y),z,u),w,v5) = K(v6,a(v7,v8,v9))
    ]]></literal>
    <justification jstring="[para(5060(a,1),7159(a,1,1))].">
      <j1 rule="para" parents="5060 7159"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      K(x,a(y,z,u)) = a(K(w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(6301,a,7161,a)].">
      <j1 rule="hyper" parents="6301 7161"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(7161(a,1),6186(a,1,2))].">
      <j1 rule="para" parents="7161 6186"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3854,a,7164,a)].">
      <j1 rule="hyper" parents="3854 7164"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a(flip),b,7165,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 7165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7165(a,1),3672(a,1))].">
      <j1 rule="para" parents="7165 3672"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      K(x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,7082,a(flip),b,7162,a),flip(a)].">
      <j1 rule="hyper" parents="325 7082 7162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      K(a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,7162,a,b,6833,a),flip(a)].">
      <j1 rule="hyper" parents="133 7162 6833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      T(x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,7175,a)].">
      <j1 rule="hyper" parents="58 7175"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      1 / a(x,y,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,7175,a(flip),b,262,a(flip))].">
      <j1 rule="hyper" parents="135 7175 262"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,7175,a(flip),b,262,a(flip))].">
      <j1 rule="hyper" parents="132 7175 262"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      K(a(x,y,z),u) = K(a(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(325,a,7177,a,b,7177,a)].">
      <j1 rule="hyper" parents="325 7177 7177"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      x * K(a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,7177,a,b,69,a)].">
      <j1 rule="hyper" parents="137 7177 69"/>
    </justification>
  </clause>

  <clause id="7185">
    <literal><![CDATA[
      K(a(x,y,z),u) * w = w
    ]]></literal>
    <justification jstring="[hyper(136,a,7177,a,b,79,a)].">
      <j1 rule="hyper" parents="136 7177 79"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7177,a)].">
      <j1 rule="hyper" parents="58 7177"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(a(x,y,z),u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(7177(a,2),138(a,1,1))].">
      <j1 rule="para" parents="7177 138"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ y)) = T(x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(7177(a,1),3891(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7177 3891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      a(x,y,z) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1998,a,7179,a),flip(a)].">
      <j1 rule="hyper" parents="1998 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(1996,a,7179,a)].">
      <j1 rule="hyper" parents="1996 7179"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(1578,a,7179,a)].">
      <j1 rule="hyper" parents="1578 7179"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(380,a,7179,a)].">
      <j1 rule="hyper" parents="380 7179"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      x / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,7179,a),flip(a)].">
      <j1 rule="hyper" parents="376 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      T(x,a(y,z,u)) = w \ (w * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,9,a,b,7179,a),flip(a)].">
      <j1 rule="hyper" parents="325 9 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(303,a,7179,a)].">
      <j1 rule="hyper" parents="303 7179"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      x * K(x * a(y,z,u),x) = R(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4667,a(flip),b,7179,a),flip(a)].">
      <j1 rule="hyper" parents="65 4667 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      a(x,y,z) / (u * u) = (u * u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,7179,a(flip),b,600,a)].">
      <j1 rule="hyper" parents="201 7179 600"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      x / (x / a(y,z,u)) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(201,a,7179,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="201 7179 115"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(201,a,7179,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="201 7179 22"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      a(x,y,z) * (u / (a(x,y,z) \ 1)) = u * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,7179,a(flip),b,565,a(flip))].">
      <j1 rule="hyper" parents="137 7179 565"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,2559,a(flip),b,7179,a(flip))].">
      <j1 rule="hyper" parents="41 2559 7179"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      x * (a(y,z,u) * w) = x * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(39,a,1652,a(flip),b,7179,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 1652 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(7179(a,1),237(a,1,2,2))].">
      <j1 rule="para" parents="7179 237"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      a(x,y,z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(7179(a,1),149(a,1)),flip(a)].">
      <j1 rule="para" parents="7179 149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      a(x,y,z) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(7179(a,1),292(a,1,2))].">
      <j1 rule="para" parents="7179 292"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      x / a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(7179(a,1),376(a,1))].">
      <j1 rule="para" parents="7179 376"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      (a(x,y,z) * u) * w = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(7179(a,1),234(a,1,1,2))].">
      <j1 rule="para" parents="7179 234"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      (a(x,y,z) * u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (u * a(x,y,z)) * w = v5
    ]]></literal>
    <justification jstring="[para(7179(a,1),529(a,1,1,2))].">
      <j1 rule="para" parents="7179 529"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(w,x,a(y,z,u)) = a(y,z,u) * (x * w)
    ]]></literal>
    <justification jstring="[para(7179(a,1),5232(a,2,2,1))].">
      <j1 rule="para" parents="7179 5232"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(7179(a,1),5236(a,1,1,1))].">
      <j1 rule="para" parents="7179 5236"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      (x \ a(y,z,u)) / (x \ 1) = (x \ 1) \ (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(135,a,7184,a(flip),b,4340,a)].">
      <j1 rule="hyper" parents="135 7184 4340"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      T(x,L(a(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,6841,a(flip),b,7184,a(flip))].">
      <j1 rule="hyper" parents="38 6841 7184"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      x * (y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(7184(a,1),6086(a,1))].">
      <j1 rule="para" parents="7184 6086"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w = (u * a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(65,a,6163,a(flip),b,7185,a),flip(a)].">
      <j1 rule="hyper" parents="65 6163 7185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2564,a(flip),b,7185,a)].">
      <j1 rule="hyper" parents="65 2564 7185"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      (a(x,y,z) * u) / w = (u * a(x,y,z)) / w
    ]]></literal>
    <justification jstring="[hyper(65,a,2495,a(flip),b,7185,a)].">
      <j1 rule="hyper" parents="65 2495 7185"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2564,a(flip),b,7185,a(flip))].">
      <j1 rule="hyper" parents="136 2564 7185"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6746,a,b,7186,a)].">
      <j1 rule="hyper" parents="65 6746 7186"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      a(x,y,z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(7186(a,1),149(a,1))].">
      <j1 rule="para" parents="7186 149"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(7186(a,1),292(a,1,2))].">
      <j1 rule="para" parents="7186 292"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7186(a,1),242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7186 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      (x * a(y,z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) * w = v5
    ]]></literal>
    <justification jstring="[para(7186(a,1),529(a,1,1,2))].">
      <j1 rule="para" parents="7186 529"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      x * L(a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),w,v5) * x = v6
    ]]></literal>
    <justification jstring="[para(7186(a,1),373(a,1,2,1))].">
      <j1 rule="para" parents="7186 373"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (w * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(7186(a,1),584(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7186 584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,u) * w = u * ((u \ w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(7186(a,1),726(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7186 726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      (a(x,y,z) * (u * u)) * w = (u * u) * (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(7186(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7186 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ (x * (w * (a(y,z,u) * v5))) = L(L(v5,a(y,z,u),w),a(y,z,u) * w,x)
    ]]></literal>
    <justification jstring="[para(7186(a,1),5237(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7186 5237"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      x / L(a(y,z,u),w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[para(7186(a,1),6585(a,1,2,1))].">
      <j1 rule="para" parents="7186 6585"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / (x * y) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,7218,a(flip),b,443,a)].">
      <j1 rule="hyper" parents="201 7218 443"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v5 * L(a(x,y,z),u,w) = v6
    ]]></literal>
    <justification jstring="[para(7218(a,1),292(a,1,2))].">
      <j1 rule="para" parents="7218 292"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      x / L(a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),w,v5) \ x = v6
    ]]></literal>
    <justification jstring="[para(7218(a,1),376(a,1))].">
      <j1 rule="para" parents="7218 376"/>
    </justification>
  </clause>

  <clause id="7239">
    <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(7180(a,1),653(a,1,1))].">
      <j1 rule="para" parents="7180 653"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      L(x \ a(y,z,u),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ 1
    ]]></literal>
    <justification jstring="[para(7180(a,1),700(a,2,1,1))].">
      <j1 rule="para" parents="7180 700"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * L(a(x,y,z),u,w) = a(x,y,z) \ L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7180(a,1),1757(a,1,1))].">
      <j1 rule="para" parents="7180 1757"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      a(a(x,y,z),u,a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,7182,a,b,6204,a),flip(a)].">
      <j1 rule="hyper" parents="133 7182 6204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      (x * a(y,z,u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) \ w = v5
    ]]></literal>
    <justification jstring="[para(6163(a,1),7187(a,1))].">
      <j1 rule="para" parents="6163 7187"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1875,a(flip),b,7190,a),flip(a)].">
      <j1 rule="hyper" parents="325 1875 7190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      a(x,y,y \ (x \ z)) * z = (x * y) * (y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(325,a,710,a(flip),b,7190,a),flip(a)].">
      <j1 rule="hyper" parents="325 710 7190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (w * a(x,y,z)) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(135,a,7190,a,b,109,a)].">
      <j1 rule="hyper" parents="135 7190 109"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      a(x,y,z) \ ((x * y) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,89,a(flip),b,7190,a)].">
      <j1 rule="hyper" parents="132 89 7190"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * x)) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,7190,a,b,648,a)].">
      <j1 rule="hyper" parents="132 7190 648"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (a(z,u,w) * (x * y)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,7190,a,b,89,a)].">
      <j1 rule="hyper" parents="132 7190 89"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = (R(x,y,z) \ x) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5805,a,b,7190,a)].">
      <j1 rule="hyper" parents="65 5805 7190"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      (x * T(y,a(z,u,w) * x)) * a(z,u,w) = L(y,x,a(z,u,w)) * (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,584,a(flip),b,7190,a),flip(a)].">
      <j1 rule="hyper" parents="65 584 7190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      x * (T(y,x * a(z,u,w)) * a(z,u,w)) = L(y,a(z,u,w),x) * (x * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,7190,a(flip),b,585,a)].">
      <j1 rule="hyper" parents="137 7190 585"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * a(x,y,z)) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,7190,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="132 7190 100"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) \ ((u * a(x,y,z)) * w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7190(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7190 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7270">
    <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(7190(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7190 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) / (x * w) = R(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[para(7190(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7190 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      a(x,y,z) * u != u * w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(7190(a,2),45(a,1))].">
      <j1 rule="para" parents="7190 45"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ w = x
    ]]></literal>
    <justification jstring="[para(7190(a,1),140(a,1))].">
      <j1 rule="para" parents="7190 140"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ w),x,a(y,z,u)) = (x * a(y,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(7190(a,1),308(a,2,1))].">
      <j1 rule="para" parents="7190 308"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      x \ y != (a(z,u,w) \ v5) * a(z,u,w)
    ]]></literal>
    <literal><![CDATA[
      x * v5 = y
    ]]></literal>
    <justification jstring="[para(7190(a,1),330(a,2))].">
      <j1 rule="para" parents="7190 330"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * (v5 * (v5 \ x)) = w
    ]]></literal>
    <justification jstring="[para(7190(a,1),534(a,1))].">
      <j1 rule="para" parents="7190 534"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(T(w,a(x,y,z)),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7190(a,2),240(a,1,1))].">
      <j1 rule="para" parents="7190 240"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(z,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(7190(a,1),709(a,1,1,2))].">
      <j1 rule="para" parents="7190 709"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (a(z,u,w) * (x * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(7190(a,2),709(a,1,2))].">
      <j1 rule="para" parents="7190 709"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      x / L(a(y,z,u),w,(w * a(y,z,u)) \ x) = (x / (a(y,z,u) * w)) * w
    ]]></literal>
    <justification jstring="[para(7190(a,2),1579(a,2,1,2))].">
      <j1 rule="para" parents="7190 1579"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      a(x \ 1,y,z) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1847(a,1),7190(a,2,2))].">
      <j1 rule="para" parents="1847 7190"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      ((x \ y) \ y) * (a(z,u,w) * (x \ y)) = x * ((y / x) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(7190(a,2),5270(a,1,2))].">
      <j1 rule="para" parents="7190 5270"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) / T(x,y) = (a(z,u,w) * (y * x)) / x
    ]]></literal>
    <justification jstring="[para(7190(a,1),6526(a,1,1))].">
      <j1 rule="para" parents="7190 6526"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      x * T(a(y,z,u),w) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(7186(a,2),7190(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7186 7190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      a(x,y,z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ w = u
    ]]></literal>
    <justification jstring="[para(7191(a,1),150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7191 150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      ((x * x) * y) / a(z,u,w) = (x * x) * (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(7191(a,1),120(a,1,1,2))].">
      <j1 rule="para" parents="7191 120"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L((a(x,y,z) \ u) \ a(x,y,z),w,v5) = (a(x,y,z) \ u) \ L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(7191(a,1),1322(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7191 1322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      x * R(a(y,z,u),w,w \ x) = (a(y,z,u) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(7203(a,1),791(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7203 791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      R(a(x,y,z),u,w) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v5 * R(a(x,y,z),u,w) = v6
    ]]></literal>
    <justification jstring="[para(7203(a,1),812(a,1,1,1))].">
      <j1 rule="para" parents="7203 812"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(135,a,7284,a(flip),b,6538,a)].">
      <j1 rule="hyper" parents="135 7284 6538"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      a(x \ 1,y,z) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(1847(a,2),7209(a,1,1))].">
      <j1 rule="para" parents="1847 7209"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      ((x * y) * z) / ((x * (y * (z * (u * u)))) / (u * u)) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,697,a(flip),b,7221,a)].">
      <j1 rule="hyper" parents="325 697 7221"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      a(x / (y * z),y,z) * x = ((x / (y * z)) * y) * z
    ]]></literal>
    <justification jstring="[para(7221(a,2),417(a,1,1))].">
      <j1 rule="para" parents="7221 417"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      ((x * L(x,y,z)) * u) / (L(x,y,z) * (x * u)) = a(L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(249(a,1),7221(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="249 7221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7295">
    <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(249(a,1),7221(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="249 7221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      (x * (y * (x * y))) / ((x * y) * (x * y)) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(7221(a,2),436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7221 436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[para(2269(a,1),7221(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2269 7221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(7223(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7223 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      a(x,y,z) \ (((x \ 1) * y) * z) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(1847(a,1),7261(a,1,1))].">
      <j1 rule="para" parents="1847 7261"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / v5 = (x * (w * a(y,z,u))) / v5
    ]]></literal>
    <justification jstring="[hyper(135,a,7206,a,b,12,a)].">
      <j1 rule="hyper" parents="135 7206 12"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      x \ (y * (a(z,u,w) * v5)) = x \ (y * (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(132,a,7206,a,b,10,a)].">
      <j1 rule="hyper" parents="132 7206 10"/>
    </justification>
  </clause>

  <clause id="7304">
    <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(135,a,7206,a(flip),b,7191,a)].">
      <j1 rule="hyper" parents="135 7206 7191"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      x \ ((a(y,z,u) * w) * v5) = x \ ((w * a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(132,a,7211,a,b,10,a)].">
      <j1 rule="hyper" parents="132 7211 10"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      (a(x,y,z) * ((u * u) * w)) \ v5 = ((u * u) * (w * a(x,y,z))) \ v5
    ]]></literal>
    <justification jstring="[para(33(a,1),7220(a,2,1))].">
      <j1 rule="para" parents="33 7220"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      a(L(x,y,z),z,y) * (z * (y * x)) = (z * y) * R(L(x,y,z),z,y)
    ]]></literal>
    <justification jstring="[para(100(a,1),7258(a,1,2))].">
      <j1 rule="para" parents="100 7258"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      (x \ a(y,z,u)) * (x * x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,390,a(flip),b,7262,a)].">
      <j1 rule="hyper" parents="65 390 7262"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      ((1 / x) \ a(y,z,u)) * (x \ (1 / x)) = (1 / (1 / x)) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[para(277(a,1),7308(a,1,2))].">
      <j1 rule="para" parents="277 7308"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / (x * w) = L(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,7206,a,b,7230,a)].">
      <j1 rule="hyper" parents="135 7206 7230"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / (y * x) = L(a(z,u,w),y,x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7230(a,1),6574(a,1,1))].">
      <j1 rule="para" parents="7230 6574"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      T(R(a(x,y,z),u,w),T(u * w,(u * a(x,y,z)) * w)) = (u * w) \ ((u * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(7271(a,1),2577(a,1,1))].">
      <j1 rule="para" parents="7271 2577"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      a((x * y) \ z,x,y) * z = ((z / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[para(1870(a,1),7293(a,1,1))].">
      <j1 rule="para" parents="1870 7293"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),u) \ (((x \ 1) * x) * u) = (R(x,y,z) \ 1) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(5588(a,1),7300(a,1,2,1))].">
      <j1 rule="para" parents="5588 7300"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),x,y) * ((x * z) * y) = (R(z * K(x,z),x,y) * x) * y
    ]]></literal>
    <justification jstring="[para(1593(a,2),7314(a,2,1,1))].">
      <j1 rule="para" parents="1593 7314"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      a(x,y,z) \ ((u * u) * w) = (u * u) * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(7210,a,7286,a)].">
      <j1 rule="hyper" parents="7210 7286"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (a(x,y,z) \ u) = (1 / a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,652,a(flip),b,7317,a),flip(a)].">
      <j1 rule="hyper" parents="65 652 7317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(a(z,u,w),y,x) * (y * x) = v5
    ]]></literal>
    <justification jstring="[para(5232(a,1),7229(a,1))].">
      <j1 rule="para" parents="5232 7229"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * w) * a(y,z,u)) = L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,7190,a(flip),b,7215,a)].">
      <j1 rule="hyper" parents="132 7190 7215"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      (((1 / x) \ x) * a(y,z,u)) / T(x,1 / (1 / x)) = (a(y,z,u) * ((1 / (1 / x)) * x)) / x
    ]]></literal>
    <justification jstring="[para(3288(a,1),7283(a,1,1,1))].">
      <j1 rule="para" parents="3288 7283"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      R(x,y * y,a(z,u,w)) = (a(z,u,w) * x) / a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,562,a(flip),b,7290,a),flip(a)].">
      <j1 rule="hyper" parents="65 562 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      R(x,y * y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,7197,a(flip),b,7322,a),flip(a)].">
      <j1 rule="hyper" parents="325 7197 7322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      R(x,y * y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(7323(a,1),53(a,2))].">
      <j1 rule="para" parents="7323 53"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      R(T(x,x * a(y,z,u)),x,a(y,z,u)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(836,a,7320,a)].">
      <j1 rule="hyper" parents="836 7320"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      ((x * x) * (y * a(z,u,w))) \ ((((x * x) * y) * v5) * a(z,u,w)) = L(v5,(x * x) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(33(a,1),7320(a,1,1))].">
      <j1 rule="para" parents="33 7320"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (x * ((y * v5) * a(z,u,w))) = L(L(v5,y,a(z,u,w)),y * a(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(7320(a,1),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7320 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,1601,a(flip),b,7224,a),flip(a)].">
      <j1 rule="hyper" parents="65 1601 7224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      a(x / y,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(288,a,7331,a),flip(a)].">
      <j1 rule="hyper" parents="288 7331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      L(K(x,y),z,y / z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,7333,a)].">
      <j1 rule="hyper" parents="54 7333"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      L(K(x,y * z),z,y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(11(a,1),7335(a,1,3))].">
      <j1 rule="para" parents="11 7335"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      K(L(x,y,z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6839,a(flip),b,7336,a)].">
      <j1 rule="hyper" parents="65 6839 7336"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(43,a,5883,a,b,7336,a),flip(a)].">
      <j1 rule="hyper" parents="43 5883 7336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      K(x,T(y \ 1,y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3406,a,b,7338,a)].">
      <j1 rule="hyper" parents="65 3406 7338"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3404,a(flip),b,7338,a),flip(a)].">
      <j1 rule="hyper" parents="65 3404 7338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = x * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(137,a,7338,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 7338 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      K(x,y \ ((y \ 1) \ z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      K(x,((y * y) \ z) \ u) = K(x,(z \ (y * y)) * u)
    ]]></literal>
    <justification jstring="[para(434(a,1),7338(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="434 7338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      K(x,L(y \ z,y,z) * u) = K(x,((1 / z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(700(a,2),7338(a,1,2,1))].">
      <j1 rule="para" parents="700 7338"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      K(x,K(y,T(z,u \ 1)) * (u \ 1)) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(3640(a,2),7338(a,1,2))].">
      <j1 rule="para" parents="3640 7338"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      K((x \ 1) \ y,z * u) = K(x * y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,6686,a,b,7341,a)].">
      <j1 rule="hyper" parents="325 6686 7341"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5357,a,b,7341,a)].">
      <j1 rule="hyper" parents="65 5357 7341"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      K(T(x,y),z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(3699,a,7348,a),flip(a)].">
      <j1 rule="hyper" parents="3699 7348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3816,a,b,7348,a)].">
      <j1 rule="hyper" parents="65 3816 7348"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,7348,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 7348 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      K(T(x,y),z * y) = 1 / K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2611,a,b,7350,a),flip(a)].">
      <j1 rule="hyper" parents="325 2611 7350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),7351(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 7351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      K(x,T(T(y * z,u),z)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(5143(a,1),7354(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5143 7354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7337(a,1),457(a,1,2))].">
      <j1 rule="para" parents="7337 457"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,7342,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 7342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3366,a,b,7357,a)].">
      <j1 rule="hyper" parents="65 3366 7357"/>
    </justification>
  </clause>

  <clause id="7359">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(85(a,1),7357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 7357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      T(x,y \ ((1 / y) \ z)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7358(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),7358(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 7358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      T(1 / x,x * y) = ((1 / x) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(381,a,7359,a),flip(a)].">
      <j1 rule="hyper" parents="381 7359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,7352,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 7352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7365">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7352(a,2),2140(a,1))].">
      <j1 rule="para" parents="7352 2140"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,3853,a,b,7364,a)].">
      <j1 rule="hyper" parents="65 3853 7364"/>
    </justification>
  </clause>

  <clause id="7367">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),7364(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      T(x,T(y * (z * u),y * z)) = T(x,L(u,z,y) * (y * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),7364(a,1,2,1))].">
      <j1 rule="para" parents="100 7364"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      T(x,y * K(z \ 1,y * z)) = T(x,T(y,y * z))
    ]]></literal>
    <justification jstring="[para(2280(a,1),7367(a,1,2))].">
      <j1 rule="para" parents="2280 7367"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,2611,a,b,7353,a(flip))].">
      <j1 rule="hyper" parents="38 2611 7353"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(3683,a,7370,a),flip(a)].">
      <j1 rule="hyper" parents="3683 7370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,7370,a(flip),b,3647,a)].">
      <j1 rule="hyper" parents="136 7370 3647"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),7370(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(7370(a,1),3106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7370 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(z * K(x,(z \ y) \ 1),T(u,y))
    ]]></literal>
    <justification jstring="[para(2058(a,2),7371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2058 7371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(2272(a,1),7374(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2272 7374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(3975(a,2),7374(a,1,1))].">
      <j1 rule="para" parents="3975 7374"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      L(T(1 / x,x * y) \ z,((1 / x) \ y) \ y,(1 / x) \ y) = y \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[para(7362(a,2),469(a,1,1,1))].">
      <j1 rule="para" parents="7362 469"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(3624,a,7366,a)].">
      <j1 rule="hyper" parents="3624 7366"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7371,a(flip),b,7379,a),flip(a)].">
      <j1 rule="hyper" parents="325 7371 7379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      K(T(x,y) * y,z) = z / T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2642,a(flip),b,7383,a),flip(a)].">
      <j1 rule="hyper" parents="325 2642 7383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7385">
    <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(7383(a,1),6687(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7383 6687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7381(a,1),2840(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7381 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(38,a,2642,a(flip),b,7384,a(flip))].">
      <j1 rule="hyper" parents="38 2642 7384"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,y * (z / y))
    ]]></literal>
    <justification jstring="[para(115(a,1),7387(a,1,2,1))].">
      <j1 rule="para" parents="115 7387"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7367,a(flip),b,7388,a),flip(a)].">
      <j1 rule="hyper" parents="65 7367 7388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      T(x / (y * (z / y)),T(z,y)) = (y * (z / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,7389,a),flip(a)].">
      <j1 rule="hyper" parents="376 7389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),7389(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 7389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      T(x,y * (T(z,u) / y)) = T(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),7389(a,2,2))].">
      <j1 rule="para" parents="23 7389"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      R(T(x / y,T(y * z,y)),y,(y * z) / y) = (T(y,z) * z) \ (x * ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(7389(a,1),3979(a,1,1))].">
      <j1 rule="para" parents="7389 3979"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(7391(a,1),7174(a,1))].">
      <j1 rule="para" parents="7391 7174"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(3853(a,2),7365(a,1))].">
      <j1 rule="para" parents="3853 7365"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7355(a,1),3683(a,1))].">
      <j1 rule="para" parents="7355 3683"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(3816(a,2),7397(a,1))].">
      <j1 rule="para" parents="3816 7397"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5357(a,1),7397(a,1))].">
      <j1 rule="para" parents="5357 7397"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(7179(a,1),7397(a,1,2))].">
      <j1 rule="para" parents="7179 7397"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(5143(a,1),7392(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5143 7392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(T(z,u),u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = w
    ]]></literal>
    <justification jstring="[para(3642(a,1),7396(a,1,1,2))].">
      <j1 rule="para" parents="3642 7396"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      K(x,y \ ((z * z) * u)) = K(x,(y \ (z * z)) * u)
    ]]></literal>
    <justification jstring="[para(554(a,1),7344(a,1,2))].">
      <j1 rule="para" parents="554 7344"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      K(x * y,(z \ 1) \ (z \ u)) = K((x \ 1) \ y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      T(x,y * K(z \ 1,y * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2988,a(flip),b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="325 2988 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      L(L(x \ 1,x,y * (z / y)) \ u,((y * (z / y)) * x) \ (y * (z / y)),(y * (z / y)) * x) = T((((y * (z / y)) * x) * u) / (y * (z / y)),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,736,a,b,7390,a)].">
      <j1 rule="hyper" parents="325 736 7390"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(u \ 1) \ (u \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),7404(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,u \ x,(u \ x) \ 1))) = K((((u \ x) \ 1) * (u \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6823,a(flip),b,7407,a),flip(a)].">
      <j1 rule="hyper" parents="65 6823 7407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / u,u))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6822,a(flip),b,7407,a),flip(a)].">
      <j1 rule="hyper" parents="65 6822 7407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / u,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(952(a,2),7409(a,1,2))].">
      <j1 rule="para" parents="952 7409"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),u \ x,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5251,a(flip),b,7411,a)].">
      <j1 rule="hyper" parents="65 5251 7411"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(2886,a,7356,a),flip(a)].">
      <j1 rule="hyper" parents="2886 7356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(195,a,7413,a(flip))].">
      <j1 rule="hyper" parents="195 7413"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      (L(x,y,z) * (x * u)) / T(x * L(x,y,z),u) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(249(a,1),7413(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="249 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      L(x,y,z) * K(z * y,x) = (z * (y * x)) / (z * y)
    ]]></literal>
    <justification jstring="[para(7413(a,2),2089(a,1,1))].">
      <j1 rule="para" parents="7413 2089"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      ((x * y) * z) / T(z * x,y) = K(x * y,z) * L(y,x,z)
    ]]></literal>
    <justification jstring="[para(7413(a,2),2495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7413 2495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      x \ T(x / (y \ 1),y) = (x * (y * y)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6715,a(flip),b,7416,a)].">
      <j1 rule="hyper" parents="65 6715 7416"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      x \ T(x / (y \ 1),y) = x / ((x * y) / (y * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,696,a(flip),b,7418,a),flip(a)].">
      <j1 rule="hyper" parents="325 696 7418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      x \ T(x / (y \ 1),y) = x / (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(570(a,1),7419(a,2,2))].">
      <j1 rule="para" parents="570 7419"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      x \ T(x / y,1 / y) = x / (x * ((1 / y) \ 1))
    ]]></literal>
    <justification jstring="[para(85(a,1),7420(a,1,2,1,2))].">
      <j1 rule="para" parents="85 7420"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      x \ (T(x / (y \ 1),y) * R(T(x / (y \ 1),y) \ x,z,u)) = (x / (x * (y \ 1))) \ R(x \ T(x / (y \ 1),y),z,u)
    ]]></literal>
    <justification jstring="[para(7420(a,1),1403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7420 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      x \ T(x / a(y,z,u),a(y,z,u) \ 1) = x / (x * ((a(y,z,u) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(7181(a,1),7420(a,1,2,1,2))].">
      <j1 rule="para" parents="7181 7420"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      x \ T(x / y,y \ 1) = x / (x * ((1 / y) \ 1))
    ]]></literal>
    <justification jstring="[para(2081(a,1),7421(a,1,2))].">
      <j1 rule="para" parents="2081 7421"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      x \ T(x / y,y \ 1) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(85(a,1),7424(a,2,2,2))].">
      <j1 rule="para" parents="85 7424"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      a(x * (y / (y * z)),u,w) = a(x * (y \ (y / z)),u,w)
    ]]></literal>
    <justification jstring="[para(7425(a,1),5113(a,1,1,2))].">
      <j1 rule="para" parents="7425 5113"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (u \ 1)) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(3812(a,1),7346(a,1,2,1))].">
      <j1 rule="para" parents="3812 7346"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      a(x * ((y * z) \ y),u,w) = a(x * (y \ (y / z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(3530,a,7427,a)].">
      <j1 rule="hyper" parents="3530 7427"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      a(x * ((y * z) \ y),u,w) = a(x * (y \ (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,5171,a(flip),b,7432,a),flip(a)].">
      <j1 rule="hyper" parents="325 5171 7432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      a(x * (T(y,T(z,u)) \ ((u * y) \ T(y,T(z,u)))),w,v5) = a(x * ((y * (u * T(y,z))) \ T(y,T(z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(4550(a,1),7433(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4550 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      x * ((y * (x * y)) / ((x * y) * (x * y))) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,704,a(flip),b,7296,a)].">
      <j1 rule="hyper" parents="65 704 7296"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      x * (y * ((x * y) \ 1)) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(570(a,1),7435(a,1,2))].">
      <j1 rule="para" parents="570 7435"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      (x * y) \ (a(x,y,x * y) \ 1) = L((x * y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,7436,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="132 7436 100"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,1312,a,b,7437,a)].">
      <j1 rule="hyper" parents="40 1312 7437"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      (x * y) * (a(x,y,x * y) \ 1) = L(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(148,a,7438,a)].">
      <j1 rule="hyper" parents="148 7438"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      a((x * y) * a(x,y,x * y),z,u) = a(L(x * y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7439(a,1),1890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7439 1890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      (x * (y * a(z * u,w,v5))) \ (a(z * u,w,v5) * (x * y)) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(2337(a,1),7263(a,2,3))].">
      <j1 rule="para" parents="2337 7263"/>
    </justification>
  </clause>

  <clause id="7442">
    <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(65,a,7220,a(flip),b,7269,a)].">
      <j1 rule="hyper" parents="65 7220 7269"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      K(x * L(x,y,z),L(x,y,z)) = a(L(x,y,z),x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2484,a,b,7294,a)].">
      <j1 rule="hyper" parents="65 2484 7294"/>
    </justification>
  </clause>

  <clause id="7444">
    <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(1249(a,1),7294(a,1,2))].">
      <j1 rule="para" parents="1249 7294"/>
    </justification>
  </clause>

  <clause id="7445">
    <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(1706(a,1),7295(a,1,1))].">
      <j1 rule="para" parents="1706 7295"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      (a(x,y,z) * ((u * u) * w)) \ v5 = (w * a(x,y,z)) \ ((u * u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,393,a(flip),b,7306,a),flip(a)].">
      <j1 rule="hyper" parents="325 393 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      (a(x,y,z) * ((u * u) * w)) * v5 = (u * u) * ((w * a(x,y,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(137,a,118,a(flip),b,7306,a)].">
      <j1 rule="hyper" parents="137 118 7306"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      a(L(x,y,z),z,y) * (z * (y * x)) = z * (y * R(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,413,a(flip),b,7307,a),flip(a)].">
      <j1 rule="hyper" parents="325 413 7307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      T(a(x,y,z) / u,u \ 1) = (1 / (1 / u)) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2083,a(flip),b,7309,a)].">
      <j1 rule="hyper" parents="65 2083 7309"/>
    </justification>
  </clause>

  <clause id="7450">
    <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(7180(a,1),7318(a,2,1))].">
      <j1 rule="para" parents="7180 7318"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      (x * (L(x,y,z) * u)) / T(x * L(x,y,z),u) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1249(a,1),7415(a,1,1))].">
      <j1 rule="para" parents="1249 7415"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      a(L(x,y,z),x,u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7298,a,7444,a),flip(a)].">
      <j1 rule="hyper" parents="7298 7444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      a(x \ y,L(x \ y,x,x),z) = a(x * y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1848,a(flip),b,7452,a),flip(a)].">
      <j1 rule="hyper" parents="65 1848 7452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      a(x,L(y,z,u),y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7298,a,7445,a),flip(a)].">
      <j1 rule="hyper" parents="7298 7445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      a(x,L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(7445(a,1),7298(a,1))].">
      <j1 rule="para" parents="7445 7298"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      (a(x,y,z) * ((u * u) * (w * v5))) \ ((u * u) * ((w * a(x,y,z)) * v5)) = a(a(x,y,z),(u * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(7447(a,1),121(a,1,2))].">
      <j1 rule="para" parents="7447 121"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (a(x,y,z) * u) = (a(x,y,z) * a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(520,a,7450,a),flip(a)].">
      <j1 rule="hyper" parents="520 7450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ 1) * u) = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(132,a,9,a(flip),b,7450,a),flip(a)].">
      <j1 rule="hyper" parents="132 9 7450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7459">
    <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(137,a,77,a(flip),b,7450,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 77 7450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      L(x,L(y,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7413,a,b,7451,a)].">
      <j1 rule="hyper" parents="65 7413 7451"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      L(x,y \ 1,L(y \ 1,z,u)) = L(x,L(y \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(1625,a,7460,a),flip(a)].">
      <j1 rule="hyper" parents="1625 7460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      L(x,y,L(y \ 1,z,u)) = L(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1514,a,b,7460,a)].">
      <j1 rule="hyper" parents="325 1514 7460"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),L(y \ R(y,z,u),y,u * z)) = L(x,a(y,z,u),y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2326(a,2),7460(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2326 7460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      L(x,L(y,z,u),y \ 1) = L(x,y,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a,b,7462,a)].">
      <j1 rule="hyper" parents="325 1499 7462"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      ((x \ 1) * L(x,y,z)) \ ((x \ 1) * (L(x,y,z) * u)) = L(u,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,18,a(flip),b,7464,a)].">
      <j1 rule="hyper" parents="65 18 7464"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),y) = L(x,y \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1514,a(flip),b,7461,a),flip(a)].">
      <j1 rule="hyper" parents="65 1514 7461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (((a(x,y,z) * u) / (a(x,y,z) \ 1)) * (w * (a(x,y,z) \ 1))) = L(T(w,a(x,y,z) \ 1),a(x,y,z) \ 1,(a(x,y,z) * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(7457(a,1),1557(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7457 1557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      a(x,y,z) \ L(u,a(x,y,z),a(x,y,z)) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,874,a(flip),b,7459,a)].">
      <j1 rule="hyper" parents="65 874 7459"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) * a(x,y,z) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(7208,a,7468,a)].">
      <j1 rule="hyper" parents="7208 7468"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      a(x,y,z) \ u != (a(x,y,z) \ 1) * w
    ]]></literal>
    <literal><![CDATA[
      L(w,a(x,y,z),a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(7468(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="7468 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      (x / (a(y,z,u) * w)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (x / (w * a(y,z,u))) * w = v5
    ]]></literal>
    <justification jstring="[para(7280(a,1),1637(a,1))].">
      <j1 rule="para" parents="7280 1637"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,7192,a(flip),b,7277,a),flip(a)].">
      <j1 rule="hyper" parents="325 7192 7277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((a(z,u,w) * x) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(z,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(7190(a,2),7278(a,1,2,1))].">
      <j1 rule="para" parents="7190 7278"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ (a(y,z,u) * (x * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,w,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(7190(a,2),7279(a,1,1,2))].">
      <j1 rule="para" parents="7190 7279"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      ((x * y) * z) / (x * ((y * (z * (u * u))) / (u * u))) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(704(a,1),7292(a,1,2))].">
      <j1 rule="para" parents="704 7292"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      x \ T(a(y,z,u) \ x,a(y,z,u) \ 1) = x / (x * ((a(y,z,u) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(7194(a,1),7423(a,1,2,1))].">
      <j1 rule="para" parents="7194 7423"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * ((z * (u * u)) / (u * u)))) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(704(a,1),7477(a,1,2,2))].">
      <j1 rule="para" parents="704 7477"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),7479(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 7479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7221,a,b,7480,a),flip(a)].">
      <j1 rule="hyper" parents="325 7221 7480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      a(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(7480(a,2),7298(a,1))].">
      <j1 rule="para" parents="7480 7298"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      a(x,y,z * (u * (w * w))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(34(a,1),7481(a,1,3))].">
      <j1 rule="para" parents="34 7481"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      a(x,y,z \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(221(a,1),7481(a,1,3)),flip(a)].">
      <j1 rule="para" parents="221 7481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(395(a,1),7481(a,1,3))].">
      <j1 rule="para" parents="395 7481"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      a(x,y,z \ (u * (w / (v5 * v5)))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(705(a,1),7481(a,1,3)),flip(a)].">
      <j1 rule="para" parents="705 7481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),u * z,w)) = a(x,y,(w * (u * z)) \ (w * u))
    ]]></literal>
    <justification jstring="[para(1064(a,1),7481(a,1,3))].">
      <j1 rule="para" parents="1064 7481"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      a(x,y,(z / (u \ 1)) / z) = a(x,y,(u * z) \ z)
    ]]></literal>
    <justification jstring="[para(5255(a,1),7481(a,1,3))].">
      <j1 rule="para" parents="5255 7481"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      a(x,y,((z * u) * z) * u) = a(x,y,a(z * u,z,u))
    ]]></literal>
    <justification jstring="[para(7223(a,1),7481(a,1,3))].">
      <j1 rule="para" parents="7223 7481"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(85(a,1),7484(a,1,3)),flip(a)].">
      <j1 rule="para" parents="85 7484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(2015(a,1),7484(a,1,3))].">
      <j1 rule="para" parents="2015 7484"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(7004(a,1),7484(a,1,3))].">
      <j1 rule="para" parents="7004 7484"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7484,a(flip),b,7485,a),flip(a)].">
      <j1 rule="hyper" parents="325 7484 7485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      a(x,y,z * (u * (z * u))) = a(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(14(a,2),7493(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14 7493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      a(x,y,z \ (z * u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(72(a,1),7493(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 7493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(221(a,1),7483(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="221 7483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1257(a,1),7496(a,1,3))].">
      <j1 rule="para" parents="1257 7496"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7491,a(flip),b,7497,a)].">
      <j1 rule="hyper" parents="65 7491 7497"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z)) = a(x,y,((1 / z) * u) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(649(a,1),7497(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="649 7497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      a(x,y,z * L(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(824(a,1),7497(a,1,3)),flip(a)].">
      <j1 rule="para" parents="824 7497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z)) = a(x,y,(z \ u) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(649(a,1),7498(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="649 7498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ 1)))) = a(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(570(a,1),7486(a,1,3,2,2))].">
      <j1 rule="para" parents="570 7486"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 / (v6 * v6))))) = a(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(704(a,1),7486(a,1,3,2,2))].">
      <j1 rule="para" parents="704 7486"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      (L(x \ 1,y,z) * x) \ ((x \ 1) * (L(x,y,z) * u)) = L(u,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1273(a,2),7465(a,1,1))].">
      <j1 rule="para" parents="1273 7465"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) * T(u,x)) = L(x \ 1,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(40,a,240,a,b,7504,a),flip(a)].">
      <j1 rule="hyper" parents="40 240 7504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      R(T(x / y,z * y),y,(y * z) / y) = (T(y,z) * z) \ (x * ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(7364(a,1),7393(a,1,1))].">
      <j1 rule="para" parents="7364 7393"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u * z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(7441(a,1),7279(a,1))].">
      <j1 rule="para" parents="7441 7279"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      L(T(1 / x,x * y) \ z,((1 / x) \ y) \ y,x \ y) = y \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5126,a(flip),b,7380,a)].">
      <j1 rule="hyper" parents="65 5126 7380"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),u \ x,(u \ x) \ 1)) = K((((u \ x) \ 1) * (u \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(952(a,2),7408(a,1,2))].">
      <j1 rule="para" parents="952 7408"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),L(y \ R(y,z,u),y,u * z)) = L(x,a(y,z,u),y * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1822,a(flip),b,7463,a),flip(a)].">
      <j1 rule="hyper" parents="325 1822 7463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),u \ x,u)) = K((((u \ x) \ 1) * (u \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6836,a(flip),b,7509,a)].">
      <j1 rule="hyper" parents="65 6836 7509"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7412,a(flip),b,7511,a),flip(a)].">
      <j1 rule="hyper" parents="65 7412 7511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5165,a(flip),b,7512,a)].">
      <j1 rule="hyper" parents="65 5165 7512"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      (1 / x) * (y \ T(y * x,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7514(a,1,1,2))].">
      <j1 rule="para" parents="9 7514"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = 1 / K(z * y,x)
    ]]></literal>
    <justification jstring="[para(7516(a,1),5207(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7516 5207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2611,a(flip),b,7517,a),flip(a)].">
      <j1 rule="hyper" parents="325 2611 7517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(7518(a,1),5939(a,1,2))].">
      <j1 rule="para" parents="7518 5939"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),7519(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5330,a,b,7520,a)].">
      <j1 rule="hyper" parents="65 5330 7520"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6682,a(flip),b,7521,a),flip(a)].">
      <j1 rule="hyper" parents="65 6682 7521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(82(a,1),7521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 7521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2700,a,b,7522,a)].">
      <j1 rule="hyper" parents="65 2700 7522"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),7522(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 7522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      (x * x) / (y * K(z,u)) = (x * x) * (K(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(201,a,7526,a(flip),b,394,a)].">
      <j1 rule="hyper" parents="201 7526 394"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,y) = x \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),7526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 7526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      (x \ K(y,z)) \ (K(y,z) * u) = T(x \ 1,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7528(a,1),675(a,1,1))].">
      <j1 rule="para" parents="7528 675"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(7528(a,1),2324(a,1,3))].">
      <j1 rule="para" parents="7528 2324"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(7528(a,1),2849(a,1,1))].">
      <j1 rule="para" parents="7528 2849"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,L(L(x,z,u),w,v5) / y)
    ]]></literal>
    <justification jstring="[para(7524(a,2),3188(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7524 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a(flip),b,7537,a),flip(a)].">
      <j1 rule="hyper" parents="325 1499 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      K(x,y) / L(z \ u,z,u) = (K(x,y) / u) * z
    ]]></literal>
    <justification jstring="[para(7541(a,1),1560(a,1,2))].">
      <j1 rule="para" parents="7541 1560"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      K(x,y) / L(a(z,z \ 1,u),L(u,z \ 1,z),u) = (K(x,y) / u) * L(u,z \ 1,z)
    ]]></literal>
    <justification jstring="[para(719(a,1),7542(a,1,2,1))].">
      <j1 rule="para" parents="719 7542"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),a(y,z,u)) = L(x,a(y,z,u),y * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2326(a,2),7510(a,1,3))].">
      <j1 rule="para" parents="2326 7510"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      R(T(a(x,y,z),T(u * w,(u * a(x,y,z)) * w)),u,w) = (u * w) \ ((u * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,27,a,b,7313,a)].">
      <j1 rule="hyper" parents="65 27 7313"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      (a(x,y,z) * ((1 / (1 / u)) * u)) / u = (((1 / u) \ u) * a(x,y,z)) / u
    ]]></literal>
    <justification jstring="[para(281(a,1),7321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="281 7321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      (a(x,y,z) * ((1 / (1 / u)) * u)) / u = ((1 / u) \ u) * (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(325,a,4072,a(flip),b,7546,a),flip(a)].">
      <j1 rule="hyper" parents="325 4072 7546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(7186(a,1),7545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7186 7545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[para(287(a,1),7297(a,1,1))].">
      <j1 rule="para" parents="287 7297"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / (z * (T(K(x,y),z) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[para(2271(a,1),7550(a,1,2,2,1))].">
      <j1 rule="para" parents="2271 7550"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,666,a(flip),b,7551,a)].">
      <j1 rule="hyper" parents="65 666 7551"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,T(K(x,y),z),u)
    ]]></literal>
    <justification jstring="[para(2271(a,1),7552(a,2,2))].">
      <j1 rule="para" parents="2271 7552"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,5306,a(flip),b,7553,a),flip(a)].">
      <j1 rule="hyper" parents="325 5306 7553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      K(x,y) * T((z * u) / (z * (K(x,y) * u)),z) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6396(a,1),7554(a,1,2))].">
      <j1 rule="para" parents="6396 7554"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      K(x,y) * T(K(y,z / ((z * (x \ u)) / u)),z) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[para(3957(a,2),7555(a,1,2,1))].">
      <j1 rule="para" parents="3957 7555"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      K(x,y) * K(y,((z * (x \ u)) / u) \ z) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[para(3124(a,1),7556(a,1,2))].">
      <j1 rule="para" parents="3124 7556"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      ((x * x) * (y * a(z,u,w))) \ (((x * x) * (y * v5)) * a(z,u,w)) = L(v5,(x * x) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(33(a,1),7327(a,1,2,1))].">
      <j1 rule="para" parents="33 7327"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      ((x * x) * (y * a(z,u,w))) \ ((x * x) * ((y * v5) * a(z,u,w))) = L(v5,(x * x) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(33(a,1),7558(a,1,2))].">
      <j1 rule="para" parents="33 7558"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y * a(z,u,w),v5 * v5) = L(x,(v5 * v5) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7328,a(flip),b,7559,a)].">
      <j1 rule="hyper" parents="65 7328 7559"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      L(x,(y * y) * z,a(u,w,v5)) = L(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(461,a,7560,a),flip(a)].">
      <j1 rule="hyper" parents="461 7560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) \ ((v5 * v5) \ ((v5 * v5) * ((x * a(z,u,w)) * y))) = a(a(z,u,w),(v5 * v5) * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7446,a(flip),b,7456,a)].">
      <j1 rule="hyper" parents="65 7446 7456"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,y \ L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,3188,a(flip),b,7540,a),flip(a)].">
      <j1 rule="hyper" parents="325 3188 7540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      a(a(x,y,z),(u * u) * w,v5) = ((w * v5) * a(x,y,z)) \ ((w * a(x,y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),7563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 7563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      a(a(x,y,z),(u * u) * w,v5) = a(a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,7442,a(flip),b,7565,a),flip(a)].">
      <j1 rule="hyper" parents="325 7442 7565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      a(a(x,y,z),((u * u) \ w) * v5,v6) = a(a(x,y,z),w * v5,v6)
    ]]></literal>
    <justification jstring="[para(119(a,1),7566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="119 7566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      a(a(x,y,z),(1 / u) * w,v5) = a(a(x,y,z),u * w,v5)
    ]]></literal>
    <justification jstring="[para(273(a,1),7568(a,1,2,1))].">
      <j1 rule="para" parents="273 7568"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      a(a(x,y,z),(u \ 1) * w,v5) = a(a(x,y,z),u * w,v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),7569(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 7569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      K(x,(1 / (y \ L(T(L(x,z,u),w),v5,v6))) \ K(w,L(L(x,z,u),v5,v6))) = K(x,y \ L(L(x,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),7564(a,1,2,1,2,2))].">
      <j1 rule="para" parents="25 7564"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),7571(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="25 7571"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ 1) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,6407,a(flip),b,7572,a)].">
      <j1 rule="hyper" parents="65 6407 7572"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      K(x,y \ L(L(T(x,z),u,w),v5,v6)) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(85(a,1),7573(a,1,2))].">
      <j1 rule="para" parents="85 7573"/>
    </justification>
  </clause>

  <clause id="7576">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(x,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,6965,a,b,7575,a)].">
      <j1 rule="hyper" parents="65 6965 7575"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,6908,a(flip),b,7576,a),flip(a)].">
      <j1 rule="hyper" parents="65 6908 7576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      K(x,(y \ 1) \ L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7579(a,1),5603(a,1,1))].">
      <j1 rule="para" parents="7579 5603"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7341(a,1),7581(a,1,1))].">
      <j1 rule="para" parents="7341 7581"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) * (K(y,x) * L(x,z,u)) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4518(a,1),7582(a,1,2))].">
      <j1 rule="para" parents="4518 7582"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      L(x,y,z) * (K(x,u * L(x,y,z)) * K(u,x)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(7039,a,7584,a)].">
      <j1 rule="hyper" parents="7039 7584"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      L(x,y,z) * (K(u,x) * K(x,u * L(x,y,z))) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(3086(a,1),7585(a,1,2))].">
      <j1 rule="para" parents="3086 7585"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      L(x,y,z) * (a(x,u,L(x,y,z)) \ 1) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(6370(a,1),7586(a,1,2))].">
      <j1 rule="para" parents="6370 7586"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,x),y,z) = a(x,u,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(140,a,7587,a)].">
      <j1 rule="hyper" parents="140 7587"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      x * a(L(y,z,u),w,L(y,z,u)) = (a(y,w,L(y,z,u)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(7588(a,1),7069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7588 7069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,7589,a,b,7205,a(flip))].">
      <j1 rule="hyper" parents="130 7589 7205"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,6809,a(flip),b,7590,a),flip(a)].">
      <j1 rule="hyper" parents="325 6809 7590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6863,a(flip),b,7591,a)].">
      <j1 rule="hyper" parents="65 6863 7591"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6347,a,7593,a)].">
      <j1 rule="hyper" parents="6347 7593"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = L(a(x,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,6261,a,b,7593,a)].">
      <j1 rule="hyper" parents="325 6261 7593"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,7593,a(flip),b,4391,a(flip))].">
      <j1 rule="hyper" parents="137 7593 4391"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(136,a,7593,a(flip),b,7310,a)].">
      <j1 rule="hyper" parents="136 7593 7310"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      (x \ 1) * a(y,z,y) = x \ a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,7593,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 7593 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(7593(a,1),6774(a,1,1))].">
      <j1 rule="para" parents="7593 6774"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(1583(a,1),7594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1583 7594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(1588(a,1),7594(a,1,2))].">
      <j1 rule="para" parents="1588 7594"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      a(x,T(y,z),x) = K(x * y,T(T(x,u),w)) * K(x,T(T(y,u),w))
    ]]></literal>
    <justification jstring="[hyper(325,a,6770,a,b,7603,a),flip(a)].">
      <j1 rule="hyper" parents="325 6770 7603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      L(a(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(7597(a,1),494(a,1)),flip(b)].">
      <j1 rule="para" parents="7597 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      a(x,y,x) * ((z \ 1) * u) = (z \ a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(7600(a,1),6268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7600 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7617">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(547,a,7598,a)].">
      <j1 rule="hyper" parents="547 7598"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(489,a,7598,a)].">
      <j1 rule="hyper" parents="489 7598"/>
    </justification>
  </clause>

  <clause id="7619">
    <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(7598(a,1),488(a,1,1))].">
      <j1 rule="para" parents="7598 488"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,1005,a,b,7618,a)].">
      <j1 rule="hyper" parents="65 1005 7618"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(7618(a,1),53(a,1)),flip(a)].">
      <j1 rule="para" parents="7618 53"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      a(x,y,x) * (z \ (a(x,y,x) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(549,a,7599,a),flip(a)].">
      <j1 rule="hyper" parents="549 7599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = a(y,z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(548,a,7599,a)].">
      <j1 rule="hyper" parents="548 7599"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,156,a(flip),b,7599,a)].">
      <j1 rule="hyper" parents="132 156 7599"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6268,a,b,7599,a)].">
      <j1 rule="hyper" parents="65 6268 7599"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = (x * u) \ (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(7599(a,1),6213(a,1,1))].">
      <j1 rule="para" parents="7599 6213"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(6184(a,2),7617(a,1,2))].">
      <j1 rule="para" parents="6184 7617"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(7598(a,1),7617(a,1,2))].">
      <j1 rule="para" parents="7598 7617"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      R(x,a(y,z,y),u) = x
    ]]></literal>
    <justification jstring="[hyper(1062,a,7627,a)].">
      <j1 rule="hyper" parents="1062 7627"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      (x / y) / a(z,u,z) = x / (a(z,u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(539,a,7627,a),flip(a)].">
      <j1 rule="hyper" parents="539 7627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      (x * a(y,z,y)) * (a(y,z,y) \ u) = x * u
    ]]></literal>
    <justification jstring="[hyper(325,a,156,a(flip),b,7627,a),flip(a)].">
      <j1 rule="hyper" parents="325 156 7627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = a(y,z,y) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,78,a(flip),b,7627,a)].">
      <j1 rule="hyper" parents="132 78 7627"/>
    </justification>
  </clause>

  <clause id="7636">
    <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(7627(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7627 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      (x / a(y,z,y)) * u = x * (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(136,a,7631,a(flip),b,496,a(flip))].">
      <j1 rule="hyper" parents="136 7631 496"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6211,a,b,7629,a)].">
      <j1 rule="hyper" parents="65 6211 7629"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) * w)) = (x \ (y * w)) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(7599(a,1),7629(a,1,2))].">
      <j1 rule="para" parents="7599 7629"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(6185(a,1),7634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6185 7634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      (a(x,y,x) / z) * (a(x,y,x) \ u) = (1 / z) * u
    ]]></literal>
    <justification jstring="[para(6235(a,1),7634(a,1,1))].">
      <j1 rule="para" parents="6235 7634"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      (x \ a(y,z,y)) * (a(y,z,y) \ u) = (x \ 1) * u
    ]]></literal>
    <justification jstring="[para(7600(a,1),7634(a,1,1))].">
      <j1 rule="para" parents="7600 7634"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u)
    ]]></literal>
    <justification jstring="[hyper(7257,a,7635,a)].">
      <j1 rule="hyper" parents="7257 7635"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      a(x,y,x) \ ((z \ 1) \ u) = (z \ a(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[para(7600(a,1),7635(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7600 7635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7646">
    <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(7637(a,1),6297(a,1,1))].">
      <j1 rule="para" parents="7637 6297"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      (x * (a(y,z,y) \ u)) \ w = ((x * u) \ w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(7626(a,1),7639(a,1,1))].">
      <j1 rule="para" parents="7626 7639"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      (K(a(x,y,x),z) * (a(x,y,x) \ ((a(x,y,x) / u) * w))) * v5 = ((T(a(x,y,x),z) / u) * w) * (a(x,y,x) \ v5)
    ]]></literal>
    <justification jstring="[para(4589(a,2),7641(a,1,1))].">
      <j1 rule="para" parents="4589 7641"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      a(x,y,x) * ((z \ 1) * (z \ (u * w))) = ((z \ a(x,y,x)) * (z \ u)) * w
    ]]></literal>
    <justification jstring="[para(7615(a,1),6264(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7615 6264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,u))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(18(a,2),7630(a,2,1))].">
      <j1 rule="para" parents="18 7630"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      ((x * (a(y,z,y) * u)) \ (x * (u * w))) * a(y,z,y) = L(w,a(y,z,y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6217,a(flip),b,7640,a),flip(a)].">
      <j1 rule="hyper" parents="65 6217 7640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      ((x * y) \ z) * a(x,u,x) = (L(x,u,x) * y) \ z
    ]]></literal>
    <justification jstring="[para(6247(a,1),7647(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6247 7647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,7604,a(flip),b,7601,a),flip(a)].">
      <j1 rule="hyper" parents="325 7604 7601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),7659(a,2,2))].">
      <j1 rule="para" parents="18 7659"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7610,a,7661,a),flip(a)].">
      <j1 rule="hyper" parents="7610 7661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,6180,a,b,7662,a),flip(a)].">
      <j1 rule="hyper" parents="325 6180 7662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) = a(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(1907(a,2),7662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1907 7662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(7662(a,1),6238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7662 6238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,6180,a,b,7664,a(flip))].">
      <j1 rule="hyper" parents="40 6180 7664"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),R(u,L(x,y,z),u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7669(a,1),7051(a,1,2,1))].">
      <j1 rule="para" parents="7669 7051"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,6238,a(flip),b,7668,a),flip(a)].">
      <j1 rule="hyper" parents="325 6238 7668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1428(a,2),7671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1428 7671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,7082,a(flip),b,7667,a),flip(a)].">
      <j1 rule="hyper" parents="65 7082 7667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,7673,a)].">
      <j1 rule="hyper" parents="54 7673"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(5316,a,7675,a)].">
      <j1 rule="hyper" parents="5316 7675"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      ((x \ 1) * a(y,z,u)) * x = (x \ 1) * (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(7675(a,1),1502(a,1,2))].">
      <j1 rule="para" parents="7675 1502"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(7675(a,1),4812(a,1,1,1))].">
      <j1 rule="para" parents="7675 4812"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      K(x * a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,7676,a(flip),b,7200,a),flip(a)].">
      <j1 rule="hyper" parents="131 7676 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,7679,a,b,2613,a),flip(a)].">
      <j1 rule="hyper" parents="133 7679 2613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      T(x,x * a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,7680,a)].">
      <j1 rule="hyper" parents="58 7680"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      R(x,x,a(y,z,u)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7681(a,1),7326(a,1,1))].">
      <j1 rule="para" parents="7681 7326"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      T(a(x,y,z) * u,u) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(7190(a,2),7678(a,1,1))].">
      <j1 rule="para" parents="7190 7678"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      (a(x,y,z) * u) * u = u * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(137,a,7683,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 7683 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = K(x * y,T(T(x,u),z))
    ]]></literal>
    <justification jstring="[hyper(6445,a,7605,a)].">
      <j1 rule="hyper" parents="6445 7605"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = T(K(x * y,T(x,u)),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3111,a(flip),b,7685,a),flip(a)].">
      <j1 rule="hyper" parents="325 3111 7685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      T(K(x * y,x) * K(x,K(y,z)),u) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[para(3719(a,2),7686(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3719 7686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      T(K(x * y,y) * K(y,K(x,z)),u) = K(y * T(x,u),T(y,z))
    ]]></literal>
    <justification jstring="[para(4651(a,2),7688(a,1,1,1))].">
      <j1 rule="para" parents="4651 7688"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(y * x,T(x,u)) = K(x * T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,6986,a,b,7689,a)].">
      <j1 rule="hyper" parents="65 6986 7689"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(7598(a,1),7656(a,1,2,2))].">
      <j1 rule="para" parents="7598 7656"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(456,a,7691,a)].">
      <j1 rule="hyper" parents="456 7691"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      L(a(x,y,x) * z,u,w) = a(x,y,x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(37,a,1773,a(flip),b,7692,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 1773 7692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * a(x,y,x) = L(z,u,w)
    ]]></literal>
    <justification jstring="[para(6185(a,1),7692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6185 7692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      a(x,y,x) * L(x,z,u) = L(R(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6196(a,1),7693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6196 7693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      x * L(a(x,y,x) * z,u,w) = R(x,y,x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(7693(a,2),6277(a,1,2))].">
      <j1 rule="para" parents="7693 6277"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      R(x,y,x) * (x \ L(x,z,u)) = L(R(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6274,a,b,7695,a)].">
      <j1 rule="hyper" parents="65 6274 7695"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5471,a,b,7697,a)].">
      <j1 rule="hyper" parents="36 5471 7697"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7071,a,b,7698,a)].">
      <j1 rule="hyper" parents="65 7071 7698"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      a(x,y,x \ L(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,7698,a)].">
      <j1 rule="hyper" parents="55 7698"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      x * (T(y,x) * (x \ L(x,z,u))) = (y * x) * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,7698,a(flip),b,239,a),flip(a)].">
      <j1 rule="hyper" parents="137 7698 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      (x * y) * (x \ L(x,z,u)) = x * (y * (x \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(137,a,7698,a(flip),b,4391,a(flip))].">
      <j1 rule="hyper" parents="137 7698 4391"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      a(x,y,x * L(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,7498,a(flip),b,7700,a)].">
      <j1 rule="hyper" parents="65 7498 7700"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      L(x * L(x,y,z),u,x) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,7704,a)].">
      <j1 rule="hyper" parents="54 7704"/>
    </justification>
  </clause>

  <clause id="7706">
    <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(7705(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7705 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      x * L(y \ (a(x,z,x) * u),w,v5) = R(x,z,x) * L(y \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(7625(a,2),7696(a,1,2,1))].">
      <j1 rule="para" parents="7625 7696"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      x \ (y * (x \ L(x,z,u))) = (x \ y) * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(547,a,7702,a)].">
      <j1 rule="hyper" parents="547 7702"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      R(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(489,a,7702,a)].">
      <j1 rule="hyper" parents="489 7702"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      R(x,y,x * L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,1039,a(flip),b,7710,a)].">
      <j1 rule="hyper" parents="65 1039 7710"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      R(R(x,y,z),u,x * L(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7711(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7711 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ L(x,u,w)) = L(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1318,a(flip),b,7709,a),flip(a)].">
      <j1 rule="hyper" parents="65 1318 7709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      a(x,y,L(x * L(x,z,u),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,7706,a)].">
      <j1 rule="hyper" parents="55 7706"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      K(x * T(y,z),x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,3865,a,b,7690,a)].">
      <j1 rule="hyper" parents="36 3865 7690"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      1 / (x \ K(y * x,T(x,z))) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(7716(a,1),2626(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7716 2626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3151,a,7717,a)].">
      <j1 rule="hyper" parents="3151 7717"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4913,a(flip),b,7718,a)].">
      <j1 rule="hyper" parents="65 4913 7718"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(y * (y \ x),z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7719(a,2),5621(a,1,2))].">
      <j1 rule="para" parents="7719 5621"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      R(x,y,x) * L(R(x,y,x) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6273(a,1),7708(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6273 7708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      T(x * y,x) * L(T(x * y,x) \ z,u,w) = y * (x * L(x \ (y \ z),u,w))
    ]]></literal>
    <justification jstring="[para(7721(a,1),7043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7721 7043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x \ L(x,y,z)) = L(x,y,z) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2018,a,b,7714,a)].">
      <j1 rule="hyper" parents="65 2018 7714"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * L(z \ 1,u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(7714(a,1),1487(a,1,3,1))].">
      <j1 rule="para" parents="7714 1487"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      a((L(x,y,z) * L(x \ 1,y,z)) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(7714(a,1),1838(a,1,1,1))].">
      <j1 rule="para" parents="7714 1838"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (L(x,y,z) \ x)) * u = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7714(a,1),7019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7714 7019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(x,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7720(a,1,2,2,1))].">
      <j1 rule="para" parents="10 7720"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      x * K(T(x,y) / y,z) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5283,a(flip),b,7727,a)].">
      <j1 rule="hyper" parents="65 5283 7727"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2164,a(flip),b,7728,a),flip(a)].">
      <j1 rule="hyper" parents="36 2164 7728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7729(a,1),5337(a,2,2))].">
      <j1 rule="para" parents="7729 5337"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(7730(a,1),6352(a,1,1,2))].">
      <j1 rule="para" parents="7730 6352"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      x / ((L(y,z,u) \ y) * (L(y,z,u) \ y)) = x * (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(7723(a,1),7003(a,2,2))].">
      <j1 rule="para" parents="7723 7003"/>
    </justification>
  </clause>

  <clause id="7733">
    <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),7731(a,1,1))].">
      <j1 rule="para" parents="9 7731"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(3661,a,7733,a)].">
      <j1 rule="hyper" parents="3661 7733"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(85(a,1),7734(a,1,2,1))].">
      <j1 rule="para" parents="85 7734"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5410,a,7736,a)].">
      <j1 rule="hyper" parents="5410 7736"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      T(x,x * K(y,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7736(a,1),601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7736 601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      (x * (x * K(y,z))) / x = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(275,a,7737,a)].">
      <j1 rule="hyper" parents="275 7737"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      K(x,y) * (z * z) = z * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,7737,a(flip),b,623,a),flip(a)].">
      <j1 rule="hyper" parents="137 7737 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      T(x,K(y,z) * T(x,u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4734,a,b,7738,a)].">
      <j1 rule="hyper" parents="65 4734 7738"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      ((x \ a(y,z,y)) * (x \ u)) * w = (x \ a(y,z,y)) * (x \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7615,a(flip),b,7649,a),flip(a)].">
      <j1 rule="hyper" parents="65 7615 7649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      ((x * y) \ (a(z,u,z) \ (x * (y * w)))) * a(z,u,z) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(7628(a,1),7657(a,1,1))].">
      <j1 rule="para" parents="7628 7657"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      T((x * y) * L((x * y) \ x,z,u),x) = y * (x * L(x \ (y \ x),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,5388,a(flip),b,7722,a)].">
      <j1 rule="hyper" parents="65 5388 7722"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = y * (x * L(x \ (y \ x),z,u))
    ]]></literal>
    <justification jstring="[para(907(a,1),7744(a,1,1))].">
      <j1 rule="para" parents="907 7744"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,1433,a(flip),b,7746,a),flip(a)].">
      <j1 rule="hyper" parents="325 1433 7746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      T(x * ((1 / y) * L(y,z,u)),x) = ((1 / y) * L((1 / y) \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(85(a,1),7747(a,1,1,2,2,1))].">
      <j1 rule="para" parents="85 7747"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),x) = ((1 / y) * L((1 / y) \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1757(a,1),7748(a,1,1,2))].">
      <j1 rule="para" parents="1757 7748"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),x) = ((1 / y) * L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(85(a,1),7749(a,2,1,2,1))].">
      <j1 rule="para" parents="85 7749"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),x) = (y \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1757(a,1),7750(a,2,1))].">
      <j1 rule="para" parents="1757 7750"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,4773,a,b,7751,a(flip))].">
      <j1 rule="hyper" parents="36 4773 7751"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      ((((x \ L(x,y,z)) * (u * u)) / ((x \ L(x,y,z)) * u)) * (x \ L(x,y,z))) * u = (x \ L(x,y,z)) * (u * u)
    ]]></literal>
    <justification jstring="[para(7752(a,1),1282(a,2,2,2))].">
      <j1 rule="para" parents="7752 1282"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ u) = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,2025,a(flip),b,7726,a)].">
      <j1 rule="hyper" parents="65 2025 7726"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      x / (y * (L(y,z,u) \ (L(y,z,u) \ y))) = x * (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(7022(a,1),7732(a,1,2))].">
      <j1 rule="para" parents="7022 7732"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      ((x * y) \ (x * (a(z,u,z) \ (y * w)))) * a(z,u,z) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(7626(a,1),7743(a,1,1,2))].">
      <j1 rule="para" parents="7626 7743"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (a(z,u,z) \ w)))) * a(z,u,z) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(7626(a,1),7756(a,1,1,2,2))].">
      <j1 rule="para" parents="7626 7756"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * a(x,y,x) = L(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),7757(a,1,1))].">
      <j1 rule="para" parents="18 7757"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7694,a(flip),b,7758,a),flip(a)].">
      <j1 rule="hyper" parents="65 7694 7758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      L(x,y * a(z,u,z),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(6184(a,1),7759(a,1,2))].">
      <j1 rule="para" parents="6184 7759"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      L(x,y \ (a(z,u,z) \ w),v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(7624(a,1),7759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7624 7759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      L(x,(y \ a(z,u,z)) * w,v5) = L(x,(y \ 1) * w,v5)
    ]]></literal>
    <justification jstring="[para(7615(a,1),7759(a,1,2))].">
      <j1 rule="para" parents="7615 7759"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      L(x,y \ (z * (a(u,w,u) \ v5)),v6) = L(x,y \ (z * v5),v6)
    ]]></literal>
    <justification jstring="[para(7626(a,1),7763(a,1,2,2))].">
      <j1 rule="para" parents="7626 7763"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      L(x,y \ ((z \ a(u,w,u)) \ v5),v6) = L(x,y \ ((z \ 1) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(7645(a,1),7763(a,1,2,2))].">
      <j1 rule="para" parents="7645 7763"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      L(x,y \ ((z \ a(u,w,u)) * v5),v6) = L(x,y \ ((z \ 1) * v5),v6)
    ]]></literal>
    <justification jstring="[para(7643(a,1),7766(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7643 7766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      L(x,y \ (T(z,z \ a(u,w,u)) \ v5),v6) = L(x,y \ (((z \ a(u,w,u)) \ 1) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(114(a,2),7767(a,1,2,2,1))].">
      <j1 rule="para" parents="114 7767"/>
    </justification>
  </clause>

  <clause id="7770">
    <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(7627(a,1),7636(a,1,2,1))].">
      <j1 rule="para" parents="7627 7636"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(6263,a,7770,a),flip(a)].">
      <j1 rule="hyper" parents="6263 7770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      a(x / a(y,z,y),a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),7771(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6899,a(flip),b,7772,a)].">
      <j1 rule="hyper" parents="65 6899 7772"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(6196(a,1),7773(a,1,2))].">
      <j1 rule="para" parents="6196 7773"/>
    </justification>
  </clause>

  <clause id="7776">
    <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(7598(a,1),7619(a,1,2))].">
      <j1 rule="para" parents="7598 7619"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),R(u,x,u) * x) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7669(a,1),7670(a,1,2,2,1))].">
      <j1 rule="para" parents="7669 7670"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),x * R(u,x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4675(a,2),7777(a,1,2))].">
      <j1 rule="para" parents="4675 7777"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),T(u * x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4773(a,1),7779(a,1,2,2))].">
      <j1 rule="para" parents="4773 7779"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),x * u) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7364(a,1),7781(a,1,2))].">
      <j1 rule="para" parents="7364 7781"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(755(a,1),7782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="755 7782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6725,a(flip),b,7783,a)].">
      <j1 rule="hyper" parents="65 6725 7783"/>
    </justification>
  </clause>

  <clause id="7785">
    <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(132,a,7784,a(flip),b,2094,a(flip))].">
      <j1 rule="hyper" parents="132 7784 2094"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(6176,a,7785,a),flip(a)].">
      <j1 rule="hyper" parents="6176 7785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,6833,a(flip),b,7786,a),flip(a)].">
      <j1 rule="hyper" parents="325 6833 7786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <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),7787(a,1,1))].">
      <j1 rule="para" parents="12 7787"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6011,a(flip),b,7788,a)].">
      <j1 rule="hyper" parents="65 6011 7788"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(6804(a,1),7789(a,2,3))].">
      <j1 rule="para" parents="6804 7789"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,6885,a(flip),b,7790,a),flip(a)].">
      <j1 rule="hyper" parents="325 6885 7790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,6633,a(flip),b,7791,a)].">
      <j1 rule="hyper" parents="65 6633 7791"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      ((x * (L(y,z,u) \ y)) / ((x * (L(y,z,u) \ y)) / x)) \ L(x,x \ (x * (L(y,z,u) \ y)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,4998,a(flip),b,7793,a)].">
      <j1 rule="hyper" parents="65 4998 7793"/>
    </justification>
  </clause>

  <clause id="7795">
    <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),7793(a,1,2))].">
      <j1 rule="para" parents="12 7793"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(7793(a,1),2659(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7793 2659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,6059,a(flip),b,7796,a),flip(a)].">
      <j1 rule="hyper" parents="325 6059 7796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = a(x,y,a(w,u,K(z,v5)))
    ]]></literal>
    <justification jstring="[para(7797(a,1),6887(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7797 6887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7799">
    <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(7798(a,1),6041(a,1,2))].">
      <j1 rule="para" parents="7798 6041"/>
    </justification>
  </clause>

  <clause id="7800">
    <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(65,a,2461,a(flip),b,7795,a)].">
      <j1 rule="hyper" parents="65 2461 7795"/>
    </justification>
  </clause>

  <clause id="7801">
    <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(65,a,6638,a(flip),b,7800,a)].">
      <j1 rule="hyper" parents="65 6638 7800"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(6806(a,1),7801(a,2,3))].">
      <j1 rule="para" parents="6806 7801"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(85(a,1),7802(a,2,3,1))].">
      <j1 rule="para" parents="85 7802"/>
    </justification>
  </clause>

  <clause id="7806">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(7803(a,1),2659(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7803 2659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,6059,a(flip),b,7806,a),flip(a)].">
      <j1 rule="hyper" parents="325 6059 7806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7809">
    <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(7807(a,1),6889(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7807 6889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7810">
    <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(7809(a,1),6835(a,1,1))].">
      <j1 rule="para" parents="7809 6835"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(6101(a,1),7799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6101 7799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,7185,a(flip),b,7811,a),flip(a)].">
      <j1 rule="hyper" parents="325 7185 7811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,7813,a,b,2613,a),flip(a)].">
      <j1 rule="hyper" parents="133 7813 2613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,7816,a)].">
      <j1 rule="hyper" parents="58 7816"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      (L(x,y,z) \ x) * u = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(1998,a,7817,a),flip(a)].">
      <j1 rule="hyper" parents="1998 7817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) = (L(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,7817,a),flip(a)].">
      <j1 rule="hyper" parents="376 7817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      T(x,a(y,z,u)) = T(x,L(w,v5,v6) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,7179,a,b,7817,a)].">
      <j1 rule="hyper" parents="325 7179 7817"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      (x * (y * (L(z,u,w) \ z))) / (x * y) = L(L(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,7817,a(flip),b,7414,a)].">
      <j1 rule="hyper" parents="201 7817 7414"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u / ((L(x,y,z) \ x) \ 1)) = u * ((L(x,y,z) \ x) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(137,a,7817,a(flip),b,565,a(flip))].">
      <j1 rule="hyper" parents="137 7817 565"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      (L(y,z,u) \ y) \ x = w
    ]]></literal>
    <justification jstring="[para(7817(a,1),376(a,1))].">
      <j1 rule="para" parents="7817 376"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = (L(x,y,z) \ x) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,4168,a,b,7818,a)].">
      <j1 rule="hyper" parents="325 4168 7818"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      (x * x) * (1 / (L(y,z,u) \ y)) = (L(y,z,u) \ y) \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,402,a,b,7819,a)].">
      <j1 rule="hyper" parents="65 402 7819"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(x,u,w) = L(x,u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4389,a(flip),b,7819,a),flip(a)].">
      <j1 rule="hyper" parents="65 4389 7819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (u * u) = (u * u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2016(a,1),7827(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2016 7827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      (L(L(x,y,z) \ x,u,w) * w) * u = w * (u * R(L(x,y,z) \ x,w,u))
    ]]></literal>
    <justification jstring="[para(7822(a,1),1282(a,1,1,1))].">
      <j1 rule="para" parents="7822 1282"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / (x * w) = L(L(y,z,u) \ y,w,x)
    ]]></literal>
    <justification jstring="[para(7818(a,2),7822(a,1,1,2))].">
      <j1 rule="para" parents="7818 7822"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * L(y,z,u))) / (x * L(y,z,u)) = (x * L(y,z,u)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,102,a(flip),b,7831,a),flip(a)].">
      <j1 rule="hyper" parents="325 102 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      (x * y) / (x * L(y,z,u)) = (x * L(y,z,u)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1774(a,1),7832(a,1,1,2))].">
      <j1 rule="para" parents="1774 7832"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      (x * T(y,x)) / (x * L(T(y,x),z,u)) = (x * L(T(y,x),z,u)) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,232,a(flip),b,7833,a),flip(a)].">
      <j1 rule="hyper" parents="325 232 7833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      (x * y) / (y * L(T(x,y),z,u)) = (y * L(T(x,y),z,u)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7834(a,1,1))].">
      <j1 rule="para" parents="113 7834"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      (x * L(T(y,x),z,u)) \ (y * x) = (y * x) / (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(242(a,1),7835(a,1,2)),flip(a)].">
      <j1 rule="para" parents="242 7835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) * y) = (L(x,z,u) * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(242(a,1),7836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="242 7836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      (L(x,y,z) * (L(x,y,z) \ u)) \ (x * (L(x,y,z) \ u)) = (x * (L(x,y,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(10(a,1),7837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / u = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(336,a,7838,a),flip(a)].">
      <j1 rule="hyper" parents="336 7838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) = R(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[hyper(490,a,7776,a),flip(a)].">
      <j1 rule="hyper" parents="490 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7621,a,7841,a)].">
      <j1 rule="hyper" parents="7621 7841"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(6185(a,1),7842(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6185 7842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6102(a,1),7810(a,1,1))].">
      <j1 rule="para" parents="6102 7810"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(138,a,7846,a)].">
      <j1 rule="hyper" parents="138 7846"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3482,a(flip),b,7847,a)].">
      <j1 rule="hyper" parents="65 3482 7847"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      x * K(x,y \ L(y,z,u)) = T(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,7849,a(flip),b,2104,a(flip))].">
      <j1 rule="hyper" parents="137 7849 2104"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(2140,a,7851,a),flip(a)].">
      <j1 rule="hyper" parents="2140 7851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u / (x \ L(x,y,z))) = u * ((L(x,y,z) \ x) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(6998(a,1),7823(a,1,2,2))].">
      <j1 rule="para" parents="6998 7823"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      a(x * (T(y,T(z,u)) \ ((u * y) \ T(y,T(z,u)))),w,v5) = a(x * L((u * y) \ 1,u * y,y),w,v5)
    ]]></literal>
    <justification jstring="[para(5360(a,1),7434(a,2,1,2))].">
      <j1 rule="para" parents="5360 7434"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      a(x * (T(y,T(z,u)) \ ((u * y) \ T(y,T(z,u)))),w,v5) = a(x * L(u * y,u * y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,1909,a(flip),b,7866,a),flip(a)].">
      <j1 rule="hyper" parents="325 1909 7866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      ((T(a(x,y,x),z) / u) * w) * (a(x,y,x) \ v5) = (1 * (a(x,y,x) \ ((a(x,y,x) / u) * w))) * v5
    ]]></literal>
    <justification jstring="[para(6182(a,1),7648(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6182 7648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      ((T(a(x,y,x),z) / u) * w) * (a(x,y,x) \ v5) = (1 * ((a(x,y,x) / u) * (a(x,y,x) \ w))) * v5
    ]]></literal>
    <justification jstring="[para(7626(a,1),7869(a,2,1,2))].">
      <j1 rule="para" parents="7626 7869"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      ((T(a(x,y,x),z) / u) * w) * (a(x,y,x) \ v5) = (1 * ((1 / u) * w)) * v5
    ]]></literal>
    <justification jstring="[para(7642(a,1),7871(a,2,1,2))].">
      <j1 rule="para" parents="7642 7871"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      ((T(a(x,y,x),z) / u) * w) * (a(x,y,x) \ v5) = ((1 / u) * w) * v5
    ]]></literal>
    <justification jstring="[para(7(a,1),7872(a,2,1))].">
      <j1 rule="para" parents="7 7872"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      ((a(x,y,x) / z) * u) * (a(x,y,x) \ w) = ((1 / z) * u) * w
    ]]></literal>
    <justification jstring="[para(112(a,1),7873(a,1,1,1,1))].">
      <j1 rule="para" parents="112 7873"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      (x * K(L(y,z,u) \ y,x)) \ L(x,x \ (x * (L(y,z,u) \ y)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3969(a,1),7794(a,1,1))].">
      <j1 rule="para" parents="3969 7794"/>
    </justification>
  </clause>

  <clause id="7877">
    <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="[para(9(a,1),7876(a,1,2,2))].">
      <j1 rule="para" parents="9 7876"/>
    </justification>
  </clause>

  <clause id="7879">
    <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(7672(a,1),7877(a,1,2))].">
      <j1 rule="para" parents="7672 7877"/>
    </justification>
  </clause>

  <clause id="7880">
    <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(65,a,4595,a(flip),b,7879,a)].">
      <j1 rule="hyper" parents="65 4595 7879"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      x \ L(T(x,L(y,z,u) \ y),a(u,z,y),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,4821,a(flip),b,7880,a)].">
      <j1 rule="hyper" parents="65 4821 7880"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      x \ L(T(x,a(y,z,u)),a(w,v5,v6),x) = a(w,v5,K(x,v6))
    ]]></literal>
    <justification jstring="[para(7820(a,2),7881(a,1,2,1))].">
      <j1 rule="para" parents="7820 7881"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(2162,a,7882,a)].">
      <j1 rule="hyper" parents="2162 7882"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,7680,a(flip),b,7883,a),flip(a)].">
      <j1 rule="hyper" parents="65 7680 7883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,7885,a,b,69,a)].">
      <j1 rule="hyper" parents="137 7885 69"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w
    ]]></literal>
    <justification jstring="[hyper(136,a,7885,a,b,79,a)].">
      <j1 rule="hyper" parents="136 7885 79"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,7885,a)].">
      <j1 rule="hyper" parents="54 7885"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,7885,a(flip),b,6827,a),flip(a)].">
      <j1 rule="hyper" parents="132 7885 6827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      (x * y) * K(z,u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(297,a,7889,a)].">
      <j1 rule="hyper" parents="297 7889"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      x * T(y,L(x,z,u)) = y * x
    ]]></literal>
    <justification jstring="[hyper(136,a,7889,a(flip),b,6848,a)].">
      <j1 rule="hyper" parents="136 7889 6848"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      T(x,L(y,z,u)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,7889,a(flip),b,6831,a),flip(a)].">
      <j1 rule="hyper" parents="135 7889 6831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      R(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,2345,a(flip),b,7889,a(flip))].">
      <j1 rule="hyper" parents="36 2345 7889"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7889(a,1),6847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7889 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      R(x,y,T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4201,a,7905,a)].">
      <j1 rule="hyper" parents="4201 7905"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      ((x * y) * T(z,u)) / (y * T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4200,a(flip),b,7905,a)].">
      <j1 rule="hyper" parents="65 4200 7905"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      (x * a(y,z,u)) * K(w,v5) = a(y,z,u) * (x * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(136,a,7905,a(flip),b,7271,a),flip(a)].">
      <j1 rule="hyper" parents="136 7905 7271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = (x * (y * z)) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(136,a,7905,a(flip),b,452,a)].">
      <j1 rule="hyper" parents="136 7905 452"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      (x / y) * (y * K(z,u)) = x * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,7905,a(flip),b,110,a(flip))].">
      <j1 rule="hyper" parents="136 7905 110"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      x * ((x \ y) * K(z,u)) = y * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,7905,a(flip),b,106,a(flip))].">
      <j1 rule="hyper" parents="136 7905 106"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      x \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(7905(a,1),481(a,1,1))].">
      <j1 rule="para" parents="7905 481"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6828,a(flip),b,7890,a),flip(a)].">
      <j1 rule="hyper" parents="65 6828 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(6518,a,7892,a)].">
      <j1 rule="hyper" parents="6518 7892"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      L(K(x,y),z,u) = L(K(x,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,7892,a,b,7892,a)].">
      <j1 rule="hyper" parents="325 7892 7892"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      K((x * y) \ z,u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6844,a(flip),b,7892,a)].">
      <j1 rule="hyper" parents="65 6844 7892"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6826,a(flip),b,7892,a),flip(a)].">
      <j1 rule="hyper" parents="65 6826 7892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      K(x,(y * z) \ u) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6825,a(flip),b,7892,a)].">
      <j1 rule="hyper" parents="65 6825 7892"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3540,a(flip),b,7892,a),flip(a)].">
      <j1 rule="hyper" parents="65 3540 7892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      L((x * x) \ K(y,z),u,w) = (x * x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,7892,a(flip),b,1307,a),flip(a)].">
      <j1 rule="hyper" parents="132 7892 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      L(K(x,y),z,u) * (w * v5) = (K(x,y) * w) * v5
    ]]></literal>
    <justification jstring="[para(7892(a,2),287(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7892 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      L(x \ (x \ K(y,z)),u,w) = x \ (x \ K(y,z))
    ]]></literal>
    <justification jstring="[para(7892(a,1),1320(a,2,2,2))].">
      <j1 rule="para" parents="7892 1320"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      L(K(x,y),z,u) * (w * (K(y,x) * v5)) = v5 * T(w,K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(7892(a,2),2775(a,1,1))].">
      <j1 rule="para" parents="7892 2775"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      T(x,L(y,z,u)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(7892(a,1),6820(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7892 6820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      K(x,y) \ (z * (u * K(x,y))) = T(z * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(7892(a,1),7414(a,1,1))].">
      <j1 rule="para" parents="7892 7414"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      T(x / L(y,z,u),y) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,7906,a),flip(a)].">
      <j1 rule="hyper" parents="376 7906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      L(x,y,z) * T(u,x) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,7906,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 7906 22"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      T(x,(y * z) \ (y * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(102(a,1),7906(a,1,2))].">
      <j1 rule="para" parents="102 7906"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      T(x,(y * z) \ u) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(308(a,1),7906(a,1,2))].">
      <j1 rule="para" parents="308 7906"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      T(x,T((y * z) \ u,w)) = T(x,T(z \ (y \ u),w))
    ]]></literal>
    <justification jstring="[para(523(a,1),7906(a,1,2))].">
      <j1 rule="para" parents="523 7906"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      T(x,T((y \ z) \ u,w)) = T(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(733(a,1),7906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="733 7906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(7906(a,1),2486(a,1,1))].">
      <j1 rule="para" parents="7906 2486"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      T(x,(y * z) \ (z * u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5236(a,1),7906(a,1,2))].">
      <j1 rule="para" parents="5236 7906"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5962(a,1),7906(a,1,2))].">
      <j1 rule="para" parents="5962 7906"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      K(x,T(L(y,z,u) * w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7906(a,1),7348(a,1,2))].">
      <j1 rule="para" parents="7906 7348"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(3036,a,7923,a),flip(a)].">
      <j1 rule="hyper" parents="3036 7923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,7892,a,b,7923,a)].">
      <j1 rule="hyper" parents="325 7892 7923"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      a(L(x,y,z),x,L(x,y,z)) = K(x * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7443,a(flip),b,7923,a)].">
      <j1 rule="hyper" parents="65 7443 7923"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,y,z)) = K(L(x,y,z) * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,97,a(flip),b,7923,a)].">
      <j1 rule="hyper" parents="65 97 7923"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      K(L(x,y,z),u) = 1 / K(u,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,7923,a(flip),b,2608,a),flip(a)].">
      <j1 rule="hyper" parents="201 7923 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((y * z) * w)) = K(x,L(u,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(477(a,1),7923(a,1,2))].">
      <j1 rule="para" parents="477 7923"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      K(x,((y * z) * u) \ ((y * (z * u)) * w)) = K(x,a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(711(a,1),7923(a,1,2))].">
      <j1 rule="para" parents="711 7923"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      K(L(x,y,z),u) * x = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,7924,a,b,2117,a(flip))].">
      <j1 rule="hyper" parents="136 7924 2117"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      K(((x * y) * z) \ ((x * (y * z)) * u),w) = K(a(x,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(711(a,1),7924(a,1,1))].">
      <j1 rule="para" parents="711 7924"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      K(x,y) * (L(x,z,u) * w) = L(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(7924(a,1),2187(a,1,1))].">
      <j1 rule="para" parents="7924 2187"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (((x \ 1) * L(x,y,z)) \ u) = K(x,x \ 1) * u
    ]]></literal>
    <justification jstring="[para(7924(a,1),2735(a,2,1))].">
      <j1 rule="para" parents="7924 2735"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      L(x,y,z) * (K(x,u) * w) = L(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(7924(a,1),4546(a,1,2,1))].">
      <j1 rule="para" parents="7924 4546"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = z
    ]]></literal>
    <justification jstring="[para(7924(a,1),6437(a,1))].">
      <j1 rule="para" parents="7924 6437"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      R(x,y,z / u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(115(a,1),7907(a,1,3)),flip(a)].">
      <j1 rule="para" parents="115 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      R(x,y,(z * u) / z) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(235(a,1),7907(a,1,3)),flip(a)].">
      <j1 rule="para" parents="235 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) = R(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[para(479(a,1),7907(a,1,3)),flip(a)].">
      <j1 rule="para" parents="479 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      R(x / y,y,z) \ (z * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[para(7907(a,1),545(a,1,1))].">
      <j1 rule="para" parents="7907 545"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(7894(a,2),2625(a,1))].">
      <j1 rule="para" parents="7894 2625"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      (x / L(y,z,u)) * y = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,250,a(flip),b,7903,a),flip(a)].">
      <j1 rule="hyper" parents="65 250 7903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) * ((y \ L(y,z,u)) * y) = (y \ L(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(7903(a,1),1763(a,2,2))].">
      <j1 rule="para" parents="7903 1763"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      T(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(7904(a,2),2523(a,1))].">
      <j1 rule="para" parents="7904 2523"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7962(a,2),3197(a,1,2))].">
      <j1 rule="para" parents="7962 3197"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(8000(a,2),2617(a,1))].">
      <j1 rule="para" parents="8000 2617"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      (x / L(y,z,u)) \ T(y,L(y,z,u) \ x) = (L(y,z,u) \ x) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,8018,a(flip),b,2570,a)].">
      <j1 rule="hyper" parents="132 8018 2570"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      L(K(x,K(y \ 1,z) * (u \ w)),v5,v6) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,6113,a(flip),b,7925,a),flip(a)].">
      <j1 rule="hyper" parents="325 6113 7925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      L(K(x,K(y,z \ 1) * (u \ w)),v5,v6) = K(x,(K(z \ K(z,u),y) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,6112,a(flip),b,7925,a),flip(a)].">
      <j1 rule="hyper" parents="325 6112 7925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(201,a,7925,a,b,5947,a)].">
      <j1 rule="hyper" parents="201 7925 5947"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(7925(a,1),216(a,1))].">
      <j1 rule="para" parents="7925 216"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),v5,v6) * w
    ]]></literal>
    <justification jstring="[para(7925(a,1),6007(a,1,1))].">
      <j1 rule="para" parents="7925 6007"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,L(z \ (y / u),w,v5))
    ]]></literal>
    <justification jstring="[para(616(a,1),7985(a,1,2))].">
      <j1 rule="para" parents="616 7985"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(x,L(y,v5,v6))) = w / L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7987(a,1),6004(a,1,2))].">
      <j1 rule="para" parents="7987 6004"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1003,a(flip),b,8036,a),flip(a)].">
      <j1 rule="hyper" parents="65 1003 8036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      R(x,y,z \ u) * (y * (u / z)) = (x * y) * (u / z)
    ]]></literal>
    <justification jstring="[hyper(136,a,8036,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="136 8036 20"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      R(x,y,R(z * K(u,z),u,w)) = R(x,y,(u * w) \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(1593(a,2),8036(a,1,3))].">
      <j1 rule="para" parents="1593 8036"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      (T(x,y) * y) \ (z * ((x * y) / x)) = R(T(z / x,y * x),x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7506,a(flip),b,8037,a)].">
      <j1 rule="hyper" parents="65 7506 8037"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      R(x,y,(z * z) * u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1003,a(flip),b,8037,a)].">
      <j1 rule="hyper" parents="65 1003 8037"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      K(x,(y * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(308(a,1),8042(a,1,2))].">
      <j1 rule="para" parents="308 8042"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      K(x,y \ (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ u) = w
    ]]></literal>
    <justification jstring="[para(469(a,1),8042(a,1,2))].">
      <j1 rule="para" parents="469 8042"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      T(x,(y * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(308(a,1),8047(a,1,2))].">
      <j1 rule="para" parents="308 8047"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      T(x,y \ (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) \ u) = w
    ]]></literal>
    <justification jstring="[para(469(a,1),8047(a,1,2))].">
      <j1 rule="para" parents="469 8047"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      K((x * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),u) = w
    ]]></literal>
    <justification jstring="[para(308(a,1),8052(a,1,1))].">
      <j1 rule="para" parents="308 8052"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((x \ z) / y,u) = w
    ]]></literal>
    <justification jstring="[para(3682(a,1),8052(a,1))].">
      <j1 rule="para" parents="3682 8052"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = v5
    ]]></literal>
    <justification jstring="[para(6686(a,2),8147(a,1,1))].">
      <j1 rule="para" parents="6686 8147"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      x / (y * ((y * y) \ x)) = R(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,107,a(flip),b,8257,a)].">
      <j1 rule="hyper" parents="65 107 8257"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      R(x,y,((z * z) \ u) * w) = R(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(391(a,1),8257(a,1,3))].">
      <j1 rule="para" parents="391 8257"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      R(x,y,(z * u) * (u \ z)) = R(x,y,a(z,u,u \ z))
    ]]></literal>
    <justification jstring="[para(90(a,1),8257(a,1,3)),flip(a)].">
      <j1 rule="para" parents="90 8257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8276">
    <literal><![CDATA[
      R(x,y,T(z * (u * w),w \ (w \ 1))) = R(x,y,z * (u * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(943(a,2),8261(a,1,3))].">
      <j1 rule="para" parents="943 8261"/>
    </justification>
  </clause>

  <clause id="8278">
    <literal><![CDATA[
      T(x,T(y,(z \ u) \ w)) = T(x,T(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(469(a,1),8050(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="469 8050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      x / (y \ L(x,y,y)) = R(y,y,x)
    ]]></literal>
    <justification jstring="[para(874(a,1),8273(a,1,2))].">
      <j1 rule="para" parents="874 8273"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      R(x,x,y) \ y = x \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(195,a,8279,a)].">
      <j1 rule="hyper" parents="195 8279"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      T(x * x,K(y,z)) = x * x
    ]]></literal>
    <justification jstring="[hyper(245,a,7899,a,b,7740,a)].">
      <j1 rule="hyper" parents="245 7899 7740"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      (T(x,y) \ z) * (u * K(x,y)) = T((x \ z) * u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(245,a,7899,a,b,4564,a),flip(a)].">
      <j1 rule="hyper" parents="245 7899 4564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      x \ (K(y,z) * (x * u)) = u * K(y,T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(132,a,3106,a(flip),b,7899,a(flip))].">
      <j1 rule="hyper" parents="132 3106 7899"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      K(x,y) / (z * z) = (z * z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(201,a,8281,a(flip),b,600,a)].">
      <j1 rule="hyper" parents="201 8281 600"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      K(x,K(y,z * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,8281,a(flip),b,3592,a),flip(a)].">
      <j1 rule="hyper" parents="133 8281 3592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      (T(x * x,K(y,z)) / u) * (u * w) = (x * x) * L(w,u,u \ (x * x))
    ]]></literal>
    <justification jstring="[para(8281(a,1),5117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8281 5117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      T(x,K(y,z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,8288,a)].">
      <j1 rule="hyper" parents="58 8288"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      T(x,K(y,z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(8290(a,1),51(a,2))].">
      <j1 rule="para" parents="8290 51"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      (x * y) / (z * K(u,y)) = (x * T(y,u)) / z
    ]]></literal>
    <justification jstring="[hyper(135,a,2851,a(flip),b,7914,a)].">
      <j1 rule="hyper" parents="135 2851 7914"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      (x * K(y,z)) / u = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(135,a,2847,a(flip),b,7914,a),flip(a)].">
      <j1 rule="hyper" parents="135 2847 7914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      (x * T(y,z)) / (u * K(y,z)) = (x * y) / u
    ]]></literal>
    <justification jstring="[hyper(135,a,2093,a(flip),b,7914,a)].">
      <j1 rule="hyper" parents="135 2093 7914"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      ((x / y) * (y * K(z \ u,z))) * (u / z) = x * (z \ u)
    ]]></literal>
    <justification jstring="[para(7914(a,2),3970(a,1,1))].">
      <j1 rule="para" parents="7914 3970"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      x \ T(y * K(z,u),z) = (x \ T(y,z)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,4606,a,b,7915,a)].">
      <j1 rule="hyper" parents="132 4606 7915"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      x \ T(y * K(z,u),u) = (x \ T(y,u)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,4592,a,b,7915,a)].">
      <j1 rule="hyper" parents="132 4592 7915"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      x \ R(y * K(z,u),w,v5) = (x \ R(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,4229,a,b,7915,a)].">
      <j1 rule="hyper" parents="132 4229 7915"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      x \ (y * (z * K(u,w))) = (x \ (y * z)) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(132,a,7899,a(flip),b,7915,a)].">
      <j1 rule="hyper" parents="132 7899 7915"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,u) = x \ (y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,6670,a(flip),b,7915,a),flip(a)].">
      <j1 rule="hyper" parents="132 6670 7915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      (x \ y) * K(z,T(u,y)) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,3106,a(flip),b,7915,a),flip(a)].">
      <j1 rule="hyper" parents="132 3106 7915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(132,a,2558,a(flip),b,7915,a),flip(a)].">
      <j1 rule="hyper" parents="132 2558 7915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,u) = x \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,2093,a(flip),b,7915,a),flip(a)].">
      <j1 rule="hyper" parents="132 2093 7915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,313,a(flip),b,7915,a),flip(a)].">
      <j1 rule="hyper" parents="132 313 7915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      x \ (y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(z,u) = w
    ]]></literal>
    <justification jstring="[para(7915(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7915 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      ((x \ y) * K(z,u)) * (z * z) = x \ (y * (z * T(z,u)))
    ]]></literal>
    <justification jstring="[para(7916(a,1),2393(a,1,1))].">
      <j1 rule="para" parents="7916 2393"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      a(x * (y \ (z * K(u,w))),v5,v6) = a((y \ z) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(7916(a,2),3521(a,1,1,2))].">
      <j1 rule="para" parents="7916 3521"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K((x * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),7944(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="113 7944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5298,a(flip),b,7945,a),flip(a)].">
      <j1 rule="hyper" parents="65 5298 7945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      K(x,L(y \ z,y,z) * u) = K(x,y \ ((1 / z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7345,a,b,7946,a)].">
      <j1 rule="hyper" parents="65 7345 7946"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      K(x,y \ (z \ ((u * u) * w))) = K(x,((z * y) \ (u * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7403,a(flip),b,7946,a),flip(a)].">
      <j1 rule="hyper" parents="65 7403 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),7946(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(113(a,1),7946(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = v6
    ]]></literal>
    <justification jstring="[para(7946(a,1),8147(a,1,1))].">
      <j1 rule="para" parents="7946 8147"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      K((L(x,y,z) \ x) \ u,w) = K(L(x,y,z) * (x \ u),w)
    ]]></literal>
    <justification jstring="[para(1246(a,1),7949(a,2,1))].">
      <j1 rule="para" parents="1246 7949"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(6857(a,1),7964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6857 7964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      (x * (y * L(z,u,w))) / T(x * y,L(z,y,x)) = L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(135,a,412,a(flip),b,7971,a)].">
      <j1 rule="hyper" parents="135 412 7971"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,6866,a(flip),b,7971,a),flip(a)].">
      <j1 rule="hyper" parents="65 6866 7971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,250,a(flip),b,7971,a)].">
      <j1 rule="hyper" parents="65 250 7971"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      L(x,y,z) * (u * x) = x * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,7971,a(flip),b,1251,a),flip(a)].">
      <j1 rule="hyper" parents="137 7971 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(135,a,7971,a(flip),b,6867,a)].">
      <j1 rule="hyper" parents="135 7971 6867"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,250,a(flip),b,7971,a(flip))].">
      <j1 rule="hyper" parents="132 250 7971"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,u) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(235(a,1),7971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="235 7971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      L(x \ 1,y,z) * (u * x) = (x \ 1) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7971(a,1),7505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7971 7505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * v5 = v5 * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(7817(a,1),7971(a,1,2))].">
      <j1 rule="para" parents="7817 7971"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      T(x,T(y,y \ z) \ u) = T(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(231(a,1),7972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 7972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      x / ((y * y) * K(z,u)) = x * (K(u,z) / (y * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,704,a(flip),b,8295,a),flip(a)].">
      <j1 rule="hyper" parents="65 704 8295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      x / L((y * K(z,u)) \ x,w,v5) = L((x * K(u,z)) / y,w,v5) \ x
    ]]></literal>
    <justification jstring="[para(8295(a,2),6588(a,2,1,1))].">
      <j1 rule="para" parents="8295 6588"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      (x * K(y,z)) / (u \ 1) = x / (u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(7528(a,1),8295(a,2,2))].">
      <j1 rule="para" parents="7528 8295"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      (x * (y * K(z,u))) / w = (x * y) / (w * K(u,z))
    ]]></literal>
    <justification jstring="[para(7899(a,1),8295(a,1,1))].">
      <j1 rule="para" parents="7899 8295"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) = x \ T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a(flip),b,8317,a),flip(a)].">
      <j1 rule="hyper" parents="325 2104 8317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      R(x,x \ y,z) \ (z * y) = (x \ y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),8041(a,1,1,1))].">
      <j1 rule="para" parents="82 8041"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      (x * y) / T(z * x,T(z,x) \ y) = (z * x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(201,a,7981,a(flip),b,114,a(flip))].">
      <j1 rule="hyper" parents="201 7981 114"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x,y) * ((x / L(z,u,w)) * z) = z * (L(z,u,w) \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2197,a,b,8045,a)].">
      <j1 rule="hyper" parents="65 2197 8045"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1707,a,b,8045,a)].">
      <j1 rule="hyper" parents="65 1707 8045"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[hyper(136,a,8045,a(flip),b,1707,a)].">
      <j1 rule="hyper" parents="136 8045 1707"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (u * x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8045(a,1),1708(a,1,1))].">
      <j1 rule="para" parents="8045 1708"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      ((x * T(x,y)) / z) \ 1 = (z * K(y,x)) / (x * x)
    ]]></literal>
    <justification jstring="[para(8294(a,1),436(a,1,1))].">
      <j1 rule="para" parents="8294 436"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      (x * T(y,z)) / (u * T(y,z)) = (x * y) / (u * y)
    ]]></literal>
    <justification jstring="[para(2851(a,1),8294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2851 8294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      (x * K(y,z)) / (T(y,z) * T(y,z)) = ((T(y,z) * y) / x) \ 1
    ]]></literal>
    <justification jstring="[para(8296(a,1),436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8296 436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8364">
    <literal><![CDATA[
      (x * (T(y,z) * T(y,z))) / (u * K(y,z)) = ((x / (T(y,z) \ 1)) * y) / u
    ]]></literal>
    <justification jstring="[para(564(a,1),8296(a,1,1))].">
      <j1 rule="para" parents="564 8296"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      (x * (y * y)) / (z * K(y / (y \ 1),y)) = (x * (y / (y \ 1))) / z
    ]]></literal>
    <justification jstring="[para(567(a,1),8296(a,1,1,2))].">
      <j1 rule="para" parents="567 8296"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      L(x,y,z \ (K(u,w) * v5)) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(8303(a,1),2324(a,1,3))].">
      <j1 rule="para" parents="8303 2324"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(8303(a,1),2340(a,1,1))].">
      <j1 rule="para" parents="8303 2340"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      a(x * (y \ (K(z,u) * w)),v5,v6) = a(x * (y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(8303(a,1),3513(a,1,1,2))].">
      <j1 rule="para" parents="8303 3513"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      L(x,y,z \ (u * T(w,v5))) = L(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(8305(a,1),2324(a,1,3))].">
      <j1 rule="para" parents="8305 2324"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      a(x \ (y * T(z,u)),w,v5) = a(x \ (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(8305(a,1),2340(a,1,1))].">
      <j1 rule="para" parents="8305 2340"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      L(x,y,z \ (u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ (u * w)) = v6
    ]]></literal>
    <justification jstring="[para(8305(a,1),2334(a,1,3))].">
      <j1 rule="para" parents="8305 2334"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8306(a,2,2,1))].">
      <j1 rule="para" parents="9 8306"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,7946,a(flip),b,8326,a),flip(a)].">
      <j1 rule="hyper" parents="325 7946 8326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(325,a,1728,a(flip),b,8336,a),flip(a)].">
      <j1 rule="hyper" parents="325 1728 8336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / L(x,y,z))) = u / x
    ]]></literal>
    <justification jstring="[hyper(325,a,1714,a(flip),b,8336,a),flip(a)].">
      <j1 rule="hyper" parents="325 1714 8336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      L(x,y \ (z / x),y) * (x \ z) = y * ((y \ (z / x)) * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,414,a(flip),b,8336,a),flip(a)].">
      <j1 rule="hyper" parents="325 414 8336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      (x / (y \ 1)) * L(y \ 1,z,u) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4134,a(flip),b,8336,a),flip(a)].">
      <j1 rule="hyper" parents="65 4134 8336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8379">
    <literal><![CDATA[
      ((x * y) \ x) * ((y \ 1) \ z) = (z / (y \ 1)) * L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,361,a(flip),b,8336,a)].">
      <j1 rule="hyper" parents="65 361 8336"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      x * ((y / x) * L(x,z,u)) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,8336,a(flip),b,1246,a)].">
      <j1 rule="hyper" parents="137 8336 1246"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      (x \ y) * (x * L(x \ y,z,u)) = L(x \ y,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(331,a,8337,a),flip(a)].">
      <j1 rule="hyper" parents="331 8337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      (x * (y * L(x,z,u))) / (y * x) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,8337,a)].">
      <j1 rule="hyper" parents="145 8337"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      R(x / (y / L(y,z,u)),L(y,z,u) \ y,L(y,z,u)) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6549,a,b,8338,a)].">
      <j1 rule="hyper" parents="65 6549 8338"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ u),x) = x \ (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8338(a,1),115(a,1,1))].">
      <j1 rule="para" parents="8338 115"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      L(x,x,y) * (x \ y) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[para(1720(a,1),8338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1720 8338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,v5) * (u \ L(u,w,v5)))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(8338(a,1),2376(a,1,3,2))].">
      <j1 rule="para" parents="8338 2376"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(8350(a,2),2109(a,1))].">
      <j1 rule="para" parents="8350 2109"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),x) = L(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[para(8357(a,1),7964(a,1,1))].">
      <j1 rule="para" parents="8357 7964"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      x * (L(x,x,y) \ y) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,1949,a,b,8358,a),flip(a)].">
      <j1 rule="hyper" parents="37 1949 8358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      y * (L(y,z,u) \ x) = w
    ]]></literal>
    <justification jstring="[para(8358(a,1),258(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8358 258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      L(x,x,y) \ y = x \ R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(140,a,8389,a),flip(a)].">
      <j1 rule="hyper" parents="140 8389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      L(x,y,(T(z,u) * w) \ v5) = L(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(2190(a,1),8366(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2190 8366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      L(x,y,z \ (((u / w) * v5) * v6)) = L(x,y,z \ (((w \ u) * v5) * v6))
    ]]></literal>
    <justification jstring="[para(2810(a,1),8366(a,1,3,2))].">
      <j1 rule="para" parents="2810 8366"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      L(x,y,z \ ((u / w) \ v5)) = L(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(4590(a,1),8366(a,1,3,2))].">
      <j1 rule="para" parents="4590 8366"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      a(x \ (T(y,z) * u),w,v5) = a(x \ (y * u),w,v5)
    ]]></literal>
    <justification jstring="[para(2114(a,1),8367(a,1,1,2))].">
      <j1 rule="para" parents="2114 8367"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      a((T(x,y) * z) \ u,w,v5) = a((x * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(2190(a,1),8367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2190 8367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      a(x \ (T(y * z,K(z,u)) * w),v5,v6) = a(x \ ((y * T(z,u)) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(2777(a,1),8367(a,1,1,2))].">
      <j1 rule="para" parents="2777 8367"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * (u * L(x \ R(x,y,z),x,z * y))) / (u * (x \ R(x,y,z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2326,a,b,8382,a),flip(a)].">
      <j1 rule="hyper" parents="325 2326 8382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      ((x * y) * T(z,z \ u)) / (y * ((z \ u) \ u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),7911(a,1,2,2))].">
      <j1 rule="para" parents="114 7911"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      (x * x) \ K(y,z) = x \ (x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(526,a,7950,a),flip(a)].">
      <j1 rule="hyper" parents="526 7950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      (x / (y * y)) * K(z,u) = x * ((y * y) \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,7950,a(flip),b,1559,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 7950 1559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      K(x,y) / (z * z) = z \ (z \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8287,a,b,8402,a)].">
      <j1 rule="hyper" parents="65 8287 8402"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      K(x,1 / L(y,z,u)) * (w * v5) = (K(x,1 / y) * w) * v5
    ]]></literal>
    <justification jstring="[para(6592(a,1),7953(a,1,1))].">
      <j1 rule="para" parents="6592 7953"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      (x / y) * (y \ K(z,u)) = x * (y \ (y \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(137,a,7958,a(flip),b,1559,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 7958 1559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(8326(a,2),8262(a,1))].">
      <j1 rule="para" parents="8326 8262"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),u) = w
    ]]></literal>
    <justification jstring="[para(8311(a,2),8267(a,1))].">
      <j1 rule="para" parents="8311 8267"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      L(x,x \ T(y,z),z) \ (y * z) = T(z * (T(y,z) / x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,232,a(flip),b,8332,a)].">
      <j1 rule="hyper" parents="65 232 8332"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      R(x,T(y,x),z) \ (z * (y * x)) = (x \ (y * x)) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),8351(a,1,1,2))].">
      <j1 rule="para" parents="22 8351"/>
    </justification>
  </clause>

  <clause id="8411">
    <literal><![CDATA[
      K(x,y) \ (z * (u \ K(x,y))) = T(z * (u \ 1),K(x,y))
    ]]></literal>
    <justification jstring="[para(7528(a,1),7963(a,1,2,2))].">
      <j1 rule="para" parents="7528 7963"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      (x * T(y,L(x,z,u) * w)) / (x * y) = K(y,w * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3736,a,b,7983,a)].">
      <j1 rule="hyper" parents="65 3736 7983"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      a(x,L(x,y,z),L(x,y,z)) = K(x * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7452,a(flip),b,7998,a)].">
      <j1 rule="hyper" parents="65 7452 7998"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      (T(x,y) * z) \ (L(T(x,y),u,w) * v5) = (x * z) \ (L(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(8025(a,1),2190(a,1,2))].">
      <j1 rule="para" parents="8025 2190"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      L(T(x,y),z,u) * (T(x,y) \ w) = L(x,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[para(4532(a,1),8029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4532 8029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(153(a,1),8272(a,1))].">
      <j1 rule="para" parents="153 8272"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      (x \ (y * (z \ u))) * K(w \ u,w) = x \ (y * (z \ ((w \ u) * w)))
    ]]></literal>
    <justification jstring="[para(8306(a,1),8301(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8306 8301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      x / (y * (y * K(z,u))) = x * (K(u,z) / (y * y))
    ]]></literal>
    <justification jstring="[para(7899(a,1),8346(a,1,2))].">
      <j1 rule="para" parents="7899 8346"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      ((x * y) * z) / ((y * (z * K(u,w))) * K(w,u)) = R(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(490,a,8349,a),flip(a)].">
      <j1 rule="hyper" parents="490 8349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      (x * x) / (x * K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,7739,a(flip),b,8349,a),flip(a)].">
      <j1 rule="hyper" parents="65 7739 8349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) / v5 = (x * (y * z)) / (v5 * K(w,u))
    ]]></literal>
    <justification jstring="[para(7899(a,1),8349(a,1,1,2))].">
      <j1 rule="para" parents="7899 8349"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      (x * x) * (K(y,z) / x) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,7530,a(flip),b,8425,a)].">
      <j1 rule="hyper" parents="65 7530 8425"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      x * (x * (K(y,z) / x)) = L(K(y,z) * x,x,x)
    ]]></literal>
    <justification jstring="[para(8427(a,1),875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8427 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(113(a,1),8362(a,1,1))].">
      <j1 rule="para" parents="113 8362"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      (x * y) / (T(x,y) * a(z,u,w)) = (y * x) / (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(7190(a,1),8429(a,1,2))].">
      <j1 rule="para" parents="7190 8429"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      L(x,y,z \ (u * (w / v5))) = L(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(115(a,1),8369(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="115 8369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ L(u,x \ L(x,y,z),x)),x) = (x \ L(x,y,z)) * T(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,728,a(flip),b,8384,a),flip(a)].">
      <j1 rule="hyper" parents="325 728 8384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      T(L(x,y,z) * (L(L(x,y,z),u,w) \ L(x,u,w)),L(x,y,z)) = L(x,u,w) * (L(L(x,u,w),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1266,a(flip),b,8388,a),flip(a)].">
      <j1 rule="hyper" parents="325 1266 8388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      a(x \ ((y * T(z,T(y \ 1,u))) * w),v5,v6) = a(x \ ((z * (y \ 1)) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,5386,a(flip),b,8396,a)].">
      <j1 rule="hyper" parents="65 5386 8396"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      (x / (y * y)) * K(z,u) = x * (y \ (y \ K(z,u)))
    ]]></literal>
    <justification jstring="[para(8402(a,1),8403(a,2,2))].">
      <j1 rule="para" parents="8402 8403"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      x / (y * (y * K(z,u))) = x * (y \ (y \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(8404(a,1),8423(a,2,2))].">
      <j1 rule="para" parents="8404 8423"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      x * (y \ (y \ K(z,y))) = x / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(2094(a,2),8436(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2094 8436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      x * (y \ (T(y,z) \ 1)) = x / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(2615(a,2),8437(a,1,2,2))].">
      <j1 rule="para" parents="2615 8437"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      x * (y \ (T(y,z) \ 1)) = x * (y \ (y \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8437,a,b,8438,a),flip(a)].">
      <j1 rule="hyper" parents="325 8437 8438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      x * (y \ (T(y,z) \ 1)) = x * (K(z,y) / (y * y))
    ]]></literal>
    <justification jstring="[para(8404(a,2),8439(a,2,2))].">
      <j1 rule="para" parents="8404 8439"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      (x * K(y,z)) / (z * z) = x * (z \ (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(325,a,704,a,b,8440,a)].">
      <j1 rule="hyper" parents="325 704 8440"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      ((x * T(x,y)) / z) \ 1 = z * (x \ (T(x,y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,8361,a,b,8441,a)].">
      <j1 rule="hyper" parents="65 8361 8441"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      K(x,T(y / (K(z,u) * w),T(w,K(z,u)))) = K(x,L(T(w,K(z,u)) \ (y / K(z,u)),v5,v6))
    ]]></literal>
    <justification jstring="[para(3626(a,1),8234(a,1,2,1,2))].">
      <j1 rule="para" parents="3626 8234"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      K(x,L(y \ z,y,z) * u) = K(x,y \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3441,a(flip),b,8322,a),flip(a)].">
      <j1 rule="hyper" parents="325 3441 8322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      K(x,a(y,z,u) \ (w \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ (a(y,z,u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(7186(a,1),8407(a,1,2,1))].">
      <j1 rule="para" parents="7186 8407"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      K(x,((y * z) \ (y * y)) * u) = K(x,z \ ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(102(a,1),8444(a,1,2,1))].">
      <j1 rule="para" parents="102 8444"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      T((x \ y) * (z * x),K(x,u)) = (T(x,u) \ y) * (z * T(x,u))
    ]]></literal>
    <justification jstring="[para(2093(a,1),8282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2093 8282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(u,w) = x * R(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1076,a(flip),b,8300,a),flip(a)].">
      <j1 rule="hyper" parents="65 1076 8300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      (x \ y) * (K(z,u) * (z * z)) = x \ (y * (z * T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,34,a(flip),b,8308,a)].">
      <j1 rule="hyper" parents="65 34 8308"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      a((x \ (y \ T(z,u))) * w,v5,v6) = a(w * (x \ (y \ z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(5108(a,1),8309(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5108 8309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(z,y)) \ w) = v7
    ]]></literal>
    <justification jstring="[para(2618(a,1),8329(a,1,1,2))].">
      <j1 rule="para" parents="2618 8329"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      a(x * (y \ K(z,u)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,1905,a(flip),b,8368,a),flip(a)].">
      <j1 rule="hyper" parents="65 1905 8368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      a(x * (y \ ((z / u) / w)),v5,v6) = a(x * (y \ ((u \ z) / w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(2571(a,1),8368(a,1,1,2,2))].">
      <j1 rule="para" parents="2571 8368"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      a(x * (y \ ((z / u) \ w)),v5,v6) = a(x * (y \ ((u \ z) \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(4590(a,1),8368(a,1,1,2,2))].">
      <j1 rule="para" parents="4590 8368"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      a(x * (y \ ((z * u) \ w)),v5,v6) = a(x * (y \ ((u * z) \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(6163(a,1),8368(a,1,1,2,2))].">
      <j1 rule="para" parents="6163 8368"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      (x * (R(y / z,z,y) \ 1)) / (y \ 1) = L(y,z,x) * (y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1731,a,b,8378,a)].">
      <j1 rule="hyper" parents="65 1731 8378"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(x,y) * T(z * (u \ 1),K(x,y)) = z * (u \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(148,a,8411,a)].">
      <j1 rule="hyper" parents="148 8411"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      L(T(x,y),z,u) * (T(x,y) \ 1) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,946,a(flip),b,8418,a),flip(a)].">
      <j1 rule="hyper" parents="325 946 8418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,946,a(flip),b,8458,a)].">
      <j1 rule="hyper" parents="65 946 8458"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ x,z,u)) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1677,a,b,8459,a)].">
      <j1 rule="hyper" parents="65 1677 8459"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      (x \ y) \ L(T(y / x,x),z,u) = (y / x) \ L(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),8459(a,1,1))].">
      <j1 rule="para" parents="115 8459"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      (((x * x) \ y) * x) \ L(T(y * (x \ 1),x * x),z,u) = (y * (x \ 1)) \ L(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(885(a,1),8459(a,1,1))].">
      <j1 rule="para" parents="885 8459"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ L(L(T(y,x),z,u),x,x) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(8459(a,1),4465(a,2,1))].">
      <j1 rule="para" parents="8459 4465"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * (u \ w))) = L(x,y,z \ ((1 / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,5208,a(flip),b,8431,a),flip(a)].">
      <j1 rule="hyper" parents="65 5208 8431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      x * (y * R(y \ K(x,z),u,w)) = T(x,z) * (y \ R(y,u,w))
    ]]></literal>
    <justification jstring="[para(8448(a,1),5058(a,1,2))].">
      <j1 rule="para" parents="8448 5058"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      x \ (y * (z * T(z,u))) = (x \ y) * (T(z,u) * z)
    ]]></literal>
    <justification jstring="[para(2114(a,1),8449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2114 8449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      x \ (y * (z * T(z,u))) = (x \ y) * (z * T(z,u))
    ]]></literal>
    <justification jstring="[para(248(a,1),8467(a,2,2))].">
      <j1 rule="para" parents="248 8467"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      x \ (y * (x * L(x \ (y \ x),z,u))) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(908(a,1),8460(a,1,2))].">
      <j1 rule="para" parents="908 8460"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) * x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1438(a,1),8470(a,1,2))].">
      <j1 rule="para" parents="1438 8470"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      T(x \ L(x,y,z),u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(301,a,8471,a)].">
      <j1 rule="hyper" parents="301 8471"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(148,a,8471,a),flip(a)].">
      <j1 rule="hyper" parents="148 8471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = (y \ L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,306,a,b,8471,a)].">
      <j1 rule="hyper" parents="41 306 8471"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,237,a,b,8471,a),flip(a)].">
      <j1 rule="hyper" parents="41 237 8471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) * (x * x)) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,8471,a(flip),b,653,a),flip(a)].">
      <j1 rule="hyper" parents="132 8471 653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * v5 = v5 * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8471(a,1),586(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8471 586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,7853,a,b,8475,a)].">
      <j1 rule="hyper" parents="65 7853 8475"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),w,v5) = L(y \ L(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,7964,a(flip),b,8475,a),flip(a)].">
      <j1 rule="hyper" parents="65 7964 8475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      T(x,y * L(y \ 1,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,7361,a(flip),b,8475,a)].">
      <j1 rule="hyper" parents="65 7361 8475"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(57,a,8475,a)].">
      <j1 rule="hyper" parents="57 8475"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) / (x * y) = L(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,8475,a(flip),b,7414,a)].">
      <j1 rule="hyper" parents="201 8475 7414"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (y \ L(y,z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(8475(a,1),376(a,1))].">
      <j1 rule="para" parents="8475 376"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      T(x,y) * (z \ L(z,u,w)) = (z \ L(z,u,w)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8475(a,1),241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8475 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(u,u,x \ L(x,y,z)) = (1 / u) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8475(a,1),1288(a,1,2,1))].">
      <j1 rule="para" parents="8475 1288"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      T(x,y \ (z * L(z \ y,u,w))) = x
    ]]></literal>
    <justification jstring="[para(1410(a,1),8475(a,1,2))].">
      <j1 rule="para" parents="1410 8475"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      x / (x * ((y \ L(y,z,u)) \ 1)) = x \ (x / ((y \ L(y,z,u)) \ 1))
    ]]></literal>
    <justification jstring="[para(8475(a,1),7420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8475 7420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1998,a,8479,a),flip(a)].">
      <j1 rule="hyper" parents="1998 8479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = (a(y,z,u) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,8479,a),flip(a)].">
      <j1 rule="hyper" parents="376 8479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      K(a(x,y,z) \ 1,u) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,8479,a,b,2635,a),flip(a)].">
      <j1 rule="hyper" parents="133 8479 2635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,7188,a,b,8479,a)].">
      <j1 rule="hyper" parents="65 7188 8479"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      x / L(a(y,z,u) \ 1,w,v5) = L(a(y,z,u) \ 1,w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,7964,a(flip),b,8479,a),flip(a)].">
      <j1 rule="hyper" parents="65 7964 8479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(56,a,8479,a)].">
      <j1 rule="hyper" parents="56 8479"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      x / (x * a(y,z,u)) = (x * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(201,a,8479,a(flip),b,2772,a(flip))].">
      <j1 rule="hyper" parents="201 8479 2772"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * (a(x,y,z) \ 1) = w
    ]]></literal>
    <justification jstring="[para(8479(a,1),292(a,1,2))].">
      <j1 rule="para" parents="8479 292"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      x / (x * ((a(y,z,u) \ 1) \ 1)) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(8479(a,1),7478(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8479 7478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      K(x,(a(y,z,u) \ 1) \ (w \ v5)) = K(x,w \ ((a(y,z,u) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[para(8479(a,1),8373(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8479 8373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ (u * L(x \ 1,y,z)) = R(u / x,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,499,a(flip),b,8481,a)].">
      <j1 rule="hyper" parents="65 499 8481"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ x),w,v5) * v6 = v6 * L(x \ (a(y,z,u) \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(8493(a,1),7971(a,1,2))].">
      <j1 rule="para" parents="8493 7971"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / y = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(201,a,8487,a(flip),b,114,a(flip))].">
      <j1 rule="hyper" parents="201 8487 114"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      T((x * y) \ L(x * y,z,u),w) = (T(x,v5) * y) \ (K(x,v5) * L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2190,a,b,8472,a),flip(a)].">
      <j1 rule="hyper" parents="325 2190 8472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      (L(x \ 1,x,x \ y) \ L(((x \ y) * x) \ (x \ y),z,u)) * y = (y / x) * (x * (x \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(8472(a,1),4475(a,2,2,2))].">
      <j1 rule="para" parents="8472 4475"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) \ 1) * x = w
    ]]></literal>
    <justification jstring="[para(8495(a,1),292(a,1,2))].">
      <j1 rule="para" parents="8495 292"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,a(x,y,z) \ 1,w) = ((a(x,y,z) \ 1) * w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(8495(a,1),5236(a,1,1,1))].">
      <j1 rule="para" parents="8495 5236"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,7702,a(flip),b,8473,a),flip(a)].">
      <j1 rule="hyper" parents="325 7702 8473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8513">
    <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(135,a,8473,a,b,484,a)].">
      <j1 rule="hyper" parents="135 8473 484"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      (x \ y) * (x \ L(x,z,u)) = y * L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1315,a(flip),b,8473,a),flip(a)].">
      <j1 rule="hyper" parents="65 1315 8473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      L(x,y,z) \ (R(x,u,w) * (x \ L(x,y,z))) = x \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(132,a,8473,a(flip),b,5363,a(flip))].">
      <j1 rule="hyper" parents="132 8473 5363"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * u)) / w = (u * u) * ((x \ L(x,y,z)) / w)
    ]]></literal>
    <justification jstring="[para(8473(a,2),556(a,1,1))].">
      <j1 rule="para" parents="8473 556"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) \ (L(x,z,u) * y) = a(x,x \ L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(8473(a,1),91(a,1,1,2))].">
      <j1 rule="para" parents="8473 91"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u * (x \ L(x,y,z)))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,x \ L(x,y,z),x) = w
    ]]></literal>
    <justification jstring="[para(8473(a,1),730(a,1,2,2))].">
      <j1 rule="para" parents="8473 730"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      L(x * (((y \ L(y,z,u)) \ 1) / (y \ L(y,z,u))),w,v5) = L(x,w,v5) * ((y \ L(y,z,u)) \ (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(8474(a,1),2021(a,2,2))].">
      <j1 rule="para" parents="8474 2021"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ u) = u * ((L(x,y,z) \ x) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(8474(a,1),7856(a,1,2))].">
      <j1 rule="para" parents="8474 7856"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) \ 1) = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,7239,a(flip),b,8489,a),flip(a)].">
      <j1 rule="hyper" parents="65 7239 8489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8524">
    <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(137,a,8489,a(flip),b,7468,a)].">
      <j1 rule="hyper" parents="137 8489 7468"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ 1) \ u) = u * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(8490(a,1),7204(a,1,2))].">
      <j1 rule="para" parents="8490 7204"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      x / (a(y,z,u) * x) = (x * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(7190(a,2),8496(a,1,2))].">
      <j1 rule="para" parents="7190 8496"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * ((u * a(x,y,z)) \ u) = R(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(8526(a,1),693(a,1,2))].">
      <j1 rule="para" parents="8526 693"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(u,L(w,v5,v6)) = T(u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7906(a,1),8485(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7906 8485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      x / (x * a(y,z,u)) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(7181(a,1),8498(a,1,2,2))].">
      <j1 rule="para" parents="7181 8498"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      x * (x / (x * a(y,z,u))) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(137,a,8529,a,b,xx)].">
      <j1 rule="hyper" parents="137 8529"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8496,a(flip),b,8529,a)].">
      <j1 rule="hyper" parents="65 8496 8529"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),u) = u \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(378,a,8532,a)].">
      <j1 rule="hyper" parents="378 8532"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(x \ (a(y,z,u) \ x),w,v5) = x * (a(y,z,u) * L(a(y,z,u) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(8532(a,1),907(a,1,2,1))].">
      <j1 rule="para" parents="8532 907"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      x \ ((x / y) * L((x / y) \ x,z,u)) = ((x / y) * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[para(85(a,1),8504(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 8504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u * (x \ L(x,y,z)))) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8512(a,1),1794(a,1,2))].">
      <j1 rule="para" parents="8512 1794"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) \ (L(x,z,u) * y) = a(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(8512(a,1),1761(a,1,1))].">
      <j1 rule="para" parents="8512 1761"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ ((1 / x) \ a(x,y,z)),u,w) = (x * a(x,y,z)) * ((1 / x) \ L(1 / x,u,w))
    ]]></literal>
    <justification jstring="[para(2405(a,1),8515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2405 8515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8540">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * ((y * z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,7899,a(flip),b,7913,a),flip(a)].">
      <j1 rule="hyper" parents="325 7899 7913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      K(x,(y * z) \ (u \ ((u * y) * w))) = K(x,L(z,y,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(8262,a,8002,a)].">
      <j1 rule="hyper" parents="8262 8002"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (v5 * v6) = (K(x,1 / K(y,z)) * v5) * v6
    ]]></literal>
    <justification jstring="[para(5989(a,1),8405(a,1,1))].">
      <j1 rule="para" parents="5989 8405"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * (y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(7899(a,1),8540(a,2,2))].">
      <j1 rule="para" parents="7899 8540"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      K(x,y \ (z \ (u \ ((u * z) * w)))) = K(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(8262,a,8541,a)].">
      <j1 rule="hyper" parents="8262 8541"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      L(x * K(y,z),u,w) = L(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(455,a,8543,a)].">
      <j1 rule="hyper" parents="455 8543"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / (y * x) = L(a(z,u,w) * K(x,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,7311,a,b,8545,a)].">
      <j1 rule="hyper" parents="325 7311 8545"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      L(x * K(y,x * (L(x,z,u) \ w)),z,u) = (x * w) / T(x * (L(x,z,u) \ w),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2878,a,b,8545,a),flip(a)].">
      <j1 rule="hyper" parents="325 2878 8545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) = K(x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(37,a,1773,a(flip),b,8545,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 1773 8545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      L(x \ y,z,u) * K(x,x \ y) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(1588(a,1),8545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1588 8545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      L(x,y,L(z * K(u,w),v5,v6)) = L(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(8545(a,2),2324(a,1,3))].">
      <j1 rule="para" parents="8545 2324"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      a(L(x * K(y,z),u,w),v5,v6) = a(L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(8545(a,2),2340(a,1,1))].">
      <j1 rule="para" parents="8545 2340"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      a(x * L(y * K(z,u),w,v5),v6,v7) = a(x * L(y,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(8545(a,2),3513(a,1,1,2))].">
      <j1 rule="para" parents="8545 3513"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      ((x * y) * z) / T(z * x,y) = L(K(x * y,z) * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7417,a,b,8549,a)].">
      <j1 rule="hyper" parents="325 7417 8549"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) * v5 = K(x,y) * (L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(136,a,8549,a,b,419,a)].">
      <j1 rule="hyper" parents="136 8549 419"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      K(x,y) * L(z,K(x,y) * z,K(x,y) * z) = ((K(x,y) * z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,848,a(flip),b,8549,a),flip(a)].">
      <j1 rule="hyper" parents="65 848 8549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) / v5 = K(x,y) * (L(z,u,w) / v5)
    ]]></literal>
    <justification jstring="[para(8549(a,2),666(a,1,1))].">
      <j1 rule="para" parents="8549 666"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      L(x,y,L(K(z,u) * w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(8549(a,2),1542(a,1,3))].">
      <j1 rule="para" parents="8549 1542"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) \ v5 = L(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(8549(a,2),2674(a,1,1))].">
      <j1 rule="para" parents="8549 2674"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      x \ L(K(y,z) * (K(z,y) * (x * u)),w,v5) = (x \ K(y,z)) * L((x \ K(y,z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(8549(a,2),2682(a,1,2))].">
      <j1 rule="para" parents="8549 2682"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      x * L(K(x,y) * (T(x,y) \ z),u,w) = L(z / T(x,y),u,w) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8549(a,2),4537(a,1,2))].">
      <j1 rule="para" parents="8549 4537"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((u * w) * z)) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(6687(a,1),8551(a,1,3))].">
      <j1 rule="para" parents="6687 8551"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      a(L(T(x,y) \ z,u,w),v5,v6) = a(L(x \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(4557(a,1),8552(a,1,1,1))].">
      <j1 rule="para" parents="4557 8552"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      a(L(x \ T(y,z),u,w),v5,v6) = a(L(x \ y,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(5089(a,1),8552(a,1,1,1))].">
      <j1 rule="para" parents="5089 8552"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      a((x * y) \ ((y * z) * x),u,w) = a(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(6687(a,1),8552(a,1,1))].">
      <j1 rule="para" parents="6687 8552"/>
    </justification>
  </clause>

  <clause id="8569">
    <literal><![CDATA[
      L(x,y,z \ (((u \ z) * w) * u)) = L(x,y,L(w,u \ z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),8565(a,1,3,1))].">
      <j1 rule="para" parents="10 8565"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),z,z) / w = K(x,y) * (((1 / z) * u) / w)
    ]]></literal>
    <justification jstring="[para(649(a,1),8559(a,2,2,1))].">
      <j1 rule="para" parents="649 8559"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      L(T(x,y) \ z,u,w) \ (K(y,x) * v5) = L(x \ z,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(4532(a,1),8561(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4532 8561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      a(L((((x * x) \ y) * x) \ z,u,w),v5,v6) = a(L((y * (x \ 1)) \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(885(a,1),8566(a,1,1,1,1))].">
      <j1 rule="para" parents="885 8566"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((x * z) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(5236(a,1),8566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5236 8566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) = a(L(T(z,x),x,y),u,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),8573(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 8573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      a(L(x \ ((y \ z) \ z),u,w),v5,v6) = a(L(x \ y,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(114(a,1),8567(a,1,1,1,2))].">
      <j1 rule="para" parents="114 8567"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      ((x * y) * z) / T(z * x,y) = L(y * K(y * x,z),x,z)
    ]]></literal>
    <justification jstring="[para(7375(a,1),8556(a,2,1))].">
      <j1 rule="para" parents="7375 8556"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1869,a(flip),b,8574,a),flip(a)].">
      <j1 rule="hyper" parents="325 1869 8574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(z,x,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(8574(a,2),1878(a,1))].">
      <j1 rule="para" parents="8574 1878"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      a((((x * (y * y)) * z) \ (z * (u * x))) * (y * y),w,v5) = a(L(u,x * (y * y),z),w,v5)
    ]]></literal>
    <justification jstring="[para(882(a,1),8577(a,1,1))].">
      <j1 rule="para" parents="882 8577"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      (L(L(x,y,z) \ x,u,w) \ v5) \ v5 = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(531,a,8343,a)].">
      <j1 rule="hyper" parents="531 8343"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      K(x,y) * (z * (L(z,u,w) \ x)) = z * (L(z,u,w) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(8045(a,1),8356(a,1,2))].">
      <j1 rule="para" parents="8045 8356"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      (x * K(y,z)) / (T(y,z) * T(y,z)) = ((y * T(y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(248(a,1),8363(a,2,1,1))].">
      <j1 rule="para" parents="248 8363"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      (T(x,y) \ z) * (x * T(x,y)) = T(z / (x \ 1),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,3851,a(flip),b,8447,a),flip(a)].">
      <j1 rule="hyper" parents="65 3851 8447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = (y \ x) \ L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),8462(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 8462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1410,a(flip),b,8585,a),flip(a)].">
      <j1 rule="hyper" parents="325 1410 8585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      ((x \ y) \ L(x \ y,z,u)) * (y / x) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(40,a,8471,a,b,8585,a)].">
      <j1 rule="hyper" parents="40 8471 8585"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      ((x / y) \ L(x / y,z,u)) \ 1 = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(8585(a,2),2015(a,1,1))].">
      <j1 rule="para" parents="8585 2015"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * (y / x) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,8586,a(flip),b,1752,a)].">
      <j1 rule="hyper" parents="136 8586 1752"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      L(T((x \ y) \ L(x \ y,z,u),y / x) \ w,(x \ y) \ L(x \ y,z,u),y / x) = L(y / x,z,u) \ ((y / x) * w)
    ]]></literal>
    <justification jstring="[para(8587(a,1),5236(a,2,1))].">
      <j1 rule="para" parents="8587 5236"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      L(x,y,z \ ((1 / u) \ w)) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,5123,a(flip),b,8465,a),flip(a)].">
      <j1 rule="hyper" parents="65 5123 8465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) \ w)) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8395,a(flip),b,8591,a)].">
      <j1 rule="hyper" parents="65 8395 8591"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      L(x,y,z \ (u / (w \ 1))) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,5116,a,b,8593,a)].">
      <j1 rule="hyper" parents="65 5116 8593"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      L(x,y,L(z,z,u)) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(1721(a,2),8594(a,1,3))].">
      <j1 rule="para" parents="1721 8594"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      R(x,y,z) * ((y * z) \ (z * (T(y,z) * (x \ R(x,u,w))))) = R(((x * y) * z) / (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(8466(a,1),5664(a,1,2,2,2))].">
      <j1 rule="para" parents="8466 5664"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      x \ (y * L(y \ (x * x),z,u)) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1439(a,1),8476(a,1,2))].">
      <j1 rule="para" parents="1439 8476"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) \ (z * L(y,x,x)) = z * y
    ]]></literal>
    <justification jstring="[hyper(65,a,7008,a(flip),b,8494,a),flip(a)].">
      <j1 rule="hyper" parents="65 7008 8494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      L(T(x,y) \ z,u,w) \ (T(x,y) \ v5) = L(x \ z,u,w) \ (x \ v5)
    ]]></literal>
    <justification jstring="[para(4526(a,1),8571(a,1,2))].">
      <j1 rule="para" parents="4526 8571"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      a(L(x \ ((y \ 1) \ (z * z)),u,w),v5,v6) = a(L(x \ ((z * z) * y),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(394(a,1),8575(a,1,1,1,2,1))].">
      <j1 rule="para" parents="394 8575"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      a(R((x * y) \ (y * (z * x)),y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(R(z,y,x),x,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(6581(a,2),8578(a,1,1))].">
      <j1 rule="para" parents="6581 8578"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      (x * K(y,z)) / (y * T(T(y,z),z)) = ((y * T(y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2880(a,1),8583(a,1,2))].">
      <j1 rule="para" parents="2880 8583"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      L(x / y,z,u) \ (x / y) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(2024,a,8588,a)].">
      <j1 rule="hyper" parents="2024 8588"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) \ ((x \ y) \ y) = L(x,z,u) \ (y / (x \ y))
    ]]></literal>
    <justification jstring="[para(82(a,1),8603(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 8603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1242,a(flip),b,8597,a)].">
      <j1 rule="hyper" parents="65 1242 8597"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      x * (K(y,z) / (y * T(T(y,z),z))) = ((y * T(y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,3958,a(flip),b,8602,a)].">
      <j1 rule="hyper" parents="65 3958 8602"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      (1 / a(x,y,z)) \ (u \ L(u,w,v5)) = (a(x,y,z) \ u) \ L(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,7287,a(flip),b,8605,a),flip(a)].">
      <j1 rule="hyper" parents="65 7287 8605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      K(x,y) / (x * T(T(x,y),y)) = x \ (T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,8442,a(flip),b,8606,a),flip(a)].">
      <j1 rule="hyper" parents="36 8442 8606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      K(x,y \ ((z * u) \ ((z * (u * y)) * w))) = K(x,a(z,u,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(8262,a,8003,a)].">
      <j1 rule="hyper" parents="8262 8003"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      K(a(x,y,z) \ z,u) = K(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1727(a,2),8023(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1727 8023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      K(a(x,y,z) \ z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,7924,a(flip),b,8610,a),flip(a)].">
      <j1 rule="hyper" parents="325 7924 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      T(a(x,y,z) \ z,T(u,a(w,v5,v6))) = (a(x,y,z) \ z) * K(z,u)
    ]]></literal>
    <justification jstring="[para(8611(a,1),7171(a,2,2))].">
      <j1 rule="para" parents="8611 7171"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,v5,v6))) = w / L(K(y,x),v7,v8)
    ]]></literal>
    <justification jstring="[para(8191(a,1),8250(a,1,1))].">
      <j1 rule="para" parents="8191 8250"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      (T(x,y) * y) \ (z * ((x * y) / x)) = (y * x) \ (z * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,6562,a(flip),b,8260,a),flip(a)].">
      <j1 rule="hyper" parents="325 6562 8260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      a((x * y) \ ((y * z) * T(x,y)),u,w) = a(R(z,y,(y * x) / y),u,w)
    ]]></literal>
    <justification jstring="[para(8617(a,1),4238(a,1,1))].">
      <j1 rule="para" parents="8617 4238"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      R(x,y,((z * u) \ z) * (u \ 1)) = R(x,y,(1 / (u \ 1)) * L(u \ 1,u,z))
    ]]></literal>
    <justification jstring="[para(8379(a,1),1017(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8379 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      (x * (((y \ L(y,z,u)) \ 1) * (y \ L(y,z,u)))) / (x * ((y \ L(y,z,u)) \ 1)) = (x * (1 / (y \ L(y,z,u)))) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,6608,a(flip),b,8483,a),flip(a)].">
      <j1 rule="hyper" parents="325 6608 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      (x * (y * (T(y,x) \ L(T(y,x),z,u)))) / (x * y) = (y * x) \ (x * L(T(y,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,5236,a(flip),b,8483,a),flip(a)].">
      <j1 rule="hyper" parents="325 5236 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (v5 * v6) = (K(x,1 / K(y,z)) * v6) * T(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,233,a(flip),b,8542,a)].">
      <j1 rule="hyper" parents="65 233 8542"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),z,z) = (K(x,y) / z) * u
    ]]></literal>
    <justification jstring="[hyper(39,a,799,a(flip),b,8570,a),flip(a)].">
      <j1 rule="hyper" parents="39 799 8570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      (K(x,y) / z) * (z * u) = L(K(x,y) * u,z,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8623(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      T(a(x,y,z) \ z,T(u,a(w,v5,v6))) = a(x,y,z) \ T(z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,6670,a(flip),b,8613,a),flip(a)].">
      <j1 rule="hyper" parents="325 6670 8613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      T(a(x,y,z) \ z,u) = a(x,y,z) \ T(z,u)
    ]]></literal>
    <justification jstring="[hyper(7174,a,8625,a)].">
      <j1 rule="hyper" parents="7174 8625"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,v5,v6))) = w * L(K(x,y),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(325,a,8143,a(flip),b,8615,a),flip(a)].">
      <j1 rule="hyper" parents="325 8143 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(z,L(y,v5,v6))) = L(K(y,z),v7,v8) * x
    ]]></literal>
    <justification jstring="[hyper(3630,a,8627,a)].">
      <j1 rule="hyper" parents="3630 8627"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      T((x * (K(y,z) * u)) * L(K(z,y),w,v5),K(y,L(z,v6,v7))) = u * T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,7959,a(flip),b,8628,a),flip(a)].">
      <j1 rule="hyper" parents="325 7959 8628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) = K(L(x,y,z) * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1785,a,b,7999,a)].">
      <j1 rule="hyper" parents="65 1785 7999"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      R(x,y,z * (u * (w \ 1))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7907,a(flip),b,8276,a),flip(a)].">
      <j1 rule="hyper" parents="65 7907 8276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      (x * (y * L(z,u,w))) / T(x * y,z) = L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(7906(a,1),8333(a,1,2))].">
      <j1 rule="para" parents="7906 8333"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      (x * (y * y)) / (z * K(y * y,y)) = (x * (y / (y \ 1))) / z
    ]]></literal>
    <justification jstring="[para(3416(a,1),8365(a,1,2,2))].">
      <j1 rule="para" parents="3416 8365"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      (x * (y * y)) / (z * a(y,y,y)) = (x * (y / (y \ 1))) / z
    ]]></literal>
    <justification jstring="[para(97(a,1),8636(a,1,2,2))].">
      <j1 rule="para" parents="97 8636"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      x / ((y * a(z,z,z)) / (z * z)) = (x * (z / (z \ 1))) / y
    ]]></literal>
    <justification jstring="[hyper(698,a,8637,a)].">
      <j1 rule="hyper" parents="698 8637"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      x / (y * (a(z,z,z) / (z * z))) = (x * (z / (z \ 1))) / y
    ]]></literal>
    <justification jstring="[para(704(a,1),8638(a,1,2))].">
      <j1 rule="para" parents="704 8638"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      x / (y * ((z * z) \ a(z,z,z))) = (x * (z / (z \ 1))) / y
    ]]></literal>
    <justification jstring="[para(7201(a,1),8639(a,1,2,2))].">
      <j1 rule="para" parents="7201 8639"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      (x * (y / (y \ 1))) / z = x / (z * ((y \ 1) / y))
    ]]></literal>
    <justification jstring="[para(5533(a,1),8640(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5533 8640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      x / ((y \ 1) / y) = x * (y / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(39,a,7632,a,b,8641,a)].">
      <j1 rule="hyper" parents="39 7632 8641"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      x \ (y / ((z \ 1) / z)) = (x \ y) * (z / (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,938,a(flip),b,8642,a)].">
      <j1 rule="hyper" parents="65 938 8642"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      R((x \ y) * (x / (x \ 1)),x,(x \ 1) / x) = T(y / T(x \ 1,x),x)
    ]]></literal>
    <justification jstring="[para(8643(a,1),4081(a,1,1))].">
      <j1 rule="para" parents="8643 4081"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      x \ (y * (z / (z \ 1))) = (x \ y) * (z / (z \ 1))
    ]]></literal>
    <justification jstring="[para(8642(a,1),8643(a,1,2))].">
      <j1 rule="para" parents="8642 8643"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      ((1 / x) * y) \ (L(T(x \ 1,x * x),z,u) * w) = ((x \ 1) * y) \ (L(x \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(597(a,1),8416(a,1,1,1))].">
      <j1 rule="para" parents="597 8416"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      a(x * (y \ ((z \ u) / w)),v5,v6) = a(x * (y \ (w \ (u / z))),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,5171,a(flip),b,8453,a),flip(a)].">
      <j1 rule="hyper" parents="65 5171 8453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      (x * (R(y / z,z,y) \ 1)) / (y \ 1) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(325,a,8374,a(flip),b,8456,a),flip(a)].">
      <j1 rule="hyper" parents="325 8374 8456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      (x * (y * (z \ 1))) / (z \ 1) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(1011(a,1),8648(a,1,1,2))].">
      <j1 rule="para" parents="1011 8648"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * (w * (a(x,y,z) \ 1))) = (u * (w * a(x,y,z))) / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8490,a(flip),b,8649,a)].">
      <j1 rule="hyper" parents="65 8490 8649"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      R(((x * (y * z)) / z) / u,u,z \ 1) = (x * (y * (z \ 1))) / (u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(8649(a,1),310(a,1,1,1))].">
      <j1 rule="para" parents="8649 310"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      K(x,y \ ((a(z,u,w) \ 1) \ v5)) = K(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(7399,a,8499,a),flip(a)].">
      <j1 rule="hyper" parents="7399 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      (((x * x) * ((y \ L(y,z,u)) / ((y \ L(y,z,u)) * x))) * (y \ L(y,z,u))) * x = (y \ L(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[para(8517(a,1),7753(a,1,1,1))].">
      <j1 rule="para" parents="8517 7753"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(8523(a,1),8510(a,1))].">
      <j1 rule="para" parents="8523 8510"/>
    </justification>
  </clause>

  <clause id="8655">
    <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(36,a,125,a,b,8525,a)].">
      <j1 rule="hyper" parents="36 125 8525"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      a(x,y,z) * u != w * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ w = u
    ]]></literal>
    <justification jstring="[para(8525(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="8525 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / x = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),8536(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="85 8536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) \ ((x \ y) \ y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(82(a,1),8604(a,2,2))].">
      <j1 rule="para" parents="82 8604"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u \ L(u,w,v5)) = (a(x,y,z) \ u) \ L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(7180(a,1),8607(a,1,1))].">
      <j1 rule="para" parents="7180 8607"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      a(x * (y \ (z \ (u / w))),v5,v6) = a(x * (y \ (z \ (w \ u))),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,5171,a(flip),b,8647,a),flip(a)].">
      <j1 rule="hyper" parents="65 5171 8647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ 1) * u) = u / (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(135,a,9,a(flip),b,8655,a),flip(a)].">
      <j1 rule="hyper" parents="135 9 8655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (a(x,y,z) \ u) = a(x,y,z) \ ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,8655,a(flip),b,8525,a),flip(a)].">
      <j1 rule="hyper" parents="132 8655 8525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      x / (a(y,z,u) * a(y,z,u)) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,7458,a(flip),b,8662,a),flip(a)].">
      <j1 rule="hyper" parents="65 7458 8662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,878,a(flip),b,8664,a),flip(a)].">
      <j1 rule="hyper" parents="39 878 8664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      x / (a(y,z,u) * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * a(y,z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(8664(a,2),7257(a,1))].">
      <j1 rule="para" parents="8664 7257"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      (T(x * x,K(y,z)) / u) * (u * w) = (x * x) * L(w,u,u)
    ]]></literal>
    <justification jstring="[para(1571(a,1),8289(a,2,2))].">
      <j1 rule="para" parents="1571 8289"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      (T(x * x,K(y,z)) / u) * (u * w) = L((x * x) * w,u,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1311,a,b,8667,a),flip(a)].">
      <j1 rule="hyper" parents="325 1311 8667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      ((x * x) / y) * (y * z) = L((x * x) * z,y,y)
    ]]></literal>
    <justification jstring="[para(1016(a,1),8668(a,1,1,1))].">
      <j1 rule="para" parents="1016 8668"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      L((x * x) * y,z,z) \ (((x * x) / z) * (z * (y * u))) = L(L(u,y,z),z * y,(x * x) / z)
    ]]></literal>
    <justification jstring="[para(8670(a,1),451(a,1,1))].">
      <j1 rule="para" parents="8670 451"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      ((((x * x) / y) \ 1) * (y * z)) \ ((((x * x) / y) \ 1) * u) = L((x * x) * z,y,y) \ (((x * x) / y) * u)
    ]]></literal>
    <justification jstring="[para(8670(a,1),1516(a,2,1))].">
      <j1 rule="para" parents="8670 1516"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      ((x * y) * z) / (y * ((z * K(u,w)) * K(w,u))) = R(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(7899(a,1),8424(a,1,2))].">
      <j1 rule="para" parents="7899 8424"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      K(x,y) * L(z,K(x,y) * z,z) = ((K(x,y) * z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1541(a,1),8558(a,1,2))].">
      <j1 rule="para" parents="1541 8558"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      a(R(x,y,(y * z) / y),u,w) = a((z * y) \ ((y * x) * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8370,a(flip),b,8618,a),flip(a)].">
      <j1 rule="hyper" parents="65 8370 8618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      a(R(x,y,(y * z) / y),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,8568,a(flip),b,8676,a),flip(a)].">
      <j1 rule="hyper" parents="325 8568 8676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8037(a,1),8678(a,1,1))].">
      <j1 rule="para" parents="8037 8678"/>
    </justification>
  </clause>

  <clause id="8680">
    <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(325,a,1859,a,b,8679,a),flip(a)].">
      <j1 rule="hyper" parents="325 1859 8679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      a((x * y) \ (((z / ((y \ 1) * x)) * (y \ 1)) * x),u,w) = a(L((x * (y \ 1)) \ z,y \ 1,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6582,a,b,8679,a)].">
      <j1 rule="hyper" parents="65 6582 8679"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,4234,a,b,8679,a)].">
      <j1 rule="hyper" parents="65 4234 8679"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      a(L(x,y,z),y,z) * ((y * x) * z) = (R(x * K(y,x),y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(8682(a,1),7316(a,1,1))].">
      <j1 rule="para" parents="8682 7316"/>
    </justification>
  </clause>

  <clause id="8685">
    <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),8680(a,1,1))].">
      <j1 rule="para" parents="29 8680"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      R((x \ y) * (x / (x \ 1)),x,x \ (x \ 1)) = T(y / T(x \ 1,x),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8036,a(flip),b,8644,a)].">
      <j1 rule="hyper" parents="65 8036 8644"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      R(x,y,z * K(u,w)) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(2847(a,1),8673(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2847 8673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      R(x,y,z * K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,20,a,b,8687,a),flip(a)].">
      <j1 rule="hyper" parents="325 20 8687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8040,a,b,8688,a)].">
      <j1 rule="hyper" parents="65 8040 8688"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      R(x,y,z * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(93(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="93 8688"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      R(x,y,(z \ u) * z) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(312(a,1),8688(a,1,3)),flip(a)].">
      <j1 rule="para" parents="312 8688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * (w * u)) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(457(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="457 8688"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      R(x,y,z * T(u,w)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(1123(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="1123 8688"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      R(x,y,T(z,u) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(2091(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="2091 8688"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      R(x,y,(z / u) * w) = R(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(3272(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="3272 8688"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      R(x,y,z * (u / w)) = R(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(4004(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="4004 8688"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      R(x,y,R(z * K(u,w),v5,v6)) = R(x,y,R(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(4229(a,2),8688(a,1,3))].">
      <j1 rule="para" parents="4229 8688"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      R(x,y,T(z,u) \ w) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(4557(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="4557 8688"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      R(x,y,z \ T(u,w)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(5089(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="5089 8688"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      R(x,y,z \ R(T(u,w),v5,v6)) = R(x,y,z \ R(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(5182(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="5182 8688"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      R(x,y,z * (u * w)) = R(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(6078(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="6078 8688"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      R(x,y,z * (u * K(w,v5))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(6824(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="6824 8688"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      R(x,y,z \ (u \ T(w,v5))) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(8302(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="8302 8688"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      R(x,y,z \ (K(u,w) * v5)) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(8303(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="8303 8688"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      R(x,y,z \ (u * w)) = R(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(8372(a,1),8688(a,1,3))].">
      <j1 rule="para" parents="8372 8688"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * v5)) = R(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(2696(a,1),8689(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2696 8689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      R(x,y,(T(z,u) \ w) * v5) = R(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(4556(a,1),8689(a,1,3))].">
      <j1 rule="para" parents="4556 8689"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      R(x,y,L(K(z,u) * w,v5,v6)) = R(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(8549(a,2),8689(a,1,3))].">
      <j1 rule="para" parents="8549 8689"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      R(x,y,(z \ 1) * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1017,a(flip),b,8690,a),flip(a)].">
      <j1 rule="hyper" parents="325 1017 8690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      R(x,y,(z * z) * (u * w)) = R(x,y,w * ((z * z) * u))
    ]]></literal>
    <justification jstring="[para(33(a,1),8690(a,1,3))].">
      <j1 rule="para" parents="33 8690"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      R(x,y,L(z,z,u) * u) = R(x,y,u / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1720(a,1),8690(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1720 8690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      R(x \ y,x,y) \ 1 = x * (((x \ y) * x) \ 1)
    ]]></literal>
    <justification jstring="[para(8691(a,1),1012(a,1,1))].">
      <j1 rule="para" parents="8691 1012"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      R(x,y,z * L(T(u,w),v5,v6)) = R(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),8693(a,1,3,2))].">
      <j1 rule="para" parents="25 8693"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      R(x,y,z \ R(T(z,u),T(z,u),w)) = R(x,y,(w / (T(z,u) * w)) * T(z,u))
    ]]></literal>
    <justification jstring="[para(1078(a,1),8698(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1078 8698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      R(x,y,z \ (u / w)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(115(a,1),8699(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="115 8699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      ((x \ 1) * y) / L(y,x \ 1,x) = R(1 / x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,513,a,b,8710,a)].">
      <j1 rule="hyper" parents="65 513 8710"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      R(x,y,(((z * z) * u) / z) * w) = R(x,y,((1 / z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(652(a,1),8695(a,2,3,1))].">
      <j1 rule="para" parents="652 8695"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      R(x,y,((z * z) \ (u \ w)) * v5) = R(x,y,(u \ (w / (z * z))) * v5)
    ]]></literal>
    <justification jstring="[para(695(a,1),8695(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="695 8695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      R(x,y,(z * u) * w) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,8690,a,b,8701,a)].">
      <j1 rule="hyper" parents="325 8690 8701"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      R(x,y,z * (u * (w / v5))) = R(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(4004(a,1),8702(a,1,3,2))].">
      <j1 rule="para" parents="4004 8702"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      R(x,y,z * (u \ T(w,v5))) = R(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(5089(a,1),8702(a,1,3,2))].">
      <j1 rule="para" parents="5089 8702"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      R(x,y,z * (u * (w * T(v5,v6)))) = R(x,y,z * (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(6075(a,1),8702(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6075 8702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      R(x,y,z * (u * (w * v5))) = R(x,y,z * (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(6078(a,1),8702(a,1,3,2))].">
      <j1 rule="para" parents="6078 8702"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      R(x,y,z * (u * (w * K(v5,v6)))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(6824(a,1),8702(a,1,3,2))].">
      <j1 rule="para" parents="6824 8702"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      R(x,y,(T(z,u) * w) \ v5) = R(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(2190(a,1),8704(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2190 8704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) * w)) = R(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1037,a(flip),b,8705,a),flip(a)].">
      <j1 rule="hyper" parents="325 1037 8705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      R(x,y,z \ ((u * (w * u)) * (u \ 1))) = R(x,y,z \ (L(w,u \ 1,u) * u))
    ]]></literal>
    <justification jstring="[para(1342(a,1),8705(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1342 8705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      R(x,y,z \ (u * ((u \ 1) \ w))) = R(x,y,z \ (w * (u / (u \ 1))))
    ]]></literal>
    <justification jstring="[para(5529(a,1),8705(a,1,3,2))].">
      <j1 rule="para" parents="5529 8705"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) * ((v5 * v5) / u))) = R(x,y,z \ L((v5 * v5) * w,u,u))
    ]]></literal>
    <justification jstring="[para(8670(a,1),8705(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8670 8705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * v5)) = R(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,8690,a,b,8707,a),flip(a)].">
      <j1 rule="hyper" parents="325 8690 8707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ (u \ (z \ u))) = R(x,y,(u / ((z \ 1) * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1299,a(flip),b,8717,a),flip(a)].">
      <j1 rule="hyper" parents="65 1299 8717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      R(x,y,z \ ((u * u) \ w)) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1006,a(flip),b,8717,a),flip(a)].">
      <j1 rule="hyper" parents="65 1006 8717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      R(x,y,z \ (z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,492,a(flip),b,8717,a),flip(a)].">
      <j1 rule="hyper" parents="65 492 8717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8736">
    <literal><![CDATA[
      (x * y) * ((z \ 1) / z) = x * (y * ((z \ 1) / z))
    ]]></literal>
    <justification jstring="[para(8735(a,1),8258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8735 8258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      R(x,y,((z * u) \ w) * v5) = R(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[para(6163(a,1),8732(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6163 8732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      R(x,y,z \ ((u * u) * w)) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),8734(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 8734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      R(x,y,z \ (((1 / u) * w) / v5)) = R(x,y,z \ ((u * w) / v5))
    ]]></literal>
    <justification jstring="[para(689(a,1),8734(a,1,3,2))].">
      <j1 rule="para" parents="689 8734"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      R(x,y,z \ ((u * (u * w)) * v5)) = R(x,y,z \ (L(w,u,u) * v5))
    ]]></literal>
    <justification jstring="[para(454(a,1),8738(a,1,3,2))].">
      <j1 rule="para" parents="454 8738"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      R(x,y,z \ L((u * u) * w,v5,v6)) = R(x,y,z \ L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(1311(a,2),8738(a,1,3,2))].">
      <j1 rule="para" parents="1311 8738"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      R(x,y,L(z,z,u) * u) = R(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,8036,a(flip),b,8712,a),flip(a)].">
      <j1 rule="hyper" parents="325 8036 8712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((z * w) * u)) = R(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8259,a(flip),b,8697,a)].">
      <j1 rule="hyper" parents="65 8259 8697"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      R(x,y,z \ (u \ R(w \ v5,w,w))) = R(x,y,z \ (u \ (v5 * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(618(a,1),8703(a,1,3,2,2))].">
      <j1 rule="para" parents="618 8703"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      R(x,y,((z / u) \ w) * v5) = R(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),8708(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="115 8708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      R(x,y,z * (u \ (w / v5))) = R(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(115(a,1),8723(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="115 8723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      R(T(x,y),z,(x * z) \ u) \ u = z * ((T(x,y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(8727(a,1),483(a,1,1))].">
      <j1 rule="para" parents="8727 483"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      R(x,y,z \ (u * L(w,u \ 1,u))) = R(x,y,z \ ((u * (u * w)) * u))
    ]]></literal>
    <justification jstring="[para(1341(a,1),8728(a,1,3,2))].">
      <j1 rule="para" parents="1341 8728"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      R(x,y,L(z,u * u,w) * w) = R(x,y,w * ((u * u) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1004,a(flip),b,8692,a)].">
      <j1 rule="hyper" parents="65 1004 8692"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      R(x,y,L(((1 / z) * u) * w,z * T(z,v5),v6) * (v6 * (z * T(z,v5)))) = R(x,y,v6 * ((T(z,v5) * u) * w))
    ]]></literal>
    <justification jstring="[para(2431(a,1),8692(a,2,3,2))].">
      <j1 rule="para" parents="2431 8692"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      R(x,y,(z * u) \ (u * (z * w))) = R(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8705,a,b,8743,a)].">
      <j1 rule="hyper" parents="65 8705 8743"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      R(x,y,L(K(z,u) * w,u,z)) = R(x,y,R(w,u,z))
    ]]></literal>
    <justification jstring="[para(5238(a,1),8752(a,1,3))].">
      <j1 rule="para" parents="5238 8752"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      R(x,y,R(z,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8709,a(flip),b,8753,a),flip(a)].">
      <j1 rule="hyper" parents="65 8709 8753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      (x * R(y \ 1,z,u)) / (y \ R(y,z,u)) = R(x / y,y,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1082,a,b,8754,a)].">
      <j1 rule="hyper" parents="65 1082 8754"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      R(x \ R(y,z,u),x,L(y,z,u)) \ 1 = x * (((x \ R(y,z,u)) * x) \ 1)
    ]]></literal>
    <justification jstring="[para(8754(a,1),8714(a,1,1))].">
      <j1 rule="para" parents="8754 8714"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      R(x,y,z * ((u * u) * w)) = R(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8261,a(flip),b,8711,a),flip(a)].">
      <j1 rule="hyper" parents="65 8261 8711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      R(x,y,z * (u * (u * w))) = R(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[para(100(a,1),8758(a,1,3,2))].">
      <j1 rule="para" parents="100 8758"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      R(x,y,T(z,u) * L(T(w,v5),v6,v7)) = R(x,y,z * L(w,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(325,a,8694,a(flip),b,8715,a),flip(a)].">
      <j1 rule="hyper" parents="325 8694 8715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      R(1 / x,x,y * x) * x = (x \ 1) * R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(8718(a,1),4294(a,1,1))].">
      <j1 rule="para" parents="8718 4294"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      R(x,y,z * (u * (w * u))) = R(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,8760,a(flip),b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="325 8760 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      R(x,y,z * (u * (T(w,v5) * v6))) = R(x,y,z * (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(2091(a,1),8726(a,1,3,2,2))].">
      <j1 rule="para" parents="2091 8726"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      R(x,y,z * (u * L(w / v5,v6,v7))) = R(x,y,z * (u * L(v5 \ w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(8550(a,1),8726(a,1,3,2,2))].">
      <j1 rule="para" parents="8550 8726"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      x \ R(x,x,y * x) = (x \ 1) * R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1080,a(flip),b,8762,a)].">
      <j1 rule="hyper" parents="65 1080 8762"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      R(x,y,L(z,u * u,w) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,8758,a(flip),b,8749,a),flip(a)].">
      <j1 rule="hyper" parents="325 8758 8749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      R(x,y,((z * z) * (u / z)) * w) = R(x,y,((1 / z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(556(a,1),8719(a,1,3,1))].">
      <j1 rule="para" parents="556 8719"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((1 / w) * v5))) = R(x,y,z \ ((w * v5) / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8717,a(flip),b,8739,a)].">
      <j1 rule="hyper" parents="65 8717 8739"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      R(x,y,z * ((T(u,w) * v5) * v6)) = R(x,y,z * (v6 * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8701,a,b,8764,a)].">
      <j1 rule="hyper" parents="65 8701 8764"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      R(x,y,(z * z) * ((u / z) * w)) = R(x,y,((1 / z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(33(a,1),8769(a,1,3))].">
      <j1 rule="para" parents="33 8769"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((1 / w) * v5))) = R(x,y,z \ (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8717,a(flip),b,8770,a),flip(a)].">
      <j1 rule="hyper" parents="325 8717 8770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      R(x,y,((1 / z) \ u) * w) = R(x,y,(u / z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8261,a(flip),b,8772,a),flip(a)].">
      <j1 rule="hyper" parents="65 8261 8772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) * w) = R(x,y,(u / z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8745,a(flip),b,8774,a)].">
      <j1 rule="hyper" parents="65 8745 8774"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) * w) = R(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,8695,a(flip),b,8776,a),flip(a)].">
      <j1 rule="hyper" parents="325 8695 8776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      R(x,y,z * ((u \ 1) \ w)) = R(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8690,a,b,8777,a)].">
      <j1 rule="hyper" parents="65 8690 8777"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      R(x,y,(z \ u) * (w * w)) = R(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1002,a(flip),b,8777,a),flip(a)].">
      <j1 rule="hyper" parents="65 1002 8777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      R(x,y,z * ((z \ 1) \ u)) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,8691,a(flip),b,8778,a),flip(a)].">
      <j1 rule="hyper" parents="325 8691 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      R(x,y,(z \ u) * L(w,w,(z \ 1) \ u)) = R(x,y,(w \ 1) \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8742,a(flip),b,8778,a),flip(a)].">
      <j1 rule="hyper" parents="65 8742 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      R(x,y,z * (u / (z \ 1))) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8696,a,b,8780,a)].">
      <j1 rule="hyper" parents="65 8696 8780"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      R(x,y,z \ R(z,u,w)) = R(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(964(a,1),8782(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="964 8782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ u) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1002,a(flip),b,8779,a),flip(a)].">
      <j1 rule="hyper" parents="65 1002 8779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      (x \ 1) * (x \ (((x \ 1) \ y) / y)) = R(x \ 1,x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,801,a,b,8784,a)].">
      <j1 rule="hyper" parents="65 801 8784"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      R(x,y,(z \ (u / (w * w))) * v5) = R(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8274,a(flip),b,8720,a),flip(a)].">
      <j1 rule="hyper" parents="65 8274 8720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8788">
    <literal><![CDATA[
      R(x,y,z \ (u * ((u \ 1) \ w))) = R(x,y,(z \ w) * (u / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(8645(a,1),8730(a,2,3))].">
      <j1 rule="para" parents="8645 8730"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      R(x,y,(z / ((u \ 1) * z)) * u) = R(x,y,u \ (z \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8784,a(flip),b,8733,a),flip(a)].">
      <j1 rule="hyper" parents="65 8784 8733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      R(x,y,(((z \ 1) * u) \ u) * z) = R(x,y,z \ (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8695,a(flip),b,8789,a)].">
      <j1 rule="hyper" parents="65 8695 8789"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      R(x,y,z \ (u * ((u \ 1) \ w))) = R(x,y,(z \ w) * ((u \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8696,a(flip),b,8788,a),flip(a)].">
      <j1 rule="hyper" parents="325 8696 8788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      R(x,y,z \ (u * ((u \ 1) \ w))) = R(x,y,(z \ w) * (u * u))
    ]]></literal>
    <justification jstring="[para(272(a,1),8791(a,2,3,2))].">
      <j1 rule="para" parents="272 8791"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      R(x,y,z \ (u * ((u \ 1) \ w))) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1002,a(flip),b,8792,a),flip(a)].">
      <j1 rule="hyper" parents="325 1002 8792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      R(x,y,((z \ 1) * u) \ w) = R(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(1511(a,1),8793(a,1,3))].">
      <j1 rule="para" parents="1511 8793"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      a(L(x,y,z),y,z) * ((y * x) * z) = (y * R(x,y,z)) * z
    ]]></literal>
    <justification jstring="[para(1599(a,1),8684(a,2,1))].">
      <j1 rule="para" parents="1599 8684"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      T(x / T(y \ 1,y),y) = (y \ x) * (y / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,8735,a(flip),b,8686,a),flip(a)].">
      <j1 rule="hyper" parents="65 8735 8686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      R(x,y,z \ (u * L(w,u \ 1,u))) = R(x,y,z \ (L(w,u,u) * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8740,a(flip),b,8748,a),flip(a)].">
      <j1 rule="hyper" parents="325 8740 8748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      R(x,y,z \ (L(u,w \ 1,w) * w)) = R(x,y,z \ (L(u,w,w) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8705,a,b,8799,a)].">
      <j1 rule="hyper" parents="65 8705 8799"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      (x * (y * T(T(y,z),z))) / (u * K(y,z)) = ((x / (T(y,z) \ 1)) * y) / u
    ]]></literal>
    <justification jstring="[para(2880(a,1),8364(a,1,1,2))].">
      <j1 rule="para" parents="2880 8364"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      a(x \ ((y * T(z,u)) * w),v5,v6) = a(x \ ((y * z) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,8396,a(flip),b,8398,a),flip(a)].">
      <j1 rule="hyper" parents="65 8396 8398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      (x * (y * x)) \ (x * (x * L(T(y,x),z,u))) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,805,a(flip),b,8464,a)].">
      <j1 rule="hyper" parents="65 805 8464"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      (x * (y * x)) \ L(x * (y * x),z,u) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(1343(a,1),8804(a,1,2))].">
      <j1 rule="para" parents="1343 8804"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(u * (x * u),y,z) \ (u * (x * u)) = w
    ]]></literal>
    <justification jstring="[para(8806(a,1),2024(a,1,1))].">
      <j1 rule="para" parents="8806 2024"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(u,u,x * L(x,y,z)) = (1 / u) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1039(a,1),8486(a,1,2))].">
      <j1 rule="para" parents="1039 8486"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8518,a(flip),b,8538,a),flip(a)].">
      <j1 rule="hyper" parents="65 8518 8538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      a(x * L(x,y,z),x,u) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1851,a(flip),b,8809,a)].">
      <j1 rule="hyper" parents="65 1851 8809"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      L(x / T(y,z),u,w) * T(y,z) = y * L(y \ x,u,w)
    ]]></literal>
    <justification jstring="[para(4532(a,1),8563(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4532 8563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(793,a,8811,a)].">
      <j1 rule="hyper" parents="793 8811"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * T(w,y) = x * (w * L(w \ (x \ (w * y)),z,u))
    ]]></literal>
    <justification jstring="[para(8812(a,1),1747(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8812 1747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (y * z),u,w) = y * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(8812(a,1),5256(a,2,2))].">
      <j1 rule="para" parents="8812 5256"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (y * z)),u,w)) = y * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(924,a,8815,a)].">
      <j1 rule="hyper" parents="924 8815"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      x * (y * L(y \ z,x,y)) = y * (x * ((y * x) \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(298,a,8815,a),flip(a)].">
      <j1 rule="hyper" parents="298 8815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),x,y)) = y * (x * ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),8818(a,2,2,2,2))].">
      <j1 rule="para" parents="10 8818"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      x * ((y \ 1) * L((y \ 1) \ (x \ z),x,y)) = (y \ 1) * (x * (((y \ 1) * x) \ z))
    ]]></literal>
    <justification jstring="[para(1499(a,1),8820(a,1,2,2))].">
      <j1 rule="para" parents="1499 8820"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      (x * (y \ 1)) \ L(x * y,z,u) = y * (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,2027,a(flip),b,8817,a)].">
      <j1 rule="hyper" parents="65 2027 8817"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      (x * R(y \ 1,z,u)) / (y \ R(y,z,u)) = R(x / y,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1765,a(flip),b,8756,a),flip(a)].">
      <j1 rule="hyper" parents="325 1765 8756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (u * R(x \ 1,y,z)) = R(u / x,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5057,a,8823,a)].">
      <j1 rule="hyper" parents="5057 8823"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,L(x,y,z)) \ 1 = x * (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1465(a,1),8757(a,2,2,1))].">
      <j1 rule="para" parents="1465 8757"/>
    </justification>
  </clause>

  <clause id="8826">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,L(x,y,z)) = 1 / (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(201,a,962,a(flip),b,8825,a),flip(a)].">
      <j1 rule="hyper" parents="201 962 8825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      R(R(x,y,z) / x,x,L(x,y,z)) = 1 / (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1464(a,2),8826(a,1,1))].">
      <j1 rule="para" parents="1464 8826"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (R(x,y,z) * R(x \ 1,y,z)) = 1 / (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8824,a,b,8827,a)].">
      <j1 rule="hyper" parents="65 8824 8827"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      R(x,y,(L(z \ u,w,v5) * v6) * v7) = R(x,y,v7 * (v6 * L(u / z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8721,a,b,8765,a)].">
      <j1 rule="hyper" parents="325 8721 8765"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      x / ((y * K(z,u)) / (z * T(T(z,u),u))) = ((x / (T(z,u) \ 1)) * z) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,3535,a(flip),b,8801,a)].">
      <j1 rule="hyper" parents="65 3535 8801"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      T(x,y * L(y \ z,u,w)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(245,a,8817,a(flip),b,8814,a)].">
      <j1 rule="hyper" parents="245 8817 8814"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      T(x,y * L(z,u,w)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8831(a,1,2,2,1))].">
      <j1 rule="para" parents="9 8831"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      T(x,(y * z) * L(L(u,z,y),w,v5)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(18(a,2),8831(a,1,2,2,1))].">
      <j1 rule="para" parents="18 8831"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      T(x,y \ ((y * z) * u)) = T(x,z * u)
    ]]></literal>
    <justification jstring="[para(448(a,1),8831(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="448 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      T(x,L(y,z,u) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(586(a,1),8831(a,1,2))].">
      <j1 rule="para" parents="586 8831"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(589(a,1),8831(a,1,2))].">
      <j1 rule="para" parents="589 8831"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      T(x,y \ L(z,u,w)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(945(a,1),8831(a,1,2))].">
      <j1 rule="para" parents="945 8831"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      T(x,T(y * L(z,u,w),v5)) = K(x,v5) * T(x * K(v5,x),y * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,8833,a(flip),b,4262,a),flip(a)].">
      <j1 rule="hyper" parents="137 8833 4262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      T(x,(y * z) * u) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(100(a,1),8833(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 8833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ w)) = T(x,y * (u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(469(a,1),8833(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="469 8833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      T(x,T(y,z * u) * (z * L(u,w,v5))) = T(x,(z * L(u,w,v5)) * y)
    ]]></literal>
    <justification jstring="[para(8833(a,1),7387(a,1,2,1))].">
      <j1 rule="para" parents="8833 7387"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      T(x,L(y,z,u) * w) = T(x,y * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,8833,a,b,8836,a),flip(a)].">
      <j1 rule="hyper" parents="325 8833 8836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),8836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      T(x,((y * z) \ u) * w) = T(x,(z \ (y \ u)) * w)
    ]]></literal>
    <justification jstring="[para(308(a,1),8836(a,1,2,1))].">
      <j1 rule="para" parents="308 8836"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      R(T(R(1 / x,y,x),x * z),L(x,y,x),z) = (L(x,y,x) * z) \ (1 * z)
    ]]></literal>
    <justification jstring="[para(8836(a,1),6284(a,1,1))].">
      <j1 rule="para" parents="8836 6284"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(1247(a,1),8837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1247 8837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      T(x,y * (L(L(y,z,u),w,v5) \ v6)) = T(x,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,8836,a(flip),b,8844,a)].">
      <j1 rule="hyper" parents="65 8836 8844"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6243(a,1),8844(a,1,2))].">
      <j1 rule="para" parents="6243 8844"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(6222(a,1),8849(a,1,2))].">
      <j1 rule="para" parents="6222 8849"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = K(x,y \ w) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,2095,a(flip),b,8847,a),flip(a)].">
      <j1 rule="hyper" parents="325 2095 8847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      K(L(x,y,z) \ u,w) = w / T(w,x \ u)
    ]]></literal>
    <justification jstring="[hyper(201,a,8847,a(flip),b,2634,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 8847 2634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      (L(x,y,z) \ u) * T(w,x \ u) = w * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(137,a,8847,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 8847 22"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      T(x,T(y,y * z) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(599(a,1),8847(a,1,2,1))].">
      <j1 rule="para" parents="599 8847"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * L(T(x,x \ 1),u,w)) = L(x,u,w) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(8847(a,1),1423(a,1,2,2,1))].">
      <j1 rule="para" parents="8847 1423"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      T(x,T(y,y \ z) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4751(a,1),8847(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4751 8847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      (x / L(y,z,u)) \ T(y,y \ x) = (L(y,z,u) \ x) \ y
    ]]></literal>
    <justification jstring="[para(8847(a,1),8053(a,1,2))].">
      <j1 rule="para" parents="8847 8053"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      T(x,T((y * z) / u,y)) = T(x,z * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2987,a(flip),b,8835,a)].">
      <j1 rule="hyper" parents="65 2987 8835"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      T(x,y \ (z * u)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),8835(a,1,2,2,1))].">
      <j1 rule="para" parents="10 8835"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      T(x,T(y,(y * z) * u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(8835(a,1),2991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8835 2991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      T(x,(y / z) * ((z * K(u \ w,u)) * (w / u))) = T(x,y * (u \ w))
    ]]></literal>
    <justification jstring="[para(8297(a,1),8840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8297 8840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(8265,a,8861,a)].">
      <j1 rule="hyper" parents="8265 8861"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      T(x,(y \ z) * ((z \ u) * L((z \ u) \ w,v5,v6))) = T(x,y \ (u * L(u \ (z * w),v5,v6)))
    ]]></literal>
    <justification jstring="[para(985(a,1),8861(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="985 8861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      T(x,1 \ ((y \ z) * u)) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(67(a,2),8864(a,2,2)),flip(a)].">
      <j1 rule="para" parents="67 8864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      K(x,L(y,z,u) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(2123,a,8852,a)].">
      <j1 rule="hyper" parents="2123 8852"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,w,v5) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,5729,a,b,8867,a)].">
      <j1 rule="hyper" parents="325 5729 8867"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      K(x,L(y,z,u) \ w) = (v5 * K(y \ w,x)) \ v5
    ]]></literal>
    <justification jstring="[hyper(325,a,2849,a,b,8867,a),flip(a)].">
      <j1 rule="hyper" parents="325 2849 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4751(a,1),8867(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4751 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6963(a,1),8867(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6963 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      K(L(x,y,z) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2642,a,b,8853,a),flip(a)].">
      <j1 rule="hyper" parents="325 2642 8853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      K(L(x,y,z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(8853(a,2),2646(a,1))].">
      <j1 rule="para" parents="8853 2646"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(w,v5,v6)) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[hyper(8030,a,8878,a)].">
      <j1 rule="hyper" parents="8030 8878"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      K(x,y * L(z,u,w)) = (z * T(x,z * L(y,v5,v6))) / (z * x)
    ]]></literal>
    <justification jstring="[para(8843(a,1),8413(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8843 8413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      T(x * y,T(x,y) \ z) = T(x * y,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4685,a(flip),b,8855,a),flip(a)].">
      <j1 rule="hyper" parents="65 4685 8855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8886">
    <literal><![CDATA[
      T(x,y \ ((z \ y) * u)) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8344,a(flip),b,8857,a)].">
      <j1 rule="hyper" parents="65 8344 8857"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      K(x,T((y * z) / u,u / z) \ 1) = K(x,L((u / z) \ y,w,v5) \ 1)
    ]]></literal>
    <justification jstring="[para(745(a,1),8872(a,1,2,1))].">
      <j1 rule="para" parents="745 8872"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,8875,a,b,8877,a)].">
      <j1 rule="hyper" parents="325 8875 8877"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(325,a,2849,a,b,8877,a),flip(a)].">
      <j1 rule="hyper" parents="325 2849 8877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      K(x / T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4987(a,1),8879(a,1,1))].">
      <j1 rule="para" parents="4987 8879"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      K(T(x,y) / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(2519(a,2),8891(a,1,1))].">
      <j1 rule="para" parents="2519 8891"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      K(L(x,y,z) * L(x,y,z),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8630,a(flip),b,8881,a)].">
      <j1 rule="hyper" parents="65 8630 8881"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      (x * y) / T(z * x,z \ y) = (z * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(8885(a,1),8355(a,1,2))].">
      <j1 rule="para" parents="8885 8355"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) * u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8861,a(flip),b,8886,a)].">
      <j1 rule="hyper" parents="65 8861 8886"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      K(x * L(x,y,z),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6797,a(flip),b,8895,a)].">
      <j1 rule="hyper" parents="65 6797 8895"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      a(x,L(x,y,z),L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8415,a,b,8899,a)].">
      <j1 rule="hyper" parents="65 8415 8899"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      L(x,L(x,y,z),L(x,y,z)) = K(x \ 1,x) \ x
    ]]></literal>
    <justification jstring="[para(8900(a,1),6374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8900 6374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      K(x,L(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(8873(a,2),2859(a,1))].">
      <j1 rule="para" parents="8873 2859"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      L(x,L(x,y,z),L(x,y,z)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,2634,a,b,8903,a),flip(a)].">
      <j1 rule="hyper" parents="325 2634 8903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      (1 / L(x,y,z)) \ T(x,x \ 1) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8905(a,1),661(a,1,2))].">
      <j1 rule="para" parents="8905 661"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      T(x,y * (z * L(u,w,v5))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(412(a,1),8834(a,1,2))].">
      <j1 rule="para" parents="412 8834"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ (L(x,y,z) \ x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(132,a,1257,a(flip),b,8854,a)].">
      <j1 rule="hyper" parents="132 1257 8854"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L(T(x,x \ 1),u,w) = L(x,y,z) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(8909(a,1),945(a,1,2,1))].">
      <j1 rule="para" parents="8909 945"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8906,a(flip),b,8859,a),flip(a)].">
      <j1 rule="hyper" parents="65 8906 8859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      a((L(x,y,z) \ x) * u,w,v5) = a((x * L(x,y,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(8911(a,1),5035(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8911 5035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      a((x * L(x,y,y)) * z,u,w) = a(a(y,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(8911(a,1),5037(a,1,1,1))].">
      <j1 rule="para" parents="8911 5037"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(8889(a,2),2859(a,1))].">
      <j1 rule="para" parents="8889 2859"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      a(x * a(y,z,y * z),u,w) = a(a(z,z,y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5275,a(flip),b,8914,a)].">
      <j1 rule="hyper" parents="65 5275 8914"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      a(a(x,x,y) * (y * x),z,u) = a(L(y * x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7440,a(flip),b,8916,a),flip(a)].">
      <j1 rule="hyper" parents="65 7440 8916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      K(x,T(y * L(z,u,w),y)) = K(x,z * L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,3736,a(flip),b,8884,a)].">
      <j1 rule="hyper" parents="325 3736 8884"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K(x,L(y,z,u) * w) = K(x,y * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(7397,a,8918,a)].">
      <j1 rule="hyper" parents="7397 8918"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      K(x,L(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(153(a,1),8920(a,2,2,2))].">
      <j1 rule="para" parents="153 8920"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),8921(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K(x \ 1,y * (L(y,z,u) \ x)) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1785,a(flip),b,8923,a),flip(a)].">
      <j1 rule="hyper" parents="325 1785 8923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6243(a,1),8923(a,1,2))].">
      <j1 rule="para" parents="6243 8923"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6185(a,1),8926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6185 8926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(7629(a,2),8926(a,1,2))].">
      <j1 rule="para" parents="7629 8926"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(7658(a,1),8926(a,1,2))].">
      <j1 rule="para" parents="7658 8926"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(7644(a,2),8927(a,1,2))].">
      <j1 rule="para" parents="7644 8927"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(6209(a,1),8928(a,1,2,2))].">
      <j1 rule="para" parents="6209 8928"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(6209(a,1),8930(a,1,2,1))].">
      <j1 rule="para" parents="6209 8930"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      K(L(x \ 1,y,z),u * (L(u,w,v5) \ x)) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7924,a,b,8925,a)].">
      <j1 rule="hyper" parents="65 7924 8925"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),8932(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ 1,u * (L(u,w,v5) \ x)) = a(x,x,x)
    ]]></literal>
    <justification jstring="[para(6594(a,2),8933(a,1,1))].">
      <j1 rule="para" parents="6594 8933"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      T(x,T(y * L(z,u,w),v5)) = T(x,T(y * z,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,4261,a(flip),b,8839,a),flip(a)].">
      <j1 rule="hyper" parents="325 4261 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      T(x,T(y / (z \ 1),u)) = T(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(1720(a,1),8936(a,1,2,1))].">
      <j1 rule="para" parents="1720 8936"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ 1) \ (x * (L(x,y,z) \ x)) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6601,a(flip),b,8935,a)].">
      <j1 rule="hyper" parents="65 6601 8935"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      a(x,x,L(x,y,z)) = (L(x \ 1,u,w) \ 1) \ (x * (L(x,u,w) \ x))
    ]]></literal>
    <justification jstring="[hyper(325,a,6809,a,b,8938,a)].">
      <j1 rule="hyper" parents="325 6809 8938"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      T(x,T(y,z * u) * (z * L(u,w,v5))) = T(x,z * (L(u,w,v5) * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,8840,a(flip),b,8842,a),flip(a)].">
      <j1 rule="hyper" parents="325 8840 8842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      T(x,(y / z) * u) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2714(a,1),8863(a,1,2,2))].">
      <j1 rule="para" parents="2714 8863"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      a(x,x,1 / L(x,y,z)) = (L(x \ 1,u,w) \ 1) \ (x * (L(x,u,w) \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,7490,a,b,8940,a)].">
      <j1 rule="hyper" parents="65 7490 8940"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      T(x,T(y,z * u) * (z * u)) = T(x,z * (L(u,w,v5) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8908,a(flip),b,8941,a)].">
      <j1 rule="hyper" parents="65 8908 8941"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      T(x,y * (L(z,u,w) * v5)) = T(x,(y * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,7387,a(flip),b,8944,a),flip(a)].">
      <j1 rule="hyper" parents="65 7387 8944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      T(x,y * (L(z,u,w) * v5)) = T(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,8840,a(flip),b,8946,a),flip(a)].">
      <j1 rule="hyper" parents="325 8840 8946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      K(x,T(((y * z) / u) \ 1,u / z)) = K(x,L((u / z) \ y,w,v5) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3204,a,8887,a)].">
      <j1 rule="hyper" parents="3204 8887"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,L((y / u) \ z,w,v5) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,4226,a(flip),b,8948,a)].">
      <j1 rule="hyper" parents="65 4226 8948"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(w * z) \ (w * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,2751,a(flip),b,8949,a),flip(a)].">
      <j1 rule="hyper" parents="325 2751 8949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,T(w,z) \ ((z \ w) * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8934,a(flip),b,8950,a),flip(a)].">
      <j1 rule="hyper" parents="325 8934 8950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      K(x,T(y / ((z / (z * u)) * w),y / w)) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / w)))
    ]]></literal>
    <justification jstring="[para(2068(a,1),8950(a,2,2,1))].">
      <j1 rule="para" parents="2068 8950"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(w,u) \ ((u \ w) * (y / (u \ z))))
    ]]></literal>
    <justification jstring="[para(10(a,1),8951(a,1,2,1,2))].">
      <j1 rule="para" parents="10 8951"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ R(x,y,z)) = R(x,y,z) * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,5795,a(flip),b,8828,a)].">
      <j1 rule="hyper" parents="137 5795 8828"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (x \ R(x,y,z)) = R(x,y,z) * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,6652,a,b,8828,a)].">
      <j1 rule="hyper" parents="40 6652 8828"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      R(x,y,z) / (R(x,y,z) * R(x \ 1,y,z)) = x * ((x \ R(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(8954(a,1),578(a,1,2))].">
      <j1 rule="para" parents="8954 578"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      R(x,y,z * (u * L(w / v5,v5,v5))) = R(x,y,(((1 / v5) * w) * u) * z)
    ]]></literal>
    <justification jstring="[para(649(a,1),8829(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="649 8829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8958">
    <literal><![CDATA[
      x / (y * (K(z,u) / (z * T(T(z,u),u)))) = ((x / (T(z,u) \ 1)) * z) / y
    ]]></literal>
    <justification jstring="[para(3958(a,1),8830(a,1,2))].">
      <j1 rule="para" parents="3958 8830"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      R(R(T(1 / x,x * y),z,x),L(x,z,x),y) = (L(x,z,x) * y) \ (1 * y)
    ]]></literal>
    <justification jstring="[para(27(a,2),8846(a,1,1))].">
      <j1 rule="para" parents="27 8846"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      a(x,x,1 / L(x,y,z)) = (L(x \ 1,u,w) \ 1) \ ((x * x) / L(x,u,w))
    ]]></literal>
    <justification jstring="[para(8357(a,2),8943(a,2,2))].">
      <j1 rule="para" parents="8357 8943"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      R(x,y,z) / (R(x,y,z) * R(x \ 1,y,z)) = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(5794(a,1),8956(a,2,2))].">
      <j1 rule="para" parents="5794 8956"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      ((x / (T(y,z) \ 1)) * y) / u = x / (u * (y \ (T(y,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(8608(a,1),8958(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8608 8958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      a(x,x,1 / L(x,y,z)) = (L(x \ 1,u,w) \ 1) \ ((x * x) * (1 / L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(402(a,2),8961(a,2,2))].">
      <j1 rule="para" parents="402 8961"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      R(x / (L(y,z,u) \ y),L(y,z,u) \ y,L(y,z,u)) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1778(a,1),8383(a,1,1,2))].">
      <j1 rule="para" parents="1778 8383"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8519,a,8537,a)].">
      <j1 rule="hyper" parents="8519 8537"/>
    </justification>
  </clause>

  <clause id="8967">
    <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(1271,a,8966,a)].">
      <j1 rule="hyper" parents="1271 8966"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x,x * L(x,y,z)) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),8967(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 8967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      L((x \ (y * L(y \ x,z,u))) \ w,x \ y,(x \ y) * L(x \ y,z,u)) = (x \ y) * (L(x \ y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(1410(a,1),8968(a,1,1,1))].">
      <j1 rule="para" parents="1410 8968"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      R(x,y,((z * u) \ z) * (u \ 1)) = R(x,y,u * L(u \ 1,u,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),8619(a,2,3,1))].">
      <j1 rule="para" parents="82 8619"/>
    </justification>
  </clause>

  <clause id="8972">
    <literal><![CDATA[
      R(x,y,((z * u) \ z) * (u \ 1)) = R(x,y,u * L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,6615,a(flip),b,8970,a),flip(a)].">
      <j1 rule="hyper" parents="325 6615 8970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      R(x,y,((z * u) \ z) * u) = R(x,y,u * L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1017,a(flip),b,8972,a)].">
      <j1 rule="hyper" parents="65 1017 8972"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      R(((x * (y * z)) / z) / u,u,z) = (x * (y * (z \ 1))) / (u * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,1005,a(flip),b,8651,a)].">
      <j1 rule="hyper" parents="65 1005 8651"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      (x * (y * (z \ 1))) / (u * (z \ 1)) = (x * (y * z)) / (u * z)
    ]]></literal>
    <justification jstring="[hyper(541,a,8974,a),flip(a)].">
      <j1 rule="hyper" parents="541 8974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / (x * w) = L(a(y,z,u),w \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7310,a(flip),b,8975,a),flip(a)].">
      <j1 rule="hyper" parents="65 7310 8975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8977">
    <literal><![CDATA[
      L(a(x,y,z),u \ 1,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7310,a(flip),b,8976,a),flip(a)].">
      <j1 rule="hyper" parents="65 7310 8976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8978">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ a(x,y,z) = a(u,u \ 1,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(8977(a,1),719(a,1,1))].">
      <j1 rule="para" parents="8977 719"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      a(x,x \ 1,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,824,a(flip),b,8978,a),flip(a)].">
      <j1 rule="hyper" parents="65 824 8978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      x / (a(y,z,u) * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) \ 1) * (a(y,z,u) \ x) = w
    ]]></literal>
    <justification jstring="[para(8664(a,2),8654(a,1))].">
      <j1 rule="para" parents="8664 8654"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      R(x,y,z \ ((u * (w * u)) * (u \ 1))) = R(x,y,z \ (L(w,u,u) * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8800,a(flip),b,8729,a),flip(a)].">
      <j1 rule="hyper" parents="325 8800 8729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      R(x,y,z \ ((u * (w * u)) * u)) = R(x,y,z \ (L(w,u,u) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1037,a(flip),b,8981,a)].">
      <j1 rule="hyper" parents="65 1037 8981"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) * ((v5 * v5) / u))) = R(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8741,a(flip),b,8731,a),flip(a)].">
      <j1 rule="hyper" parents="325 8741 8731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) * u)) = R(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),8983(a,1,3,2,2))].">
      <j1 rule="para" parents="11 8983"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      R(x,y,z \ L(u * w,w,w)) = R(x,y,z \ (L(u,w,w) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8982,a(flip),b,8985,a),flip(a)].">
      <j1 rule="hyper" parents="65 8982 8985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      R(x,y,(z \ u) * L(w,w,(z \ 1) \ u)) = R(x,y,w \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8784,a(flip),b,8781,a),flip(a)].">
      <j1 rule="hyper" parents="325 8784 8781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      R(x,y,(z \ u) * L(w,w,z \ u)) = R(x,y,w \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(5127(a,1),8987(a,1,3,2))].">
      <j1 rule="para" parents="5127 8987"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      R(x,y,(z \ u) / (w \ 1)) = R(x,y,w \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1720(a,1),8988(a,1,3))].">
      <j1 rule="para" parents="1720 8988"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ (u \ w)) = R(x,y,z \ ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8036,a(flip),b,8989,a)].">
      <j1 rule="hyper" parents="65 8036 8989"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) \ w)) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8784,a(flip),b,8990,a),flip(a)].">
      <j1 rule="hyper" parents="65 8784 8990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,L(x,y,z)) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(7819(a,1),8965(a,1,1))].">
      <j1 rule="para" parents="7819 8965"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) * L(y,z,u) = (y \ L(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(1755(a,1),8046(a,1,2))].">
      <j1 rule="para" parents="1755 8046"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / L(x,y,z) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,8993,a)].">
      <j1 rule="hyper" parents="145 8993"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      R(x,y,y \ L(y,z,u)) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8513,a(flip),b,8995,a)].">
      <j1 rule="hyper" parents="65 8513 8995"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      R(x,y,y \ L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1767,a(flip),b,8996,a),flip(a)].">
      <j1 rule="hyper" parents="325 1767 8996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      R(x,y,y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1039,a(flip),b,8997,a)].">
      <j1 rule="hyper" parents="65 1039 8997"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      a(x \ ((y * (z \ 1)) * u),w,v5) = a(x \ ((z * y) * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8802,a(flip),b,8434,a),flip(a)].">
      <j1 rule="hyper" parents="65 8802 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ (u * L(x \ 1,y,z)) = R(u / x,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1765,a(flip),b,8501,a),flip(a)].">
      <j1 rule="hyper" parents="325 1765 8501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x \ 1,y,z)) = R(u / x,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1310(a,1),9002(a,1,1))].">
      <j1 rule="para" parents="1310 9002"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((u * x) * L(x \ 1,y,z)) = R(u,L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1734,a(flip),b,9003,a),flip(a)].">
      <j1 rule="hyper" parents="325 1734 9003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((u * x) * L(x \ 1,y,z)) = R(u,L(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,1005,a,b,9004,a),flip(a)].">
      <j1 rule="hyper" parents="325 1005 9004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      ((x * y) * L(y \ 1,z,u)) / (y \ L(y,z,u)) = R(x,L(y,z,u),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,8474,a,b,9005,a)].">
      <j1 rule="hyper" parents="65 8474 9005"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      ((x * y) * L(y \ 1,z,u)) / (L(y,z,u) * (y \ 1)) = R(x,L(y,z,u),y \ 1)
    ]]></literal>
    <justification jstring="[para(946(a,2),9006(a,1,2))].">
      <j1 rule="para" parents="946 9006"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      T((x * y) \ L(x * y,z,u),w) = (T(x,v5) * y) \ L(K(x,v5) * (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(8549(a,2),8507(a,2,2))].">
      <j1 rule="para" parents="8549 8507"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      L(1 / (1 / a(x,y,z)),a(x,y,z),u) = R(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1645,a(flip),b,8527,a)].">
      <j1 rule="hyper" parents="65 1645 8527"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z),u) = L(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7202(a,1),9009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7202 9009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      L(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(9010(a,1),8280(a,1,1))].">
      <j1 rule="para" parents="9010 8280"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) \ u = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(325,a,7468,a(flip),b,9012,a),flip(a)].">
      <j1 rule="hyper" parents="325 7468 9012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9014">
    <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(40,a,8391,a(flip),b,9012,a(flip))].">
      <j1 rule="hyper" parents="40 8391 9012"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      x \ y != (a(z,u,w) \ 1) * y
    ]]></literal>
    <literal><![CDATA[
      L(a(z,u,w),a(z,u,w),y) = x
    ]]></literal>
    <justification jstring="[para(9013(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="9013 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9016">
    <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(132,a,9014,a(flip),b,1894,a)].">
      <j1 rule="hyper" parents="132 9014 1894"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      L(x,a(y,y,z),a(y,y,z)) / (z \ L(z,y,y)) = x * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(9014(a,1),7007(a,1,1))].">
      <j1 rule="para" parents="9014 7007"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ L(z,a(y,y,x),a(y,y,x)) = z * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(8484,a,9017,a)].">
      <j1 rule="hyper" parents="8484 9017"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      a(L((x * y) \ ((y * y) * z),u,w),v5,v6) = a(L((x * (y \ 1)) \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(691(a,1),8572(a,1,1,1))].">
      <j1 rule="para" parents="691 8572"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      a(L(x \ ((y \ 1) \ 1),z,u),w,v5) = a(L(x \ ((v6 * v6) * y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,1904,a(flip),b,8600,a)].">
      <j1 rule="hyper" parents="65 1904 8600"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      a(L(x \ ((y * y) * z),u,w),v5,v6) = a(L(x \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,8575,a(flip),b,9020,a),flip(a)].">
      <j1 rule="hyper" parents="65 8575 9020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      a(L(((1 / x) * y) \ z,u,w),v5,v6) = a(L((x * y) \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(692(a,1),9022(a,1,1,1))].">
      <j1 rule="para" parents="692 9022"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      a(L(((x \ 1) * y) \ z,u,w),v5,v6) = a(L((x * y) \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(82(a,1),9024(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 9024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      a(L((x * y) \ (y * (z * x)),y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(R(z,y,x),x,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(8679(a,1),8601(a,1))].">
      <j1 rule="para" parents="8679 8601"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ x) = x * (L(x,u,w) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8910(a,1),8856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8910 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,u,w) = x * (L(x,y,z) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7818,a,b,9028,a)].">
      <j1 rule="hyper" parents="65 7818 9028"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      x * (x * (1 / L(x,y,z))) = L(x \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(151,a,8964,a(flip))].">
      <j1 rule="hyper" parents="151 8964"/>
    </justification>
  </clause>

  <clause id="9031">
    <literal><![CDATA[
      K((x * (1 / L(x,y,z))) \ (x \ u),w) = K((L(x \ 1,y,z) \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(9030(a,1),7944(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9030 7944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      K((x * (1 / L(x,y,z))) \ (x \ u),w) = K(L(x \ 1,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,6686,a(flip),b,9031,a),flip(a)].">
      <j1 rule="hyper" parents="325 6686 9031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      K((1 / L(x,y,z)) \ (x \ (x \ u)),w) = K(L(x \ 1,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(8267,a,9032,a)].">
      <j1 rule="hyper" parents="8267 9032"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      K(L(x,y,z) * (x \ (x \ u)),w) = K(L(x \ 1,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6696,a(flip),b,9033,a)].">
      <j1 rule="hyper" parents="65 6696 9033"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      (x * L(y,z,u)) * (y \ 1) = (x * y) * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,20,a(flip),b,9007,a)].">
      <j1 rule="hyper" parents="39 20 9007"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      T((x * y) \ L(x * y,z,u),w) = (T(x,v5) * y) \ L(T(x,v5) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2114(a,1),9008(a,2,2,1))].">
      <j1 rule="para" parents="2114 9008"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      (T(x,y) * z) \ L(T(x,y) * z,u,w) = (x * z) \ L(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(8291,a,9036,a),flip(a)].">
      <j1 rule="hyper" parents="8291 9036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      R(x,y,(z * u) \ L(z * u,u,z)) = R(x,y,T(z,w) * (u * (T(z,w) * u)))
    ]]></literal>
    <justification jstring="[para(9037(a,1),1632(a,1,3))].">
      <j1 rule="para" parents="9037 1632"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      L(x,y,(z * u) \ L(z * u,u,z)) = L(x,y,T(z,w) * (u * (T(z,w) * u)))
    ]]></literal>
    <justification jstring="[para(9037(a,1),1790(a,1,3))].">
      <j1 rule="para" parents="9037 1790"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      R(x,y,T(z,u) * (w * (T(z,u) * w))) = R(x,y,a(z,w,z * w) \ 1)
    ]]></literal>
    <justification jstring="[para(7438(a,1),9038(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7438 9038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      R(x,y,T(z,u) * (w * (T(z,u) * w))) = R(x,y,a(z,w,z * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,1005,a(flip),b,9040,a),flip(a)].">
      <j1 rule="hyper" parents="325 1005 9040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      R(x,y,L(T(z,u),w,w) * T(z,u)) = R(x,y,a(z,w,z * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8763,a(flip),b,9042,a)].">
      <j1 rule="hyper" parents="65 8763 9042"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      R(x,y,T(z,u) * L(T(z,u),w,w)) = R(x,y,a(z,w,z * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8690,a,b,9043,a)].">
      <j1 rule="hyper" parents="65 8690 9043"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      R(x,y,a(z,u,z * u)) = R(x,y,z * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8761,a(flip),b,9044,a),flip(a)].">
      <j1 rule="hyper" parents="65 8761 9044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9047">
    <literal><![CDATA[
      R(x,y,a(z,u,z * u)) = R(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1268,a(flip),b,9045,a),flip(a)].">
      <j1 rule="hyper" parents="325 1268 9045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      L(x,y,T(z,u) * (w * (T(z,u) * w))) = L(x,y,a(z,w,z * w) \ 1)
    ]]></literal>
    <justification jstring="[para(7438(a,1),9039(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7438 9039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      L(x,y,T(z,u) * (w * (T(z,u) * w))) = L(x,y,a(z,w,z * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a(flip),b,9048,a),flip(a)].">
      <j1 rule="hyper" parents="325 1499 9048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,w) * T(z,u)) = L(x,y,a(z,w,z * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,2400,a(flip),b,9050,a)].">
      <j1 rule="hyper" parents="65 2400 9050"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      L(x,y,T(z,u) * L(T(z,u),w,w)) = L(x,y,a(z,w,z * w))
    ]]></literal>
    <justification jstring="[hyper(2349,a,9051,a)].">
      <j1 rule="hyper" parents="2349 9051"/>
    </justification>
  </clause>

  <clause id="9053">
    <literal><![CDATA[
      L(x,y,a(z,u,z * u)) = L(x,y,z * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(7980(a,1),9052(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7980 9052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      L(x,y,a(z,u,z * u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1639,a(flip),b,9053,a),flip(a)].">
      <j1 rule="hyper" parents="325 1639 9053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      a(L((x * (y \ 1)) \ z,u,w),v5,v6) = a(L((x * y) \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,9022,a(flip),b,9019,a),flip(a)].">
      <j1 rule="hyper" parents="65 9022 9019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      (x * y) / T(x * (L(x,z,u) \ y),w) = L(x * K(w,y),z,u)
    ]]></literal>
    <justification jstring="[para(8923(a,1),8547(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8923 8547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      L(x * K(y,z),u,w) \ (x * z) = T(x * (L(x,u,w) \ z),y)
    ]]></literal>
    <justification jstring="[hyper(195,a,9057,a)].">
      <j1 rule="hyper" parents="195 9057"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      (x \ 1) * (y * (((x \ 1) * y) \ z)) = y * (x * L(x \ (y \ z),y,x))
    ]]></literal>
    <justification jstring="[para(1338(a,1),8821(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1338 8821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      (x \ 1) \ (x * (y * ((x * y) \ z))) = y * (((x \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,8820,a(flip),b,9060,a)].">
      <j1 rule="hyper" parents="132 8820 9060"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      ((x \ 1) \ (x * (a(y,z,y) * ((x * a(y,z,y)) \ u)))) * w = a(y,z,y) * ((((x \ 1) * a(y,z,y)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(9061(a,2),6210(a,1,1))].">
      <j1 rule="para" parents="9061 6210"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      x * ((L(y,z,u) \ y) * (L(y,z,u) \ y)) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,7754,a(flip),b,8522,a),flip(a)].">
      <j1 rule="hyper" parents="65 7754 8522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      (x \ y) * ((L(z,u,w) \ z) * (L(z,u,w) \ z)) = x \ ((L(z,u,w) * L(z \ 1,u,w)) \ y)
    ]]></literal>
    <justification jstring="[hyper(132,a,9063,a(flip),b,125,a),flip(a)].">
      <j1 rule="hyper" parents="132 9063 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      (x * y) \ (y * L(T(x,y),z,u)) = (y * (x * (x \ L(x,z,u)))) / (y * x)
    ]]></literal>
    <justification jstring="[para(8459(a,1),8621(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8459 8621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9066">
    <literal><![CDATA[
      (x * y) \ (y * L(T(x,y),z,u)) = (y * L(x,z,u)) / (y * x)
    ]]></literal>
    <justification jstring="[para(10(a,1),9065(a,2,1,2))].">
      <j1 rule="para" parents="10 9065"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      (x * L(y,z,u)) / (x * y) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(242(a,1),9066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="242 9066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,L(u,w,v5))) = y * T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6959(a,1),8629(a,1,1))].">
      <j1 rule="para" parents="6959 8629"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(132,a,7982,a(flip),b,9070,a(flip))].">
      <j1 rule="hyper" parents="132 7982 9070"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(132,a,4790,a(flip),b,9070,a(flip))].">
      <j1 rule="hyper" parents="132 4790 9070"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(3617(a,1),9072(a,1,2,1,2))].">
      <j1 rule="para" parents="3617 9072"/>
    </justification>
  </clause>

  <clause id="9074">
    <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(3784(a,1),9072(a,1,2,1,2))].">
      <j1 rule="para" parents="3784 9072"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9071,a(flip),b,9073,a)].">
      <j1 rule="hyper" parents="65 9071 9073"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,z \ u)) = T(y,K(z \ u,z) * x)
    ]]></literal>
    <justification jstring="[para(3713(a,1),9073(a,1,2,1,2))].">
      <j1 rule="para" parents="3713 9073"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,9075,a,b,2094,a(flip))].">
      <j1 rule="hyper" parents="132 9075 2094"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(z,y))) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(113(a,1),9075(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 9075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2114(a,1),9075(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2114 9075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(2109,a,9077,a)].">
      <j1 rule="hyper" parents="2109 9077"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(9077(a,1),2109(a,1))].">
      <j1 rule="para" parents="9077 2109"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(3192(a,1),9080(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3192 9080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4526(a,1),9080(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4526 9080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      T(x,((y * z) / y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2476(a,1),9079(a,1,2))].">
      <j1 rule="para" parents="2476 9079"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4544(a,2),9083(a,1,2))].">
      <j1 rule="para" parents="4544 9083"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(236(a,1),9084(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="236 9084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(7402,a,9086,a),flip(a)].">
      <j1 rule="hyper" parents="7402 9086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(4784(a,1),9085(a,1,2,1))].">
      <j1 rule="para" parents="4784 9085"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(3623(a,1),9078(a,1,2))].">
      <j1 rule="para" parents="3623 9078"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(201,a,9089,a,b,2634,a(flip))].">
      <j1 rule="hyper" parents="201 9089 2634"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(7396,a,9087,a),flip(a)].">
      <j1 rule="hyper" parents="7396 9087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(235(a,1),9091(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="235 9091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(201,a,9092,a(flip),b,2634,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 9092 2634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2642,a,b,9093,a),flip(a)].">
      <j1 rule="hyper" parents="325 2642 9093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      K((x \ y) * ((z * ((x \ y) \ (x \ u))) / z),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(1120(a,1),9094(a,2,1))].">
      <j1 rule="para" parents="1120 9094"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8929,a(flip),b,9088,a),flip(a)].">
      <j1 rule="hyper" parents="65 8929 9088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(3782(a,1),9074(a,1,2))].">
      <j1 rule="para" parents="3782 9074"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9073,a(flip),b,9098,a),flip(a)].">
      <j1 rule="hyper" parents="65 9073 9098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,9099,a(flip),b,2094,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 9099 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a,b,9100,a),flip(a)].">
      <j1 rule="hyper" parents="325 2104 9100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(9081,a,9101,a)].">
      <j1 rule="hyper" parents="9081 9101"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,u * T(u \ (y \ u),z))
    ]]></literal>
    <justification jstring="[para(2283(a,1),9101(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2283 9101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),v5,v6) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(9101(a,1),8116(a,1,1))].">
      <j1 rule="para" parents="9101 8116"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(2744(a,1),9102(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2744 9102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(3785(a,1),9102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3785 9102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),v5,v6) = K(x,(K(y \ K(y,u),z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(9102(a,1),8117(a,1,1))].">
      <j1 rule="para" parents="9102 8117"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z * K(y,z),u) * y)
    ]]></literal>
    <justification jstring="[para(1584(a,1),9103(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1584 9103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(3623(a,1),9106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3623 9106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(201,a,9109,a(flip),b,2608,a),flip(a)].">
      <j1 rule="hyper" parents="201 9109 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2611,a(flip),b,9110,a),flip(a)].">
      <j1 rule="hyper" parents="325 2611 9110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(z * K(z \ y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7377,a,b,9111,a)].">
      <j1 rule="hyper" parents="65 7377 9111"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z \ u,z) * x)
    ]]></literal>
    <justification jstring="[para(3713(a,1),9076(a,1,2))].">
      <j1 rule="para" parents="3713 9076"/>
    </justification>
  </clause>

  <clause id="9114">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9073,a(flip),b,9113,a),flip(a)].">
      <j1 rule="hyper" parents="65 9073 9113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),9114(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,9115,a(flip),b,2094,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 9115 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a,b,9116,a),flip(a)].">
      <j1 rule="hyper" parents="325 2104 9116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),9117(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 9117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(9081,a,9118,a)].">
      <j1 rule="hyper" parents="9081 9118"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9105,a(flip),b,9118,a)].">
      <j1 rule="hyper" parents="65 9105 9118"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      K(x,K((y \ 1) \ z,y) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4352(a,1),9119(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4352 9119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9083,a(flip),b,9120,a)].">
      <j1 rule="hyper" parents="65 9083 9120"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[para(3192(a,1),9120(a,1,2))].">
      <j1 rule="para" parents="3192 9120"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(y,(y \ 1) \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(9121(a,1),5926(a,1,1))].">
      <j1 rule="para" parents="9121 5926"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4526(a,1),9122(a,2,2))].">
      <j1 rule="para" parents="4526 9122"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,9082,a(flip),b,9123,a),flip(a)].">
      <j1 rule="hyper" parents="325 9082 9123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(6124(a,1),9126(a,1,2))].">
      <j1 rule="para" parents="6124 9126"/>
    </justification>
  </clause>

  <clause id="9128">
    <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(2407(a,1),9127(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2407 9127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9129">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(8451,a,9104,a),flip(a)].">
      <j1 rule="hyper" parents="8451 9104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(3469(a,1),9129(a,1,2,1))].">
      <j1 rule="para" parents="3469 9129"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(8451,a,9107,a),flip(a)].">
      <j1 rule="hyper" parents="8451 9107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(3362(a,1),9131(a,1,2,1))].">
      <j1 rule="para" parents="3362 9131"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      K(x,(y * K((z \ 1) \ 1,(z \ 1) \ u)) \ w) = K(x,(y * K(z * u,z \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(4343(a,1),9132(a,2,2,1,2))].">
      <j1 rule="para" parents="4343 9132"/>
    </justification>
  </clause>

  <clause id="9134">
    <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(4901(a,1),9132(a,2,2))].">
      <j1 rule="para" parents="4901 9132"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      K(x,(y * K(z,(z \ 1) \ u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * K(u,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(9124(a,1),8451(a,1))].">
      <j1 rule="para" parents="9124 8451"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      K(x \ (y * ((z * (y \ u)) / z)),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(1687(a,1),9095(a,1,1))].">
      <j1 rule="para" parents="1687 9095"/>
    </justification>
  </clause>

  <clause id="9139">
    <literal><![CDATA[
      K(x \ (y * T(y \ 1,z)),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(2057(a,1),9138(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2057 9138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      K(x \ K(y \ 1,z),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(2145(a,1),9139(a,1,1,2))].">
      <j1 rule="para" parents="2145 9139"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      (x \ K(y \ K(z,u \ 1),w)) \ (x \ 1) = K(w,y \ K(u \ 1,z))
    ]]></literal>
    <justification jstring="[para(9140(a,1),7538(a,1,1,2))].">
      <j1 rule="para" parents="9140 7538"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(4878,a,9141,a),flip(a)].">
      <j1 rule="hyper" parents="4878 9141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * (w * (a(x,y,z) \ 1))) = a(x,y,z) \ (u * (w * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,7194,a(flip),b,8650,a),flip(a)].">
      <j1 rule="hyper" parents="325 7194 8650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      K(x,(y * K(z * u,z \ 1)) \ w) = K(x,(y * K(z,(z \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[para(2211(a,1),9133(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2211 9133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      K(x,(y * K(z,(z \ 1) \ u)) \ w) = K(x,(y * K(z * u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9130,a(flip),b,9144,a),flip(a)].">
      <j1 rule="hyper" parents="65 9130 9144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      K(x,(y * K(z * u,z)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(9137,a,9145,a),flip(a)].">
      <j1 rule="hyper" parents="9137 9145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(4651(a,2),9146(a,1,2,1,2))].">
      <j1 rule="para" parents="4651 9146"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(u,L(x,y,z)) = T((x \ L(x,y,z)) * u,x)
    ]]></literal>
    <justification jstring="[para(1248(a,1),8432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1248 8432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      T((x \ L(x,y,z)) * u,x) = T(u,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8528,a(flip),b,9148,a),flip(a)].">
      <j1 rule="hyper" parents="65 8528 9148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      x * T((x \ L(x,y,z)) * u,x) = (u * x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9149(a,2),7701(a,1,2))].">
      <j1 rule="para" parents="9149 7701"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * x = (u * x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(292,a,9151,a)].">
      <j1 rule="hyper" parents="292 9151"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      ((x * y) * (y \ L(y,z,u))) / T((y \ L(y,z,u)) * x,y) = y
    ]]></literal>
    <justification jstring="[hyper(145,a,9151,a)].">
      <j1 rule="hyper" parents="145 9151"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * y = (x * y) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8473(a,1),9152(a,1,1))].">
      <j1 rule="para" parents="8473 9152"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * (y \ L(y,z,u))) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(9154(a,1),1760(a,1,2))].">
      <j1 rule="para" parents="9154 1760"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      L(x * K(x * y,x \ L(x,z,u)),y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,8576,a(flip),b,9153,a)].">
      <j1 rule="hyper" parents="65 8576 9153"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      L(x * 1,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(8482(a,1),9156(a,1,1,2))].">
      <j1 rule="para" parents="8482 9156"/>
    </justification>
  </clause>

  <clause id="9158">
    <literal><![CDATA[
      L(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(8(a,1),9157(a,1,1))].">
      <j1 rule="para" parents="8 9157"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      L(x,y,x * L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(2366,a,9158,a)].">
      <j1 rule="hyper" parents="2366 9158"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      L(x,y,L(x,z,u) * L(L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(152,a,9160,a)].">
      <j1 rule="hyper" parents="152 9160"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      L(x,y,L(x * L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,4471,a(flip),b,9161,a)].">
      <j1 rule="hyper" parents="65 4471 9161"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      a(L(x * L(x,y,z),u,w),v5,x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,9162,a)].">
      <j1 rule="hyper" parents="55 9162"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(859,a,9155,a),flip(a)].">
      <j1 rule="hyper" parents="859 9155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,7498,a(flip),b,9164,a),flip(a)].">
      <j1 rule="hyper" parents="325 7498 9164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(x,T(y / (K(z,u) * w),T(w,K(z,u)))) = K(x,(K(z,u) * T(w,K(z,u))) \ T(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(3744(a,1),8443(a,2,2))].">
      <j1 rule="para" parents="3744 8443"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      a(((x * (y * y)) * z) \ (z * (u * x)),w,v5) = a(L(u,x * (y * y),z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(1881,a,8580,a)].">
      <j1 rule="hyper" parents="1881 8580"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      (x \ K(y,z)) * L((x \ K(y,z)) \ u,w,v5) = x \ L(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(2619(a,1),8562(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2619 8562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      (x \ K(y,z)) * L((x \ K(y,z)) \ u,w,v5) = x * L(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,1322,a(flip),b,9169,a),flip(a)].">
      <j1 rule="hyper" parents="325 1322 9169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      L(x,y,z) * (x \ K(u,w)) = x * L(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(817,a,9170,a)].">
      <j1 rule="hyper" parents="817 9170"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      ((x / y) \ 1) * L(((y \ x) \ K(y \ x,y)) \ z,u,w) = (y \ x) * L((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(2592(a,1),9170(a,1,1))].">
      <j1 rule="para" parents="2592 9170"/>
    </justification>
  </clause>

  <clause id="9174">
    <literal><![CDATA[
      (K(x,y) / z) * L(z,u,w) = z * L(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8336,a(flip),b,9172,a)].">
      <j1 rule="hyper" parents="65 8336 9172"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      ((1 / x) * y) \ (L(1 / x,z,u) * w) = ((x \ 1) * y) \ (L(x \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(597(a,1),8646(a,1,2,1,1))].">
      <j1 rule="para" parents="597 8646"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      ((1 / x) * y) \ (L(1 / x,z,u) * w) = (x * y) \ (L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,4289,a(flip),b,9175,a),flip(a)].">
      <j1 rule="hyper" parents="325 4289 9175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      T(x,(y \ z) * ((z \ u) * L((z \ u) \ w,v5,v6))) = T(x,(y \ u) * L(u \ (z * w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,8861,a(flip),b,8865,a),flip(a)].">
      <j1 rule="hyper" parents="325 8861 8865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ (u \ w) = u \ ((L(x,y,z) * L(x \ 1,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9063,a(flip),b,9064,a)].">
      <j1 rule="hyper" parents="65 9063 9064"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z,T(u,y)) * y)
    ]]></literal>
    <justification jstring="[para(3656(a,1),9108(a,2,2,1))].">
      <j1 rule="para" parents="3656 9108"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(3640(a,1),9179(a,2,2))].">
      <j1 rule="para" parents="3640 9179"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ y,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(1584(a,1),9180(a,1,2,2,1,2))].">
      <j1 rule="para" parents="1584 9180"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(2207(a,1),9181(a,1,2))].">
      <j1 rule="para" parents="2207 9181"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = 1 / K(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(201,a,9182,a(flip),b,2608,a),flip(a)].">
      <j1 rule="hyper" parents="201 9182 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2611,a(flip),b,9183,a),flip(a)].">
      <j1 rule="hyper" parents="325 2611 9183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7378,a(flip),b,9184,a),flip(a)].">
      <j1 rule="hyper" parents="65 7378 9184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9112,a,b,9185,a)].">
      <j1 rule="hyper" parents="65 9112 9185"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(6733,a,9186,a)].">
      <j1 rule="hyper" parents="6733 9186"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,6727,a(flip),b,9187,a)].">
      <j1 rule="hyper" parents="325 6727 9187"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(5156(a,1),9188(a,1,1))].">
      <j1 rule="para" parents="5156 9188"/>
    </justification>
  </clause>

  <clause id="9190">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(3792,a,9189,a),flip(a)].">
      <j1 rule="hyper" parents="3792 9189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(T(x,y) / T(z,T(x,y)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5334,a,b,9190,a)].">
      <j1 rule="hyper" parents="65 5334 9190"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      K(T(x,y) / T(z,T(x,y)),u) = K(z \ (x * K(y,x)),u)
    ]]></literal>
    <justification jstring="[hyper(8892,a,9191,a),flip(a)].">
      <j1 rule="hyper" parents="8892 9191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8891,a,9192,a),flip(a)].">
      <j1 rule="hyper" parents="8891 9192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(1583(a,1),9193(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1583 9193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,9194,a(flip),b,2608,a),flip(a)].">
      <j1 rule="hyper" parents="201 9194 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2611,a(flip),b,9195,a),flip(a)].">
      <j1 rule="hyper" parents="325 2611 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(1589(a,1),9196(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1589 9196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(2549(a,1),9196(a,1,2,2,1))].">
      <j1 rule="para" parents="2549 9196"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(8263,a,9197,a)].">
      <j1 rule="hyper" parents="8263 9197"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(2081(a,2),9199(a,2,2,2))].">
      <j1 rule="para" parents="2081 9199"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8931,a(flip),b,9198,a)].">
      <j1 rule="hyper" parents="65 8931 9198"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(2503(a,1),9201(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2503 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9203">
    <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(4288(a,1),9128(a,2,2))].">
      <j1 rule="para" parents="4288 9128"/>
    </justification>
  </clause>

  <clause id="9204">
    <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(3676(a,1),9203(a,1,2))].">
      <j1 rule="para" parents="3676 9203"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(4107(a,1),9204(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4107 9204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3812,a(flip),b,9205,a),flip(a)].">
      <j1 rule="hyper" parents="325 3812 9205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ w)))) = K(x,T(u / w,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8953,a(flip),b,9206,a)].">
      <j1 rule="hyper" parents="65 8953 9206"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      K(x,T(y,T(y,z) / z) \ (T(z,y) * (u / ((T(y,z) / z) \ w)))) = K(x,T(u / w,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(2521(a,1),9208(a,1,2,2,1))].">
      <j1 rule="para" parents="2521 9208"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      K(x,T(y / (K(z,u) * w),T(w,K(z,u)))) = K(x,(w * K(z,u)) \ T(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(113(a,1),9166(a,2,2,1))].">
      <j1 rule="para" parents="113 9166"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      ((x / y) \ 1) * L(((x / y) \ 1) \ z,u,w) = (y \ x) * L((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(2592(a,1),9173(a,1,2,1,1))].">
      <j1 rule="para" parents="2592 9173"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      (x / y) * L((x / y) \ z,u,w) = (y \ x) * L((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1338,a(flip),b,9211,a)].">
      <j1 rule="hyper" parents="65 1338 9211"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1323,a(flip),b,9212,a),flip(a)].">
      <j1 rule="hyper" parents="65 1323 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      (1 / x) \ (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8605,a(flip),b,9213,a)].">
      <j1 rule="hyper" parents="65 8605 9213"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(u,u,x * L(x,y,z)) = (x / u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8808,a,b,9214,a)].">
      <j1 rule="hyper" parents="65 8808 9214"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      (x * x) * (y \ L(y,z,u)) = x * ((y / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,9214,a(flip),b,652,a),flip(a)].">
      <j1 rule="hyper" parents="137 9214 652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (u * u) = u * ((x / u) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7829,a,b,9216,a)].">
      <j1 rule="hyper" parents="65 7829 9216"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      R(x,x,y * L(y,z,u)) * (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8473,a(flip),b,9215,a)].">
      <j1 rule="hyper" parents="65 8473 9215"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      T(x,(y \ z) * ((z \ u) * L((z \ u) \ w,v5,v6))) = T(x,(y \ u) * (u \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8833,a(flip),b,9177,a),flip(a)].">
      <j1 rule="hyper" parents="325 8833 9177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * (u * a(x,y,z))) / (u * (x \ R(x,y,z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2326(a,2),8399(a,1,1,2,2))].">
      <j1 rule="para" parents="2326 8399"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      L(a(x,y,z) * K(x \ R(x,y,z),u),u,x \ R(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8546,a(flip),b,9221,a)].">
      <j1 rule="hyper" parents="65 8546 9221"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      L(a(x,y,z) * 1,u,x \ R(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5053(a,1),9222(a,1,1,2))].">
      <j1 rule="para" parents="5053 9222"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      L(a(x,y,z),u,x \ R(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),9223(a,1,1))].">
      <j1 rule="para" parents="8 9223"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      L(a(x,y,z),u,x * R(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2367,a,9224,a)].">
      <j1 rule="hyper" parents="2367 9224"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      R(x,y,z) * L(x \ R(x,u,w),y,z) = R(((x * y) * z) / (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(5231(a,2),8596(a,1,2))].">
      <j1 rule="para" parents="5231 8596"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      R(x,y,z) * L(x \ R(x,u,w),y,z) = R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),9227(a,2,1))].">
      <j1 rule="para" parents="20 9227"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),u,w) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,9228,a)].">
      <j1 rule="hyper" parents="140 9228"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      L((x * x) * y,z,z) \ L((x * x) * (y * u),z,z) = L(L(u,y,z),z * y,(x * x) / z)
    ]]></literal>
    <justification jstring="[para(8670(a,1),8671(a,1,2))].">
      <j1 rule="para" parents="8670 8671"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      L(x,y,y) \ ((z * z) \ L((z * z) * (x * u),y,y)) = L(L(u,x,y),y * x,(z * z) / y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1331,a(flip),b,9230,a)].">
      <j1 rule="hyper" parents="65 1331 9230"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      L(x,y,y) \ ((z * z) * L((z * z) \ (x * u),y,y)) = L(L(u,x,y),y * x,(z * z) / y)
    ]]></literal>
    <justification jstring="[para(1322(a,1),9231(a,1,2))].">
      <j1 rule="para" parents="1322 9231"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      L(L(x,y,z),z * y,(u * u) / z) = L(y,z,z) \ L(y * x,z,z)
    ]]></literal>
    <justification jstring="[para(1307(a,1),9232(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1307 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      L(x,y,y) \ L(x * z,y,y) = L(L(z,x,y),y * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1572,a(flip),b,9233,a),flip(a)].">
      <j1 rule="hyper" parents="65 1572 9233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      L(L(x,y,y \ L(y,z,u)),(y \ L(y,z,u)) * y,y \ L(y,z,u)) = y \ L(y * x,y \ L(y,z,u),y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7012(a,1),9234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7012 9234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9237">
    <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(4661(a,1),9134(a,1,2,2,2))].">
      <j1 rule="para" parents="4661 9134"/>
    </justification>
  </clause>

  <clause id="9239">
    <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(3582(a,2),9237(a,1,2,2))].">
      <j1 rule="para" parents="3582 9237"/>
    </justification>
  </clause>

  <clause id="9242">
    <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(3768(a,1),9239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3768 9239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9244">
    <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(325,a,2752,a(flip),b,9242,a),flip(a)].">
      <j1 rule="hyper" parents="325 2752 9242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,8929,a(flip),b,9244,a)].">
      <j1 rule="hyper" parents="65 8929 9244"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(2801,a,9246,a),flip(a)].">
      <j1 rule="hyper" parents="2801 9246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9142,a,b,9248,a)].">
      <j1 rule="hyper" parents="65 9142 9248"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9200,a(flip),b,9249,a),flip(a)].">
      <j1 rule="hyper" parents="65 9200 9249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9199,a(flip),b,9250,a),flip(a)].">
      <j1 rule="hyper" parents="65 9199 9250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(82(a,1),9251(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="82 9251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(3329(a,1),9252(a,1,2,2))].">
      <j1 rule="para" parents="3329 9252"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      (((x * x) \ y) * x) \ L(((x * x) \ y) * x,z,u) = (y * (x \ 1)) \ L(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(885(a,1),8463(a,1,2,1))].">
      <j1 rule="para" parents="885 8463"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      (x * y) \ ((y * y) * L(((y * y) \ x) * y,z,u)) = (x * (y \ 1)) \ L(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,691,a(flip),b,9254,a)].">
      <j1 rule="hyper" parents="65 691 9254"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      (x * y) \ L((y * y) * (((y * y) \ x) * y),z,u) = (x * (y \ 1)) \ L(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(1311(a,2),9255(a,1,2))].">
      <j1 rule="para" parents="1311 9255"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      (x * (y \ 1)) \ L(x * (y \ 1),z,u) = (x * y) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(119(a,1),9256(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="119 9256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = ((x * y) \ L(x * y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9257(a,1),2015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9257 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = L(x * y,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2015,a(flip),b,9259,a),flip(a)].">
      <j1 rule="hyper" parents="325 2015 9259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(x \ (a(y,z,u) \ x),w,v5) = x * (a(y,z,u) \ L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(1310(a,1),8535(a,2,2))].">
      <j1 rule="para" parents="1310 8535"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ x),w,v5) * (x * a(y,z,u)) = x * (a(y,z,u) \ L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,8503,a,b,9261,a)].">
      <j1 rule="hyper" parents="65 8503 9261"/>
    </justification>
  </clause>

  <clause id="9263">
    <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),8952(a,1,2,1,2))].">
      <j1 rule="para" parents="12 8952"/>
    </justification>
  </clause>

  <clause id="9264">
    <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(65,a,9127,a(flip),b,9263,a),flip(a)].">
      <j1 rule="hyper" parents="65 9127 9263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9265">
    <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(65,a,9130,a(flip),b,9264,a)].">
      <j1 rule="hyper" parents="65 9130 9264"/>
    </justification>
  </clause>

  <clause id="9266">
    <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(65,a,9147,a(flip),b,9265,a)].">
      <j1 rule="hyper" parents="65 9147 9265"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(2094(a,2),9266(a,1,2,1))].">
      <j1 rule="para" parents="2094 9266"/>
    </justification>
  </clause>

  <clause id="9268">
    <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(2500(a,1),9267(a,1,2,1))].">
      <j1 rule="para" parents="2500 9267"/>
    </justification>
  </clause>

  <clause id="9269">
    <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(113(a,1),9268(a,1,2,2,1))].">
      <j1 rule="para" parents="113 9268"/>
    </justification>
  </clause>

  <clause id="9270">
    <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(113(a,1),9269(a,1,2,2,2,2))].">
      <j1 rule="para" parents="113 9269"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(3671(a,1),9270(a,2,2))].">
      <j1 rule="para" parents="3671 9270"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9202,a(flip),b,9271,a)].">
      <j1 rule="hyper" parents="65 9202 9271"/>
    </justification>
  </clause>

  <clause id="9274">
    <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(4357(a,1),9272(a,1,2,2,2))].">
      <j1 rule="para" parents="4357 9272"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ (T(z,y) * (u / ((T(y,z) / z) \ w)))) = K(x,T(u / w,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(4971(a,1),9209(a,1,2,1))].">
      <j1 rule="para" parents="4971 9209"/>
    </justification>
  </clause>

  <clause id="9276">
    <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(2521(a,1),9275(a,1,2,2,2,2))].">
      <j1 rule="para" parents="2521 9275"/>
    </justification>
  </clause>

  <clause id="9278">
    <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(65,a,9125,a(flip),b,9276,a)].">
      <j1 rule="hyper" parents="65 9125 9276"/>
    </justification>
  </clause>

  <clause id="9279">
    <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(8850(a,1),9278(a,2,2))].">
      <j1 rule="para" parents="8850 9278"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9202,a(flip),b,9279,a)].">
      <j1 rule="hyper" parents="65 9202 9279"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      (L(x \ 1,x,x \ y) \ L(((x \ y) * x) \ (x \ y),z,u)) * y = (y / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,156,a(flip),b,8509,a),flip(a)].">
      <j1 rule="hyper" parents="325 156 8509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      (L(x \ 1,x,x * y) \ L(((x \ y) * x) \ (x \ y),z,u)) * y = (y / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6611(a,1),9281(a,1,1,1))].">
      <j1 rule="para" parents="6611 9281"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      (L(x \ 1,x,x * y) \ L(L(x \ 1,x,x * y),z,u)) * y = (y / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6612(a,1),9284(a,1,1,2,1))].">
      <j1 rule="para" parents="6612 9284"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      L((x \ 1) \ L(x \ 1,y,z),x,x * u) * u = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4458(a,1),9285(a,1,1))].">
      <j1 rule="para" parents="4458 9285"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      L(x \ (1 * L(1 \ x,y,z)),x,x * u) * u = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1410(a,1),9286(a,1,1,1))].">
      <j1 rule="para" parents="1410 9286"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      L(x \ (1 * L(x,y,z)),x,x * u) * u = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(67(a,1),9287(a,1,1,1,2,2,1))].">
      <j1 rule="para" parents="67 9287"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * u) * u = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),9288(a,1,1,1,2))].">
      <j1 rule="para" parents="7 9288"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * u) = u \ ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,9289,a(flip),b,8478,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 9289 8478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * (z * y)) = (z * y) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[para(1728(a,1),9290(a,2,2))].">
      <j1 rule="para" parents="1728 9290"/>
    </justification>
  </clause>

  <clause id="9292">
    <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(65,a,8888,a(flip),b,9274,a)].">
      <j1 rule="hyper" parents="65 8888 9274"/>
    </justification>
  </clause>

  <clause id="9293">
    <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(7405(a,1),9292(a,1,2,2))].">
      <j1 rule="para" parents="7405 9292"/>
    </justification>
  </clause>

  <clause id="9294">
    <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(8915,a,9293,a),flip(a)].">
      <j1 rule="hyper" parents="8915 9293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,9096,a(flip),b,9294,a),flip(a)].">
      <j1 rule="hyper" parents="325 9096 9294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(3325(a,1),9295(a,1,2))].">
      <j1 rule="para" parents="3325 9295"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(3829,a,9296,a)].">
      <j1 rule="hyper" parents="3829 9296"/>
    </justification>
  </clause>

  <clause id="9298">
    <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(2280(a,1),9297(a,2,2,1))].">
      <j1 rule="para" parents="2280 9297"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      ((x / (y * y)) * (x * z)) \ ((((y * y) / x) \ 1) * u) = L((y * y) * z,x,x) \ (((y * y) / x) * u)
    ]]></literal>
    <justification jstring="[para(436(a,1),8672(a,1,1,1))].">
      <j1 rule="para" parents="436 8672"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      ((x / (y * y)) * (x * z)) \ ((x / (y * y)) * u) = L((y * y) * z,x,x) \ (((y * y) / x) * u)
    ]]></literal>
    <justification jstring="[para(436(a,1),9299(a,1,2,1))].">
      <j1 rule="para" parents="436 9299"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      (((x * x) \ y) * (y * z)) \ (((x * x) \ y) * u) = L((x * x) * z,y,y) \ (((x * x) / y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3460,a(flip),b,9300,a)].">
      <j1 rule="hyper" parents="65 3460 9300"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      (x * (x * y)) \ ((z * z) * (((z * z) \ x) * u)) = L((z * z) * y,x,x) \ (((z * z) / x) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,691,a(flip),b,9301,a)].">
      <j1 rule="hyper" parents="65 691 9301"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      L((x * x) * y,z,z) \ (((x * x) / z) * u) = (z * (z * y)) \ (z * u)
    ]]></literal>
    <justification jstring="[para(119(a,1),9302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="119 9302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      L(x,y,y) \ (((z * z) \ ((z * z) / y)) * u) = (y * (y * x)) \ (y * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1349,a(flip),b,9303,a)].">
      <j1 rule="hyper" parents="65 1349 9303"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      L(x,y,y) \ ((1 / y) * z) = (y * (y * x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(438(a,1),9304(a,1,2,1))].">
      <j1 rule="para" parents="438 9304"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      (x * (x * y)) \ (x * y) = R(T(1 / x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5543,a(flip),b,9306,a),flip(a)].">
      <j1 rule="hyper" parents="65 5543 9306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ ((1 / x) \ a(x,y,z)),u,w) = (x * a(x,y,z)) * (x \ (1 * L(1 \ x,u,w)))
    ]]></literal>
    <justification jstring="[para(8586(a,1),8539(a,2,2))].">
      <j1 rule="para" parents="8586 8539"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      L((x \ (y * ((y \ z) * (z \ x)))) \ u,x \ z,(x \ z) * L(x \ z,y \ z,y)) = (x \ z) * (L(x \ z,y \ z,y) \ u)
    ]]></literal>
    <justification jstring="[para(414(a,1),8969(a,1,1,1,2))].">
      <j1 rule="para" parents="414 8969"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      ((x \ 1) \ (x * (a(y,z,y) * (a(y,z,y) \ (x \ u))))) * w = a(y,z,y) * ((((x \ 1) * a(y,z,y)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(7635(a,1),9062(a,1,1,2,2,2))].">
      <j1 rule="para" parents="7635 9062"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ ((1 / x) \ a(x,y,z)),u,w) = (x * a(x,y,z)) * (x \ (1 * L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(67(a,1),9308(a,2,2,2,2,1))].">
      <j1 rule="para" parents="67 9308"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ ((1 / x) \ a(x,y,z)),u,w) = (x * a(x,y,z)) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7(a,1),9311(a,2,2,2))].">
      <j1 rule="para" parents="7 9311"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ ((1 / x) \ a(x,y,z)),u,w) = x * (a(x,y,z) * (x \ L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,7702,a(flip),b,9312,a),flip(a)].">
      <j1 rule="hyper" parents="325 7702 9312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ (x * a(x,y,z)),u,w) = x * (a(x,y,z) * (x \ L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(2405(a,1),9313(a,1,2,1,2))].">
      <j1 rule="para" parents="2405 9313"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      x * (a(x,y,z) * (x \ L(x,u,w))) = a(x,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(7193(a,1),9314(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7193 9314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      a(x,y,x) * ((((z \ 1) * a(x,y,x)) \ u) * w) = ((z \ 1) \ u) * w
    ]]></literal>
    <justification jstring="[para(78(a,1),9310(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="78 9310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      a(x,y,x) * (((z \ a(x,y,x)) \ u) * w) = ((z \ 1) \ u) * w
    ]]></literal>
    <justification jstring="[para(7600(a,1),9316(a,1,2,1,1))].">
      <j1 rule="para" parents="7600 9316"/>
    </justification>
  </clause>

  <clause id="9318">
    <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(6295(a,1),7646(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6295 7646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9319">
    <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(7637(a,1),9318(a,2,2))].">
      <j1 rule="para" parents="7637 9318"/>
    </justification>
  </clause>

  <clause id="9320">
    <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(325,a,20,a,b,9319,a),flip(a)].">
      <j1 rule="hyper" parents="325 20 9319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      R(x,y * (a(z,u,z) \ 1),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(7620(a,1),9320(a,1,1))].">
      <j1 rule="para" parents="7620 9320"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      R(x,y / a(z,u,z),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(6295(a,1),9321(a,1,2))].">
      <j1 rule="para" parents="6295 9321"/>
    </justification>
  </clause>

  <clause id="9323">
    <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),9322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 9322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      R(x,y * a(z,u,z),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7844,a(flip),b,9323,a)].">
      <j1 rule="hyper" parents="65 7844 9323"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      R(x,L(y,z,y),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(6242(a,1),9324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6242 9324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      R(R(T(1 / x,x * y),z,x),x,y) = (L(x,z,x) * y) \ (1 * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8959,a(flip),b,9326,a),flip(a)].">
      <j1 rule="hyper" parents="65 8959 9326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      R((x * y) \ (1 * y),z,x) = (L(x,z,x) * y) \ (1 * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,870,a(flip),b,9327,a)].">
      <j1 rule="hyper" parents="65 870 9327"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      (L(x,y,x) * z) \ (1 * z) = R((x * z) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),9329(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 9329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      R((x * y) \ y,z,x) = (L(x,z,x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(305,a,9330,a),flip(a)].">
      <j1 rule="hyper" parents="305 9330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      (x * K((y \ L(y,z,u)) \ 1,y \ L(y,z,u))) / (x * ((y \ L(y,z,u)) \ 1)) = (x * (1 / (y \ L(y,z,u)))) \ x
    ]]></literal>
    <justification jstring="[para(262(a,2),8620(a,1,1,2))].">
      <j1 rule="para" parents="262 8620"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      (x * 1) / (x * ((y \ L(y,z,u)) \ 1)) = (x * (1 / (y \ L(y,z,u)))) \ x
    ]]></literal>
    <justification jstring="[para(8482(a,1),9332(a,1,1,2))].">
      <j1 rule="para" parents="8482 9332"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      x / (x * ((y \ L(y,z,u)) \ 1)) = (x * (1 / (y \ L(y,z,u)))) \ x
    ]]></literal>
    <justification jstring="[para(8(a,1),9333(a,1,1))].">
      <j1 rule="para" parents="8 9333"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      x / (x * ((y \ L(y,z,u)) \ 1)) = (x * ((y \ L(y,z,u)) \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(8474(a,1),9334(a,2,1,2))].">
      <j1 rule="para" parents="8474 9334"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      (x * ((y \ L(y,z,u)) \ 1)) \ x = x \ (x / ((y \ L(y,z,u)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,8488,a(flip),b,9336,a),flip(a)].">
      <j1 rule="hyper" parents="65 8488 9336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9338">
    <literal><![CDATA[
      x \ (x / ((y \ L(y,z,u)) \ 1)) = (x * (L(y,z,u) \ y)) \ x
    ]]></literal>
    <justification jstring="[para(2015(a,1),9337(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2015 9337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ x = x \ (x / (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(2015(a,1),9338(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2015 9338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ x = x \ ((L(y,z,u) \ y) \ x)
    ]]></literal>
    <justification jstring="[para(7819(a,1),9339(a,2,2))].">
      <j1 rule="para" parents="7819 9339"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ x = x \ ((L(x,y,z) \ x) \ x)
    ]]></literal>
    <justification jstring="[para(4168(a,2),9340(a,1,1))].">
      <j1 rule="para" parents="4168 9340"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1779(a,1),9341(a,2,2))].">
      <j1 rule="para" parents="1779 9341"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) * (y \ L(y,z,u)) = T(L(1 / y,z,u) \ 1,x) \ y
    ]]></literal>
    <justification jstring="[hyper(137,a,9342,a(flip),b,4533,a)].">
      <j1 rule="hyper" parents="137 9342 4533"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      K(x,(1 / y) \ 1) * (y \ L(y,z,u)) = T(L(1 / y,z,u) \ 1,x) \ y
    ]]></literal>
    <justification jstring="[para(8867(a,1),9343(a,1,1))].">
      <j1 rule="para" parents="8867 9343"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      T(L(1 / x,y,z) \ 1,u) \ x = K(u,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(85(a,1),9344(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="85 9344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      T(L(1 / x,y,z) \ 1,u) \ x = T(x,u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,4526,a(flip),b,9345,a),flip(a)].">
      <j1 rule="hyper" parents="325 4526 9345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      x \ (T(x / (y \ 1),y) * R(T(x / (y \ 1),y) \ x,z,u)) = (x / (x * (y \ 1))) \ R(x / (x * (y \ 1)),z,u)
    ]]></literal>
    <justification jstring="[para(7420(a,1),7422(a,2,2,1))].">
      <j1 rule="para" parents="7420 7422"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      x \ (T(x / (y \ 1),y) * R(T(x / (y \ 1),y) \ x,z,u)) = (x * (y \ 1)) \ (x * R(x \ (x * (y \ 1)),z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,4241,a(flip),b,9348,a),flip(a)].">
      <j1 rule="hyper" parents="325 4241 9348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9350">
    <literal><![CDATA[
      x \ (T(x / (y \ 1),y) * R(T(x / (y \ 1),y) \ x,z,u)) = (x * (y \ 1)) \ (x * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9349(a,2,2,2,1))].">
      <j1 rule="para" parents="9 9349"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      x \ ((x / (y \ 1)) * R((x / (y \ 1)) \ x,z,u)) = (x * (y \ 1)) \ (x * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(4906(a,1),9350(a,1,2))].">
      <j1 rule="para" parents="4906 9350"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * R(y \ 1,z,u)) = x \ ((x / (y \ 1)) * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),9352(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="85 9352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * R(y \ 1,z,u)) = x \ (R(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(5542(a,1),9353(a,2,2))].">
      <j1 rule="para" parents="5542 9353"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      (x * y) \ (x * R((1 / y) \ 1,z,u)) = x \ (R(1 / y,z,u) * ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[para(85(a,1),9356(a,1,1,2))].">
      <j1 rule="para" parents="85 9356"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      x \ (R(1 / y,z,u) * ((1 / y) \ x)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),9357(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="85 9357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = x \ (R(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(1667(a,1),9358(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1667 9358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(543,a,9359,a)].">
      <j1 rule="hyper" parents="543 9359"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      L(x \ (R(y,z,u) * (y \ x)),y,u * z) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(9360(a,1),2346(a,1,1))].">
      <j1 rule="para" parents="9360 2346"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      L(((x \ y) \ L(x \ y,z,u)) \ w,(x \ y) \ L(x \ y,z,u),y / x) = L(y / x,z,u) \ ((y / x) * w)
    ]]></literal>
    <justification jstring="[para(8472(a,1),8590(a,1,1,1))].">
      <j1 rule="para" parents="8472 8590"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      L(((x \ y) \ L(x \ y,z,u)) \ w,(x \ y) \ L(x \ y,z,u),x \ y) = L(y / x,z,u) \ ((y / x) * w)
    ]]></literal>
    <justification jstring="[hyper(2351,a,9363,a)].">
      <j1 rule="hyper" parents="2351 9363"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      L(x / y,z,u) \ ((x / y) * w) = L(y \ x,z,u) \ ((y \ x) * w)
    ]]></literal>
    <justification jstring="[hyper(538,a,9364,a),flip(a)].">
      <j1 rule="hyper" parents="538 9364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      L(x \ y,z,u) \ ((x \ y) * w) = (y / x) * (L(y / x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(1265,a,9366,a),flip(a)].">
      <j1 rule="hyper" parents="1265 9366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9368">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ w) = (y \ x) * (L(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(1265,a,9367,a),flip(a)].">
      <j1 rule="hyper" parents="1265 9367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) = L(y / x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,1262,a(flip),b,9368,a),flip(a)].">
      <j1 rule="hyper" parents="65 1262 9368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (L(y / x,z,u) \ y) = v5
    ]]></literal>
    <justification jstring="[para(9369(a,2),533(a,1))].">
      <j1 rule="para" parents="9369 533"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      x \ ((x \ y) * (L(x \ y,z,u) \ x)) = (L(y / x,z,u) \ y) / x
    ]]></literal>
    <justification jstring="[para(9369(a,1),7839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9369 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) / y = y \ (L(x / y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(9369(a,1),9371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9369 9371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      L(L(x,y,y \ L(y,z,u)),(y \ L(y,z,u)) * y,y \ L(y,z,u)) = y \ L(y * x,y \ L(y,z,u),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1767(a,1),9236(a,2,2))].">
      <j1 rule="para" parents="1767 9236"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      L(((x \ y) * (y \ x)) \ z,x \ y,(x \ y) * L(x \ y,x \ y,x)) = (x \ y) * (L(x \ y,x \ y,x) \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9309(a,1,1,1))].">
      <j1 rule="para" parents="9 9309"/>
    </justification>
  </clause>

  <clause id="9375">
    <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(3674(a,1),9298(a,2,2,2))].">
      <j1 rule="para" parents="3674 9298"/>
    </justification>
  </clause>

  <clause id="9376">
    <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(3894(a,1),9375(a,2,2,2))].">
      <j1 rule="para" parents="3894 9375"/>
    </justification>
  </clause>

  <clause id="9377">
    <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(325,a,9253,a(flip),b,9376,a),flip(a)].">
      <j1 rule="hyper" parents="325 9253 9376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9378">
    <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(325,a,9132,a(flip),b,9377,a),flip(a)].">
      <j1 rule="hyper" parents="325 9132 9377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9379">
    <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(325,a,9147,a(flip),b,9378,a),flip(a)].">
      <j1 rule="hyper" parents="325 9147 9378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9380">
    <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(2094(a,2),9379(a,2,2,1))].">
      <j1 rule="para" parents="2094 9379"/>
    </justification>
  </clause>

  <clause id="9381">
    <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(325,a,9280,a(flip),b,9380,a),flip(a)].">
      <j1 rule="hyper" parents="325 9280 9380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9382">
    <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),9381(a,1,2,1,2))].">
      <j1 rule="para" parents="10 9381"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(2991(a,1),9382(a,1,2))].">
      <j1 rule="para" parents="2991 9382"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(7364(a,1),9383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7364 9383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(11(a,1),9384(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 9384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      K(x,T(y / z,(z / u) * z)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),9384(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="85 9384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(11(a,1),9385(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 9385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(3828,a,9387,a)].">
      <j1 rule="hyper" parents="3828 9387"/>
    </justification>
  </clause>

  <clause id="9390">
    <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(9387(a,1),3829(a,1))].">
      <j1 rule="para" parents="9387 3829"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(9388(a,1),3828(a,1))].">
      <j1 rule="para" parents="9388 3828"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      K(x,T(y / z,z * (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(8942(a,1),9386(a,1,2))].">
      <j1 rule="para" parents="8942 9386"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K(x,T(y / z,T(u,z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(9390,a,9393,a)].">
      <j1 rule="hyper" parents="9390 9393"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      K(x,T(y / z,u)) * K(z \ y,T(x,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9394(a,1),5672(a,1,1))].">
      <j1 rule="para" parents="9394 5672"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5278,a,9396,a)].">
      <j1 rule="hyper" parents="5278 9396"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(3807,a,9397,a)].">
      <j1 rule="hyper" parents="3807 9397"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      K(T(x,y),K(z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(3603,a,9397,a)].">
      <j1 rule="hyper" parents="3603 9397"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,9399,a(flip),b,3072,a),flip(a)].">
      <j1 rule="hyper" parents="137 9399 3072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      (x \ y) * K(x,K(z,u)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(4633,a,9404,a),flip(a)].">
      <j1 rule="hyper" parents="4633 9404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      T(x,K(K(y,z),u)) = x
    ]]></literal>
    <justification jstring="[hyper(2843,a,9404,a)].">
      <j1 rule="hyper" parents="2843 9404"/>
    </justification>
  </clause>

  <clause id="9407">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (w * u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,3871,a(flip),b,9404,a),flip(a)].">
      <j1 rule="hyper" parents="325 3871 9404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      K(K(x,y),K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,9404,a,b,3567,a),flip(a)].">
      <j1 rule="hyper" parents="131 9404 3567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,4108,a(flip),b,9404,a),flip(a)].">
      <j1 rule="hyper" parents="36 4108 9404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7386,a,9406,a),flip(a)].">
      <j1 rule="hyper" parents="7386 9406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(9406(a,1),7386(a,1))].">
      <j1 rule="para" parents="9406 7386"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9409,a)].">
      <j1 rule="hyper" parents="58 9409"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      T(K(x,y) * z,T(u,z)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(3830,a,9411,a)].">
      <j1 rule="hyper" parents="3830 9411"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      T(x,(y * (z / K(u,w))) / y) = T(x,(y * (K(u,w) \ z)) / y)
    ]]></literal>
    <justification jstring="[para(670(a,1),9411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="670 9411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(3842(a,1),9411(a,1,2))].">
      <j1 rule="para" parents="3842 9411"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      T(x,T(y,z / u)) = T(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(3941(a,1),9411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3941 9411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      T(x,T(y,z * u)) = T(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(7381(a,1),9411(a,1,2))].">
      <j1 rule="para" parents="7381 9411"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      K(x,T(y / (K(z,u) * w),w)) = K(x,(w * K(z,u)) \ T(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(9411(a,1),9210(a,1,2))].">
      <j1 rule="para" parents="9411 9210"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3668,a,9415,a),flip(a)].">
      <j1 rule="hyper" parents="3668 9415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3635,a(flip),b,9415,a)].">
      <j1 rule="hyper" parents="65 3635 9415"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(9415(a,1),3668(a,1))].">
      <j1 rule="para" parents="9415 3668"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(3941(a,1),9426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3941 9426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(9426(a,1),7398(a,1))].">
      <j1 rule="para" parents="9426 7398"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(7381(a,1),9436(a,1,2))].">
      <j1 rule="para" parents="7381 9436"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(K(z,u) * y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,9412,a(flip),b,2634,a(flip))].">
      <j1 rule="hyper" parents="201 9412 2634"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      ((x * K(y,z)) / T(u,K(y,z) * x)) * u = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9412(a,2),2503(a,1,1,2))].">
      <j1 rule="para" parents="9412 2503"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      T(x,(y \ z) * K(u,y)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[para(4526(a,1),9412(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4526 9412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) / T(y,K(u,w) * z) = (x * ((z * K(u,w)) * y)) / y
    ]]></literal>
    <justification jstring="[para(9412(a,2),6526(a,1,2))].">
      <j1 rule="para" parents="9412 6526"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      K(x,R((y \ 1) / z,z,y)) = K(x,(z * y) \ K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(500(a,2),9430(a,1,2))].">
      <j1 rule="para" parents="500 9430"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      K((x / y) / z,T(u,y \ x)) = K(z \ (x / y),u)
    ]]></literal>
    <justification jstring="[hyper(3265,a,9443,a),flip(a)].">
      <j1 rule="hyper" parents="3265 9443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      T(K(x,y) * z,T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(9416(a,1),3672(a,1))].">
      <j1 rule="para" parents="9416 3672"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9090,a(flip),b,9451,a),flip(a)].">
      <j1 rule="hyper" parents="65 9090 9451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      K((x \ y) * K(x,z),u) = K(T(x,z) \ y,u)
    ]]></literal>
    <justification jstring="[para(4526(a,1),9458(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4526 9458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      K((T(x,y) \ z) * K(y,x),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(4532(a,1),9458(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4532 9458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      K(x / (y * z),T(u,z \ x)) = K(y \ (x / z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2997,a(flip),b,9456,a)].">
      <j1 rule="hyper" parents="65 2997 9456"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      (K(x,1 / K(y,z)) * u) * T(w,u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8622,a(flip),b,9407,a)].">
      <j1 rule="hyper" parents="65 8622 9407"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      K(x,(y * z) \ K(z \ 1,z)) = K(x,(z \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(3002,a,9455,a),flip(a)].">
      <j1 rule="hyper" parents="3002 9455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      K(x,(y \ 1) / z) = K(x,(z * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,3396,a(flip),b,9464,a),flip(a)].">
      <j1 rule="hyper" parents="65 3396 9464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      K(x,(R(1 / y,z,u) * (w * (R(1 / y,z,u) \ 1))) / R(y \ 1,z,u)) = K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,7117,a,b,9465,a)].">
      <j1 rule="hyper" parents="65 7117 9465"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      T(x,(y * (z / K(u,w))) / y) = T(x,(y * (K(w,u) * z)) / y)
    ]]></literal>
    <justification jstring="[para(2618(a,1),9419(a,2,2,1,2))].">
      <j1 rule="para" parents="2618 9419"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      (x / (T(y,K(z,u) * x) * K(u,z))) * y = T(x * K(z,u),y)
    ]]></literal>
    <justification jstring="[para(8295(a,1),9452(a,1,1))].">
      <j1 rule="para" parents="8295 9452"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * T(w,u) = w * (u * K(x,K(z,y)))
    ]]></literal>
    <justification jstring="[para(2611(a,1),9462(a,1,1,1,2))].">
      <j1 rule="para" parents="2611 9462"/>
    </justification>
  </clause>

  <clause id="9472">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * T(w,u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(3594(a,1),9471(a,1,1,1))].">
      <j1 rule="para" parents="3594 9471"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,T(w,u)) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(245,a,9472,a,b,4514,a)].">
      <j1 rule="hyper" parents="245 9472 4514"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9457,a,9473,a)].">
      <j1 rule="hyper" parents="9457 9473"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9404(a,1),9474(a,1,1))].">
      <j1 rule="para" parents="9404 9474"/>
    </justification>
  </clause>

  <clause id="9476">
    <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(9475(a,1),2866(a,1,1,2))].">
      <j1 rule="para" parents="9475 2866"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      T(x,(y * (z / K(u,w))) / y) = T(x,T(K(w,u) * z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3675,a(flip),b,9468,a),flip(a)].">
      <j1 rule="hyper" parents="325 3675 9468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      T(x,(y * (z * K(u,w))) / y) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[para(2848(a,1),9477(a,1,2,1,2))].">
      <j1 rule="para" parents="2848 9477"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      T(x,(y * z) / (y * K(u,w))) = T(x,T(K(w,u) * z,y))
    ]]></literal>
    <justification jstring="[para(8349(a,1),9478(a,1,2))].">
      <j1 rule="para" parents="8349 9478"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ T(w * (K(z,u) * y),K(z,u))) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[para(11(a,1),9425(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 9425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      K(x,((K(y,z) \ u) * K(y,z)) \ T(w * u,K(y,z))) = K(x,T(w,K(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9481(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10 9481"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      (x * (y * z)) / (T(y,K(u,w) * z) * K(w,u)) = (x * ((z * K(u,w)) * y)) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,8426,a(flip),b,9454,a)].">
      <j1 rule="hyper" parents="65 8426 9454"/>
    </justification>
  </clause>

  <clause id="9484">
    <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="[hyper(65,a,8934,a(flip),b,9482,a)].">
      <j1 rule="hyper" parents="65 8934 9482"/>
    </justification>
  </clause>

  <clause id="9485">
    <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(2618(a,1),9484(a,2,2,2))].">
      <j1 rule="para" parents="2618 9484"/>
    </justification>
  </clause>

  <clause id="9486">
    <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(65,a,6119,a(flip),b,9476,a)].">
      <j1 rule="hyper" parents="65 6119 9476"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      K(x,L(y,K(z,K(u,w)),v5)) = K(x,y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(9436,a,9486,a)].">
      <j1 rule="hyper" parents="9436 9486"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8042,a,9487,a),flip(a)].">
      <j1 rule="hyper" parents="8042 9487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(9445,a,9488,a)].">
      <j1 rule="hyper" parents="9445 9488"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(1230(a,1),9488(a,1,2))].">
      <j1 rule="para" parents="1230 9488"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(9405(a,1),9488(a,1,2))].">
      <j1 rule="para" parents="9405 9488"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      ((K(x,K(y,z)) * u) * K(w,u)) * w = w * (K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(9490(a,1),1585(a,1,1,2))].">
      <j1 rule="para" parents="9490 1585"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      K(x,y \ T(z * y,K(u,w))) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9485,a(flip),b,9493,a),flip(a)].">
      <j1 rule="hyper" parents="65 9485 9493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      K(x,T(y * z,K(u,w)) / y) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(5162,a,9496,a)].">
      <j1 rule="hyper" parents="5162 9496"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,(w * y) / w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9492,a(flip),b,9497,a),flip(a)].">
      <j1 rule="hyper" parents="65 9492 9497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,3652,a(flip),b,9499,a),flip(a)].">
      <j1 rule="hyper" parents="325 3652 9499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9502">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9450,a,9501,a)].">
      <j1 rule="hyper" parents="9450 9501"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      K(x,T(y,z / K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9502(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      T(x,T(y,z / K(u,w))) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,9507,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 9507 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      T(x,T(y,z / K(u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,9510,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 9510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9421,a(flip),b,9511,a)].">
      <j1 rule="hyper" parents="65 9421 9511"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w))) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(3735(a,1),9512(a,1,2,2))].">
      <j1 rule="para" parents="3735 9512"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(245,a,9494,a(flip),b,2082,a(flip))].">
      <j1 rule="hyper" parents="245 9494 2082"/>
    </justification>
  </clause>

  <clause id="9515">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * K(w,u))) * w = w * (K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(287(a,1),9494(a,1,1))].">
      <j1 rule="para" parents="287 9494"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,(u * K(y,z)) / w)
    ]]></literal>
    <justification jstring="[para(2495(a,1),9514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2495 9514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9518">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[para(8295(a,1),9516(a,2,2))].">
      <j1 rule="para" parents="8295 9516"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,K(w,u) * (y / z))
    ]]></literal>
    <justification jstring="[para(666(a,1),9518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="666 9518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * w) / u)) = T(x,T(K(y,z) * w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9479,a(flip),b,9519,a),flip(a)].">
      <j1 rule="hyper" parents="65 9479 9519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9092,a(flip),b,9520,a),flip(a)].">
      <j1 rule="hyper" parents="65 9092 9520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u * (z / y)) / u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(2554(a,1),9520(a,2,2,1))].">
      <j1 rule="para" parents="2554 9520"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      T(x,T(K(y,z) * x,u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7741,a(flip),b,9521,a),flip(a)].">
      <j1 rule="hyper" parents="325 7741 9521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      K(x,K(y,z)) * ((u * K(w,u)) * w) = w * (K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(667,a,9515,a)].">
      <j1 rule="hyper" parents="667 9515"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * (y / z)) / u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9114,a(flip),b,9522,a)].">
      <j1 rule="hyper" parents="65 9114 9522"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      T(x,T(K(y,z) * (y / z),u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9520,a(flip),b,9525,a)].">
      <j1 rule="hyper" parents="65 9520 9525"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      T(x,T(T(y,z) / z,u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(2127(a,1),9526(a,1,2,1))].">
      <j1 rule="para" parents="2127 9526"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(1585(a,1),9524(a,1,2))].">
      <j1 rule="para" parents="1585 9524"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      K(x,y) * (z * (K(x,K(y,u)) * w)) = K(x,T(y,u)) * (z * w)
    ]]></literal>
    <justification jstring="[para(9528(a,1),3708(a,1,2))].">
      <j1 rule="para" parents="9528 3708"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      K(x,y) * ((z / T(u,z)) * (K(x,K(y,w)) * u)) = K(x,T(y,w)) * T(z,u)
    ]]></literal>
    <justification jstring="[para(2503(a,1),9529(a,2,2))].">
      <j1 rule="para" parents="2503 9529"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      K(x,((1 / y) * (z * (R(1 / y,u,w) \ 1))) / (y \ 1)) = K(x,((R(y \ 1,u,w) / (z / (y \ 1))) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(5632(a,1),9467(a,1,2))].">
      <j1 rule="para" parents="5632 9467"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,((1 / y) * (w * (R(1 / y,z,u) \ 1))) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3422,a(flip),b,9531,a),flip(a)].">
      <j1 rule="hyper" parents="65 3422 9531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w * (R(1 / y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(325,a,4327,a(flip),b,9532,a),flip(a)].">
      <j1 rule="hyper" parents="325 4327 9532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(1 / y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2963,a(flip),b,9534,a),flip(a)].">
      <j1 rule="hyper" parents="325 2963 9534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(T(x,y \ 1),w / R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,3452,a(flip),b,9535,a),flip(a)].">
      <j1 rule="hyper" parents="325 3452 9535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,T(w / R(y \ 1,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(325,a,3813,a(flip),b,9536,a),flip(a)].">
      <j1 rule="hyper" parents="325 3813 9536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      K(x,((R(y \ 1,z,u) / (w / (y \ 1))) * y) \ 1) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,3819,a(flip),b,9537,a),flip(a)].">
      <j1 rule="hyper" parents="325 3819 9537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,R(z \ 1,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5660,a(flip),b,9538,a)].">
      <j1 rule="hyper" parents="65 5660 9538"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,R(z \ 1,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5356,a(flip),b,9539,a)].">
      <j1 rule="hyper" parents="65 5356 9539"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(7398,a,9541,a),flip(a)].">
      <j1 rule="hyper" parents="7398 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      K(x,R(y,z,u) \ w) = K(x,T(((y \ 1) \ 1) \ 1,y) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5773,a(flip),b,9542,a)].">
      <j1 rule="hyper" parents="65 5773 9542"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      K(x,R(y,z,u) \ w) = K(x,T(y \ 1,y) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,3880,a(flip),b,9543,a),flip(a)].">
      <j1 rule="hyper" parents="325 3880 9543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      K(x,R(y,z,u) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,7340,a(flip),b,9545,a),flip(a)].">
      <j1 rule="hyper" parents="325 7340 9545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      K(x,((y * (z \ u)) / u) \ w) = K(x,(y / z) \ w)
    ]]></literal>
    <justification jstring="[para(496(a,1),9546(a,1,2,1))].">
      <j1 rule="para" parents="496 9546"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      a(x,K(y,z),u) = K(y,z) * K(z,(x / y) \ x)
    ]]></literal>
    <justification jstring="[para(9552(a,1),7557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9552 7557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      a(x,K(y,z),u) = K(y,z) * K(z,y)
    ]]></literal>
    <justification jstring="[para(85(a,1),9553(a,2,2,2))].">
      <j1 rule="para" parents="85 9553"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      a(x,K(y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,2613,a(flip),b,9554,a),flip(a)].">
      <j1 rule="hyper" parents="325 2613 9554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      L(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,9556,a)].">
      <j1 rule="hyper" parents="54 9556"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      (x * K(y,z)) * u = x * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(989,a,9558,a),flip(a)].">
      <j1 rule="hyper" parents="989 9558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      (x * K(y,z)) \ u = K(z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,2679,a(flip),b,9558,a)].">
      <j1 rule="hyper" parents="65 2679 9558"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      x / (K(y,z) \ u) = (x / u) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,9558,a(flip),b,4196,a(flip))].">
      <j1 rule="hyper" parents="201 9558 4196"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,9558,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="201 9558 18"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * u) = K(y,z) * u
    ]]></literal>
    <justification jstring="[hyper(137,a,448,a(flip),b,9558,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 448 9558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      K(x,y) * ((z * K(x,y)) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(137,a,308,a(flip),b,9558,a(flip))].">
      <j1 rule="hyper" parents="137 308 9558"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      (x / K(y,z)) \ u = K(y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(39,a,867,a(flip),b,9558,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 867 9558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(9558(a,1),52(a,2))].">
      <j1 rule="para" parents="9558 52"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      (x * K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(9558(a,1),298(a,1,2))].">
      <j1 rule="para" parents="9558 298"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,L(u,K(y,z),x),x * K(y,z))
    ]]></literal>
    <justification jstring="[para(9558(a,1),450(a,1,2,2,1))].">
      <j1 rule="para" parents="9558 450"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      x \ (y * (K(z,u) * x)) = T(y * K(z,u),x)
    ]]></literal>
    <justification jstring="[para(9558(a,1),7414(a,1,1))].">
      <j1 rule="para" parents="9558 7414"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      (x * K(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(2679(a,1),9573(a,1))].">
      <j1 rule="para" parents="2679 9573"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      R(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(1062,a,9559,a)].">
      <j1 rule="hyper" parents="1062 9559"/>
    </justification>
  </clause>

  <clause id="9581">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3727,a,b,9559,a)].">
      <j1 rule="hyper" parents="65 3727 9559"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,3664,a,b,9559,a)].">
      <j1 rule="hyper" parents="65 3664 9559"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      ((x * (y * K(z,u))) * w) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(201,a,9559,a(flip),b,192,a)].">
      <j1 rule="hyper" parents="201 9559 192"/>
    </justification>
  </clause>

  <clause id="9584">
    <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(9559(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9559 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9585">
    <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(9559(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9559 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      (x * y) * (K(y,z) * u) = (x * T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(2093(a,1),9559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2093 9559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9591">
    <literal><![CDATA[
      (x * y) * (K(z,z \ y) * u) = (x * (z * (y / z))) * u
    ]]></literal>
    <justification jstring="[para(6523(a,1),9559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6523 9559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * u) = (x \ T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6670(a,1),9559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6670 9559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      (x \ 1) * (K(y,z) * u) = (x \ K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7528(a,1),9559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7528 9559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(7899(a,1),9559(a,1,1))].">
      <j1 rule="para" parents="7899 9559"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      (x * (y \ (y \ K(z,u)))) * w = (x / (y * y)) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(8435(a,1),9559(a,1,1))].">
      <j1 rule="para" parents="8435 9559"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * v5 = L(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(8545(a,2),9559(a,1,1))].">
      <j1 rule="para" parents="8545 9559"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      x / (K(y,z) * u) = (x / u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(2863,a,9580,a)].">
      <j1 rule="hyper" parents="2863 9580"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3622,a(flip),b,9580,a)].">
      <j1 rule="hyper" parents="65 3622 9580"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      K(x,y) * (z \ (K(y,x) * u)) = T(z,K(y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,675,a(flip),b,9566,a),flip(a)].">
      <j1 rule="hyper" parents="65 675 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      K(x,y) * ((z * y) \ u) = (z * T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(2093(a,1),9566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2093 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = (K(y,x) * z) \ u
    ]]></literal>
    <justification jstring="[para(3075(a,1),9566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3075 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ u) = (z \ T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(6670(a,1),9566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6670 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ u) = (z \ K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(7528(a,1),9566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7528 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ w = K(u,z) * ((x * y) \ w)
    ]]></literal>
    <justification jstring="[para(7899(a,1),9566(a,1,1))].">
      <j1 rule="para" parents="7899 9566"/>
    </justification>
  </clause>

  <clause id="9612">
    <literal><![CDATA[
      K(x,y) * ((z \ (u * y)) \ w) = (z \ (u * T(y,x))) \ w
    ]]></literal>
    <justification jstring="[para(8305(a,1),9566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8305 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      L(x * K(y,z),u,w) \ v5 = K(z,y) * (L(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(8545(a,2),9566(a,1,1))].">
      <j1 rule="para" parents="8545 9566"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      x / L(K(y,z) * (u \ x),w,v5) = L((x * K(y,z)) / u,w,v5) \ x
    ]]></literal>
    <justification jstring="[para(9566(a,1),8347(a,1,2,1))].">
      <j1 rule="para" parents="9566 8347"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      (x / (y * z)) * K(u,y) = x / (T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(2647(a,1),9567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2647 9567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      L(x,x,y * (K(z,u) * (x \ 1))) = (y * (K(z,u) * (x \ 1))) \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,9568,a(flip),b,1720,a),flip(a)].">
      <j1 rule="hyper" parents="132 9568 1720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      (x * ((K(y,z) * u) * u)) / u = (x * K(y,z)) * L(u,K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(9568(a,1),1728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9568 1728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      (x \ K(y,z)) \ ((x \ 1) * u) = K(z,y) * u
    ]]></literal>
    <justification jstring="[para(7531(a,1),9569(a,1,2,1))].">
      <j1 rule="para" parents="7531 9569"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,v5)) = (x / a(y,z,u)) * K(v5,w)
    ]]></literal>
    <justification jstring="[para(7190(a,2),9597(a,1,2))].">
      <j1 rule="para" parents="7190 9597"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      x / L(K(y,z) * u,w,v5) = (x / L(u,w,v5)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(8549(a,2),9597(a,1,2))].">
      <j1 rule="para" parents="8549 9597"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(3625,a,9599,a)].">
      <j1 rule="hyper" parents="3625 9599"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      T(x,K(y,z) * u) * K(z,y) = K(z,y) * T(x,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,9599,a(flip),b,3628,a)].">
      <j1 rule="hyper" parents="136 9599 3628"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) * K(y,z) = T(y,K(u,x) * z) / y
    ]]></literal>
    <justification jstring="[para(9599(a,1),3613(a,2,1))].">
      <j1 rule="para" parents="9599 3613"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y) * u) = T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(2842(a,1),9622(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2842 9622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * T(x,K(y,z))) = T(u * K(z,y),x * K(y,z))
    ]]></literal>
    <justification jstring="[para(2658(a,1),9578(a,1,2,2))].">
      <j1 rule="para" parents="2658 9578"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      x \ K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(421,a,9582,a)].">
      <j1 rule="hyper" parents="421 9582"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * u) * w) = (z * (K(x,y) * u)) * w
    ]]></literal>
    <justification jstring="[hyper(136,a,9582,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 9582 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9632">
    <literal><![CDATA[
      L(x,y,(z * T(u,w)) * v5) = L(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(9586(a,1),3507(a,1,3))].">
      <j1 rule="para" parents="9586 3507"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      (x * T(y,z)) * (T(y,z) \ u) = (x * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(4532(a,1),9586(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4532 9586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      R(x,y,(z \ T(u,w)) * v5) = R(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(9592(a,1),8707(a,1,3))].">
      <j1 rule="para" parents="9592 8707"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      L(K(x,y) * z,u \ 1,u) = u * ((u \ K(x,y)) * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,9593,a(flip),b,389,a),flip(a)].">
      <j1 rule="hyper" parents="137 9593 389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ u) = x * ((z * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(137,a,9607,a(flip),b,4507,a)].">
      <j1 rule="hyper" parents="137 9607 4507"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      T(x,y) \ ((z * x) \ u) = x \ ((z * T(x,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,9607,a(flip),b,2652,a),flip(a)].">
      <j1 rule="hyper" parents="132 9607 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      L(x,y,(z * T(u,w)) \ v5) = L(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(9607(a,1),1541(a,1,3))].">
      <j1 rule="para" parents="9607 1541"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      a((x * T(y,z)) \ u,w,v5) = a((x * y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(9607(a,1),1865(a,1,1))].">
      <j1 rule="para" parents="9607 1865"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y / (x \ 1)) / y) = x * ((T(y,x) * T(x,y)) \ y)
    ]]></literal>
    <justification jstring="[para(9607(a,1),4608(a,2,2))].">
      <j1 rule="para" parents="9607 4608"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      (x * T(y,z)) \ ((y * x) * u) = K(z,y) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(6156(a,1),9607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6156 9607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      R(x,y,(z * T(u,w)) \ v5) = R(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(9607(a,1),8689(a,1,3))].">
      <j1 rule="para" parents="9607 8689"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2674,a(flip),b,9608,a),flip(a)].">
      <j1 rule="hyper" parents="325 2674 9608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      L(x,y,(z \ K(u,w)) \ v5) = L(x,y,(z \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(9610(a,1),1541(a,1,3))].">
      <j1 rule="para" parents="9610 1541"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ K(x \ y,x)) \ z) = y * ((((x \ y) \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(9610(a,1),4579(a,1,2))].">
      <j1 rule="para" parents="9610 4579"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      (x / (T(y,z) * u)) * T(y,z) = (x / (y * u)) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,9615,a(flip),b,2877,a)].">
      <j1 rule="hyper" parents="136 9615 2877"/>
    </justification>
  </clause>

  <clause id="9647">
    <literal><![CDATA[
      (x \ K(y,z)) * (K(z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * u = w
    ]]></literal>
    <justification jstring="[para(9618(a,1),259(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9618 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      x \ (K(y,z) * (x * u)) = K(y,T(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(520,a,9643,a),flip(a)].">
      <j1 rule="hyper" parents="520 9643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ u) * w) = (z \ (K(x,y) * u)) * w
    ]]></literal>
    <justification jstring="[hyper(136,a,9643,a(flip),b,419,a),flip(a)].">
      <j1 rule="hyper" parents="136 9643 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      R(x,y,z * (u \ (K(w,v5) * v6))) = R(x,y,(u \ v6) * z)
    ]]></literal>
    <justification jstring="[para(9643(a,1),8732(a,1,3,2))].">
      <j1 rule="para" parents="9643 8732"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      x * K(y,T(z,u * x)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,8285,a(flip),b,9648,a)].">
      <j1 rule="hyper" parents="65 8285 9648"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      K(x / y,T(z,u * x)) = K(y \ x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(2226,a,9651,a)].">
      <j1 rule="hyper" parents="2226 9651"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(36,a,3106,a,b,9651,a)].">
      <j1 rule="hyper" parents="36 3106 9651"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      K(x,T(y / z,y * u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4869,a(flip),b,9653,a),flip(a)].">
      <j1 rule="hyper" parents="65 4869 9653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      K(x / y,T(z,u \ x)) = K(y \ x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(9392,a,9652,a)].">
      <j1 rule="hyper" parents="9392 9652"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      K(x,(y * z) \ (u * z)) = K(x,T(y \ u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,3487,a(flip),b,9654,a)].">
      <j1 rule="hyper" parents="65 3487 9654"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      T(x,T(y / z,y * u)) = x * K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,9654,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 9654 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9461,a(flip),b,9655,a),flip(a)].">
      <j1 rule="hyper" parents="65 9461 9655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      K(x,y \ (z \ (u * y))) = K(x,T(z \ u,y))
    ]]></literal>
    <justification jstring="[hyper(8262,a,9656,a)].">
      <j1 rule="hyper" parents="8262 9656"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      K((x \ y) / z,u) = K(x \ (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(8270,a,9658,a)].">
      <j1 rule="hyper" parents="8270 9658"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      K((x \ (y * z)) / z,u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),9660(a,2,1,2))].">
      <j1 rule="para" parents="11 9660"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      T(x,y \ (z \ (u * y))) = x * K(x,T(z \ u,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,9659,a(flip),b,2104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 9659 2104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,z) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(2838(a,1),9581(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2838 9581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(3617(a,1),9581(a,1,2,1))].">
      <j1 rule="para" parents="3617 9581"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * (K(u,z) * w) = (x * (y \ 1)) * w
    ]]></literal>
    <justification jstring="[para(7531(a,1),9594(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7531 9594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      K(x,y) * (z \ ((T(y,x) * u) * w)) = T(z,K(y,x)) \ ((y * u) * w)
    ]]></literal>
    <justification jstring="[para(2186(a,1),9606(a,1,2,2))].">
      <j1 rule="para" parents="2186 9606"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      T(x,K(y,z)) \ ((z * y) * u) = K(z,y) * (x \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(2488(a,1),9606(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2488 9606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      K(x,x \ (y \ z)) * ((y * x) \ z) = L((y \ z) / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6890,a(flip),b,9611,a),flip(a)].">
      <j1 rule="hyper" parents="65 6890 9611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      K(x,y) * ((z * K(u,u \ K(x,y))) \ w) = (z * (((u \ K(x,y)) * u) \ 1)) \ w
    ]]></literal>
    <justification jstring="[para(2903(a,1),9611(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2903 9611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      K(x,y) * ((y * x) \ z) = (T(y,x) * x) \ z
    ]]></literal>
    <justification jstring="[para(3973(a,1),9611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3973 9611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      K(x,y) * ((z * (u \ 1)) \ w) = (z * (u \ K(y,x))) \ w
    ]]></literal>
    <justification jstring="[para(7528(a,1),9611(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7528 9611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      T(x,K(y,z) * ((y * z) \ u)) = T(x,(T(y,z) * z) \ u)
    ]]></literal>
    <justification jstring="[para(9674(a,1),9075(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9674 9075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9677">
    <literal><![CDATA[
      (x / (K(y,z) * T(u,x))) * u = T(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(9624(a,1),9469(a,1,1,2))].">
      <j1 rule="para" parents="9624 9469"/>
    </justification>
  </clause>

  <clause id="9678">
    <literal><![CDATA[
      (x * (y * z)) / (K(u,w) * T(y,z)) = (x * ((z * K(w,u)) * y)) / y
    ]]></literal>
    <justification jstring="[para(9624(a,1),9483(a,1,2))].">
      <j1 rule="para" parents="9624 9483"/>
    </justification>
  </clause>

  <clause id="9679">
    <literal><![CDATA[
      T(x * K(y,z),u * K(z,y)) = T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(9414,a,9626,a)].">
      <j1 rule="hyper" parents="9414 9626"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      (x * (y \ z)) * (T(z / y,y) \ u) = (x * (z / y)) * ((z / y) \ u)
    ]]></literal>
    <justification jstring="[para(115(a,1),9633(a,1,1,2))].">
      <j1 rule="para" parents="115 9633"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      R(x,y,(z \ (u / w)) * v5) = R(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),9634(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="115 9634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      (x \ y) * ((z * T(y / x,x)) \ u) = (y / x) * ((z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(115(a,1),9636(a,1,1))].">
      <j1 rule="para" parents="115 9636"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      a(x * (y \ ((z * T(y,T(u,z))) \ T(y,T(u,z)))),w,v5) = a(x * L(z * y,z * y,y),w,v5)
    ]]></literal>
    <justification jstring="[para(9637(a,1),7867(a,1,1,2))].">
      <j1 rule="para" parents="9637 7867"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      a(((x * x) * T(T(y,x * x) * z,u)) \ w,v5,v6) = a(((y * (x * x)) * z) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(244(a,1),9639(a,2,1,1))].">
      <j1 rule="para" parents="244 9639"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      R(x,y,(z * R(u \ w,u,u)) \ v5) = R(x,y,(z * (w * (u \ 1))) \ v5)
    ]]></literal>
    <justification jstring="[para(618(a,1),9642(a,1,3,1,2))].">
      <j1 rule="para" parents="618 9642"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      R(x,y,((z * z) * T(u * (w * (z \ 1)),v5)) \ v6) = R(x,y,T(u * (w * z),z \ (z \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[para(943(a,2),9642(a,2,3,1))].">
      <j1 rule="para" parents="943 9642"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      L(x,y,(z \ K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,5127,a(flip),b,9644,a),flip(a)].">
      <j1 rule="hyper" parents="325 5127 9644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      R(x,y,z \ R(T(z,u),T(z,u),w)) = R(x,y,(w / (z * w)) * z)
    ]]></literal>
    <justification jstring="[para(9646(a,1),8716(a,2,3))].">
      <j1 rule="para" parents="9646 8716"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      T(x,T(y / z,y * u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,9657,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 9657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      T(x,T(y / z,u * y)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9424,a,b,9689,a)].">
      <j1 rule="hyper" parents="65 9424 9689"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      T(x,T(y \ z,z \ u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9689(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      T(x,T(y \ (z * y),u)) = T(x,T(z,(z * y) * u))
    ]]></literal>
    <justification jstring="[para(11(a,1),9689(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 9689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      T(x,T(T(y,z) / z,u * y)) = T(x,T(T(z,y) \ y,u))
    ]]></literal>
    <justification jstring="[para(2519(a,2),9690(a,1,2,1))].">
      <j1 rule="para" parents="2519 9690"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      T(x,T(y \ (z * u),u \ w)) = T(x,T(u / (z \ y),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,7976,a(flip),b,9691,a)].">
      <j1 rule="hyper" parents="65 7976 9691"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      T(x,T(y \ (z * u),u \ w)) = T(x,T((z * u) / y,z * w))
    ]]></literal>
    <justification jstring="[para(7972(a,1),9691(a,1,2))].">
      <j1 rule="para" parents="7972 9691"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      T(x,y \ (z \ (u * y))) = T(x,T(z \ u,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,2094,a,b,9664,a),flip(a)].">
      <j1 rule="hyper" parents="325 2094 9664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      T(x,(y * z) \ (u * z)) = T(x,T(y \ u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7973,a,b,9697,a)].">
      <j1 rule="hyper" parents="65 7973 9697"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      T(x,T(y / z,y * u)) = T(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,9689,a,b,9698,a)].">
      <j1 rule="hyper" parents="325 9689 9698"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ T(z,K(x,y)) = (z * (K(x,y) * u)) \ z
    ]]></literal>
    <justification jstring="[para(9667(a,1),2264(a,1,1))].">
      <j1 rule="para" parents="9667 2264"/>
    </justification>
  </clause>

  <clause id="9702">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (T(z,K(x,y)) * w) = (z * (K(x,y) * u)) \ (z * w)
    ]]></literal>
    <justification jstring="[para(9667(a,1),2265(a,1,1))].">
      <j1 rule="para" parents="9667 2265"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (K(y,z) * w) = (T(x,K(y,z)) * u) \ w
    ]]></literal>
    <justification jstring="[para(9668(a,1),470(a,1,1))].">
      <j1 rule="para" parents="9668 470"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      ((x / T(y,x)) * K(z,u)) * y = T(x * K(z,u),y)
    ]]></literal>
    <justification jstring="[para(9597(a,1),9677(a,1,1))].">
      <j1 rule="para" parents="9597 9677"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      T(x,T(y \ (z * y),u)) = T(x,T(z,y * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8862,a(flip),b,9692,a),flip(a)].">
      <j1 rule="hyper" parents="325 8862 9692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      T(x,T(T(y,z),u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(22(a,2),9705(a,1,2,1))].">
      <j1 rule="para" parents="22 9705"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      T(x,T(T(y,z),z * u)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3831,a(flip),b,9706,a),flip(a)].">
      <j1 rule="hyper" parents="65 3831 9706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      T(x,T(T(y,z),u * z)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9424,a,b,9707,a)].">
      <j1 rule="hyper" parents="65 9424 9707"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      T(x,T(y,z * (z * u))) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9706,a(flip),b,9707,a)].">
      <j1 rule="hyper" parents="65 9706 9707"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      T(x,T(y * z,y * u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7401,a(flip),b,9707,a)].">
      <j1 rule="hyper" parents="65 7401 9707"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      T(x,T(y \ z,y * u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(115(a,1),9707(a,1,2,1))].">
      <j1 rule="para" parents="115 9707"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      T(x,T(y,z * (u * z))) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9706,a(flip),b,9708,a)].">
      <j1 rule="hyper" parents="65 9706 9708"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      T(x,T(y * z,u * y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7401,a(flip),b,9708,a)].">
      <j1 rule="hyper" parents="65 7401 9708"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      T(x,T(y,z \ u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9709(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      T(x,T(y \ (z * u),u)) = T(x,T((z * u) / y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9690,a(flip),b,9712,a)].">
      <j1 rule="hyper" parents="65 9690 9712"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      T(x,T(y \ z,u * z)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9689,a(flip),b,9712,a)].">
      <j1 rule="hyper" parents="65 9689 9712"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      T(x,T(y,z \ (u * w))) = T(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8278,a(flip),b,9714,a)].">
      <j1 rule="hyper" parents="65 8278 9714"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),T(z,u * w)) = T(x,T(T(z,u \ w),y))
    ]]></literal>
    <justification jstring="[hyper(137,a,9714,a(flip),b,4262,a)].">
      <j1 rule="hyper" parents="137 9714 4262"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      T(x,T(y,z \ (u \ w))) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(7973(a,1),9714(a,1,2))].">
      <j1 rule="para" parents="7973 9714"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      T(x,L(y,z,u) * (u * z)) = T(x,T((z * y) * u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7368,a(flip),b,9710,a)].">
      <j1 rule="hyper" parents="65 7368 9710"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      T(x,T(y \ z,y * u)) = T(x,T(z / y,T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,9420,a,b,9711,a),flip(a)].">
      <j1 rule="hyper" parents="325 9420 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      T(x,T(y / z,L(z \ u,w,v5))) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8831(a,1),9711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8831 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      T(x,T((y * z) * u,y)) = T(x,T(u * (y * z),z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9712,a(flip),b,9713,a)].">
      <j1 rule="hyper" parents="65 9712 9713"/>
    </justification>
  </clause>

  <clause id="9724">
    <literal><![CDATA[
      T(x,T(y / z,y * T(u,z))) = T(x,(u * z) \ (y * T(u,z)))
    ]]></literal>
    <justification jstring="[para(113(a,1),9699(a,2,2,1))].">
      <j1 rule="para" parents="113 9699"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      (x / T(y,x)) * (K(z,u) * y) = T(x * K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(9574,a,9704,a)].">
      <j1 rule="hyper" parents="9574 9704"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      T(x,T(y \ (z * (u * w)),w)) = T(x,T((u * w) / (z \ y),u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7976,a(flip),b,9715,a)].">
      <j1 rule="hyper" parents="65 7976 9715"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      T(x,T(y,(z \ u) * w)) = T(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9714,a(flip),b,9717,a),flip(a)].">
      <j1 rule="hyper" parents="65 9714 9717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9714,a(flip),b,9719,a),flip(a)].">
      <j1 rule="hyper" parents="65 9714 9719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      K(x,y) * T(z * K(x,K(y,u)),w) = K(x,T(y,u)) * T(z,w)
    ]]></literal>
    <justification jstring="[para(9725(a,1),9530(a,1,2))].">
      <j1 rule="para" parents="9725 9530"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      K(x,y) * (L(z,u \ 1,u) * w) = (u * ((u \ K(x,y)) * z)) * w
    ]]></literal>
    <justification jstring="[para(9635(a,1),8557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9635 8557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      T(x,T(y * (z * u),u)) = T(x,L(u,z,y) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,9723,a(flip),b,9720,a)].">
      <j1 rule="hyper" parents="325 9723 9720"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      T(x,T(y / (z \ u),L((z \ u) \ w,v5,v6))) = T(x,T(u \ (z * y),w))
    ]]></literal>
    <justification jstring="[hyper(325,a,7976,a(flip),b,9722,a),flip(a)].">
      <j1 rule="hyper" parents="325 7976 9722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      T(x,T(y * (z * u),u)) = T(x,u * (y * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,8836,a(flip),b,9731,a),flip(a)].">
      <j1 rule="hyper" parents="325 8836 9731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9735">
    <literal><![CDATA[
      L(x,y,z) * (K(y * x,z) * u) = ((z * y) \ ((y * x) * z)) * u
    ]]></literal>
    <justification jstring="[para(6687(a,1),9596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6687 9596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) \ (z * x)) = T(z * (L(z,u,w) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9058,a(flip),b,9613,a),flip(a)].">
      <j1 rule="hyper" parents="65 9058 9613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) \ w) = L(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(2094(a,2),9613(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2094 9613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ w) = x * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(137,a,9737,a(flip),b,4507,a)].">
      <j1 rule="hyper" parents="137 9737 4507"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (w * L(x,z,u)) = K(y,x) * T(w,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),9737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 9737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      L(T(x,y),z,z) \ x = K(y,x) * a(z,z,x)
    ]]></literal>
    <justification jstring="[para(824(a,1),9737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="824 9737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      L(L(T(x,x \ 1),y,z) \ u,x,x) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(9737(a,1),4159(a,1,1))].">
      <j1 rule="para" parents="9737 4159"/>
    </justification>
  </clause>

  <clause id="9742">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ y = K(x,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(655(a,1),9740(a,1,1))].">
      <j1 rule="para" parents="655 9740"/>
    </justification>
  </clause>

  <clause id="9743">
    <literal><![CDATA[
      K(x \ 1,y) * a(x \ 1,x \ 1,y) = (x * (y * (x \ 1))) \ y
    ]]></literal>
    <justification jstring="[para(82(a,1),9742(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 9742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,v5)) = (a(y,z,u) \ x) * K(v5,w)
    ]]></literal>
    <justification jstring="[para(7194(a,1),9620(a,2,1))].">
      <j1 rule="para" parents="7194 9620"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) * K(y,z) = K(y,K(u,x) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2117,a,b,9625,a),flip(a)].">
      <j1 rule="hyper" parents="325 2117 9625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(y,u) = K(y,K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(3113(a,1),9745(a,1,1,2))].">
      <j1 rule="para" parents="3113 9745"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9398(a,1),9746(a,1,1))].">
      <j1 rule="para" parents="9398 9746"/>
    </justification>
  </clause>

  <clause id="9749">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,u) = K(y,K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(3582(a,1),9748(a,1,1))].">
      <j1 rule="para" parents="3582 9748"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(y,z)) * K(x,w)
    ]]></literal>
    <justification jstring="[para(9398(a,1),9749(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9398 9749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9748,a(flip),b,9751,a),flip(a)].">
      <j1 rule="hyper" parents="325 9748 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9753">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ 1)) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,7430,a(flip),b,9752,a),flip(a)].">
      <j1 rule="hyper" parents="65 7430 9752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      K(x,y \ K(z,u)) * K(u,z) = K(u,z) * K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(9753(a,1),3234(a,1,1))].">
      <j1 rule="para" parents="9753 3234"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      R(x,y,(z \ (K(u,w) * v5)) * v6) = R(x,y,(z \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(9649(a,1),8689(a,1,3))].">
      <j1 rule="para" parents="9649 8689"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      R(x,y,z * (u \ (w \ T(v5,v6)))) = R(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[para(5164(a,1),9650(a,1,3,2,2))].">
      <j1 rule="para" parents="5164 9650"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * (K(u,z) * (a(w,v5,w) * v6)) = ((x * (y \ 1)) * a(w,v5,w)) * v6
    ]]></literal>
    <justification jstring="[hyper(325,a,7627,a,b,9669,a),flip(a)].">
      <j1 rule="hyper" parents="325 7627 9669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      T(x,(T(y,z) * z) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(6163(a,1),9676(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6163 9676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(8264,a,9759,a)].">
      <j1 rule="hyper" parents="8264 9759"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,7973,a(flip),b,9760,a),flip(a)].">
      <j1 rule="hyper" parents="325 7973 9760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (w \ v5)) = T(x,w \ (a(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(7179(a,1),9761(a,1,2,2,1))].">
      <j1 rule="para" parents="7179 9761"/>
    </justification>
  </clause>

  <clause id="9763">
    <literal><![CDATA[
      T(x,(a(y,z,u) \ 1) \ (w \ v5)) = T(x,w \ ((a(y,z,u) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[para(8479(a,1),9761(a,1,2,2,1))].">
      <j1 rule="para" parents="8479 9761"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      R(x,y,(z \ ((u * u) \ w)) * v5) = R(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8786,a(flip),b,9681,a),flip(a)].">
      <j1 rule="hyper" parents="65 8786 9681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9765">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,u)) = T(x,T(y \ z,u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9527,a(flip),b,9693,a),flip(a)].">
      <j1 rule="hyper" parents="65 9527 9693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,9716,a(flip),b,9765,a),flip(a)].">
      <j1 rule="hyper" parents="325 9716 9765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      T(x,T(T(y,z) \ L(z,u,w),v5)) = T(x,T(L(z,u,w) / y,v5))
    ]]></literal>
    <justification jstring="[para(7906(a,1),9766(a,1,2,1,1))].">
      <j1 rule="para" parents="7906 9766"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      (x * (L(x,y,z) \ T(x,u))) \ 1 = L(T(x,u) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(9738(a,1),6594(a,1,1))].">
      <j1 rule="para" parents="9738 6594"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      R(x,y,(z \ ((u / w) \ v5)) * v6) = R(x,y,(z \ ((w \ u) \ v5)) * v6)
    ]]></literal>
    <justification jstring="[para(4590(a,1),9756(a,1,3,1,2))].">
      <j1 rule="para" parents="4590 9756"/>
    </justification>
  </clause>

  <clause id="9770">
    <literal><![CDATA[
      T(x,(y / z) \ (a(u,w,v5) \ y)) = T(x,a(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[para(85(a,1),9762(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="85 9762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w * w) \ v5))) = R(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8690,a,b,9764,a)].">
      <j1 rule="hyper" parents="65 8690 9764"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      R(x,y,((((z * z) / u) * w) \ v5) * v6) = R(x,y,(((1 / u) * w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(770(a,1),9764(a,1,3,1))].">
      <j1 rule="para" parents="770 9764"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      T(x,T((y * z) / u,y * w)) = T(x,T(z / (y \ u),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9695,a(flip),b,9696,a),flip(a)].">
      <j1 rule="hyper" parents="65 9695 9696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      (x * y) \ (K(z,u) * T(x,K(u,z))) = (x * (K(u,z) * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,2674,a(flip),b,9701,a)].">
      <j1 rule="hyper" parents="65 2674 9701"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      T(x,T(y / z,y * u)) = T(x,(u * z) \ (y * T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9513,a(flip),b,9724,a)].">
      <j1 rule="hyper" parents="65 9513 9724"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      T(x,(y * z) \ (u * T(y,z))) = T(x,T(z \ u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9689,a(flip),b,9775,a),flip(a)].">
      <j1 rule="hyper" parents="65 9689 9775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      T(x,y \ (z \ (u * T(z,y)))) = T(x,T(y \ u,z))
    ]]></literal>
    <justification jstring="[hyper(8264,a,9777,a)].">
      <j1 rule="hyper" parents="8264 9777"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      T(x,y \ T(z * K(u,y),u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(2086(a,2),9778(a,1,2,2))].">
      <j1 rule="para" parents="2086 9778"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      T(x,(y \ T(z,u)) * K(u,y)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(8298(a,1),9779(a,1,2))].">
      <j1 rule="para" parents="8298 9779"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u,z)) = T(x,T(y \ u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9453,a(flip),b,9780,a)].">
      <j1 rule="hyper" parents="65 9453 9780"/>
    </justification>
  </clause>

  <clause id="9782">
    <literal><![CDATA[
      T(x,T(y,z) \ L(T(u,z),w,v5)) = T(x,T(y \ L(u,w,v5),z))
    ]]></literal>
    <justification jstring="[para(25(a,2),9781(a,1,2,2))].">
      <j1 rule="para" parents="25 9781"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      T(x,T(y \ (z * (u * w)),w)) = T(x,w * ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8860,a(flip),b,9726,a),flip(a)].">
      <j1 rule="hyper" parents="325 8860 9726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      T(x,T(y \ (z * (u * w)),w)) = T(x,w * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8841,a(flip),b,9783,a),flip(a)].">
      <j1 rule="hyper" parents="325 8841 9783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      K(x,y) * (z * (L(z,u,w) \ x)) = T(z * (L(z,u,w) \ x),y)
    ]]></literal>
    <justification jstring="[para(1256(a,1),9736(a,1,2))].">
      <j1 rule="para" parents="1256 9736"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      K(x,y) * K(z,z \ K(x,y)) = ((z \ K(y,x)) * z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2903,a(flip),b,9755,a),flip(a)].">
      <j1 rule="hyper" parents="65 2903 9755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      ((x \ K(y,z)) * x) \ 1 = x * (K(z,y) / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,2558,a(flip),b,9786,a),flip(a)].">
      <j1 rule="hyper" parents="65 2558 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ x = (x * u) \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(3623(a,1),9774(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3623 9774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ x = ((x * u) \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,7916,a(flip),b,9788,a),flip(a)].">
      <j1 rule="hyper" parents="325 7916 9788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9790">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) \ x) * K(y,z) = (x * u) \ x
    ]]></literal>
    <justification jstring="[hyper(136,a,9789,a,b,2848,a)].">
      <j1 rule="hyper" parents="136 9789 2848"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      T(x,T(y \ L(z,u,w),v5)) = T(x,T(y,v5) \ T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,8838,a(flip),b,9782,a),flip(a)].">
      <j1 rule="hyper" parents="65 8838 9782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      T(x,T(y \ L(z,u,w),v5)) = T(x,T(y \ z,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,9781,a(flip),b,9791,a),flip(a)].">
      <j1 rule="hyper" parents="325 9781 9791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,u)) = T(x,T(L(z,w,v5) / y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9767,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="65 9767 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      T(x,T(L(y,z,u) / w,v5)) = T(x,T(y / w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,9766,a(flip),b,9794,a),flip(a)].">
      <j1 rule="hyper" parents="65 9766 9794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),w) = x * (L(x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8582,a(flip),b,9785,a),flip(a)].">
      <j1 rule="hyper" parents="65 8582 9785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(37,a,2095,a(flip),b,9785,a)].">
      <j1 rule="hyper" parents="37 2095 9785"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      K(L(x,y,z) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),9798(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      K(((x * y) \ z) * u,w) = K((y \ (x \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(308(a,1),9799(a,1,1,1))].">
      <j1 rule="para" parents="308 9799"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,w) = K((y \ (x * z)) * u,w)
    ]]></literal>
    <justification jstring="[para(469(a,1),9799(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="469 9799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ x),u) \ 1 = L(T(x,u) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(9797(a,2),9768(a,1,1))].">
      <j1 rule="para" parents="9797 9768"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      R(x,y,z \ R(T(z,u),T(z,u),w)) = R(x,y,((z * w) \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,8695,a(flip),b,9688,a),flip(a)].">
      <j1 rule="hyper" parents="325 8695 9688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      (x * ((x \ K(x,x \ 1)) * y)) * x = L(y * x,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,1345,a(flip),b,9730,a),flip(a)].">
      <j1 rule="hyper" parents="65 1345 9730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      (x * ((1 / x) * y)) * x = L(y * x,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1368(a,1),9807(a,1,1,2,1))].">
      <j1 rule="para" parents="1368 9807"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      (x * ((1 / x) * y)) * x = L(y * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a(flip),b,9808,a),flip(a)].">
      <j1 rule="hyper" parents="325 1499 9808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      R(x,y,z \ (u * (u * ((1 / u) * w)))) = R(x,y,z \ L(w * u,u,u))
    ]]></literal>
    <justification jstring="[para(9809(a,1),8705(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9809 8705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      L(x,y,z) * (K(y * x,z) * R(((z * y) \ ((y * x) * z)) \ 1,u,w)) = ((z * y) \ ((y * x) * z)) \ R((z * y) \ ((y * x) * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1077,a(flip),b,9735,a),flip(a)].">
      <j1 rule="hyper" parents="325 1077 9735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      K(x * L(y,z,u),w) * L(L(T(y,(w * x) \ ((x * L(y,z,u)) * w)),x,w),z,u) = (w * x) \ ((x * L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(36,a,1658,a(flip),b,9735,a),flip(a)].">
      <j1 rule="hyper" parents="36 1658 9735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (w * L(x,z,u)) = K(y,x) * T(w,x)
    ]]></literal>
    <justification jstring="[para(7906(a,1),9739(a,2,2))].">
      <j1 rule="para" parents="7906 9739"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (w * L(x,z,u)) = T(K(y,x) * w,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,4576,a,b,9813,a),flip(a)].">
      <j1 rule="hyper" parents="325 4576 9813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      K(x \ 1,y) * a(x,x \ 1,y) = (x * (y * (x \ 1))) \ y
    ]]></literal>
    <justification jstring="[para(1847(a,1),9743(a,1,2))].">
      <j1 rule="para" parents="1847 9743"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      R(x,y,z \ R(T(z,u),T(z,u),w)) = R(x,y,z * ((w * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,8737,a(flip),b,9805,a),flip(a)].">
      <j1 rule="hyper" parents="325 8737 9805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      L((x * K(y,z)) / u,w,v5) \ x = (x / L(u \ x,w,v5)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9621,a(flip),b,9614,a),flip(a)].">
      <j1 rule="hyper" parents="65 9621 9614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      K(x,y) * (z \ (u * T(z,K(y,x)))) = T(u * K(x,y),z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(9579,a,9628,a)].">
      <j1 rule="hyper" parents="9579 9628"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y / (x \ 1)) / y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2487(a,1),9640(a,2,2,1))].">
      <j1 rule="para" parents="2487 9640"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      R(x,y,(z * K(u,z)) * L(z * K(u,z),z,u)) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(9820(a,1),1725(a,2,3))].">
      <j1 rule="para" parents="9820 1725"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      ((x * (y * z)) / T(y,z)) * K(u,w) = (x * ((z * K(u,w)) * y)) / y
    ]]></literal>
    <justification jstring="[hyper(65,a,9597,a(flip),b,9678,a)].">
      <j1 rule="hyper" parents="65 9597 9678"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      (x * (y / z)) * ((y / z) \ u) = (x * (z \ y)) * ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(115(a,1),9680(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 9680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      ((x \ 1) * (1 / x)) * ((1 / x) \ y) = ((x \ 1) / x) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(420(a,1),9823(a,2,1))].">
      <j1 rule="para" parents="420 9823"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      (x / y) * ((z * (x / y)) \ u) = (y \ x) * ((z * (y \ x)) \ u)
    ]]></literal>
    <justification jstring="[para(115(a,1),9682(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="115 9682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      T(x,T(T(y,z \ u),w)) = T(x,T(T(y,z * u),w))
    ]]></literal>
    <justification jstring="[hyper(4263,a,9718,a),flip(a)].">
      <j1 rule="hyper" parents="4263 9718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      T(x,T(T(y,z \ u),w)) = T(x,T(y,(z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,9706,a(flip),b,9826,a),flip(a)].">
      <j1 rule="hyper" parents="325 9706 9826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      T(x,T(T(y,z \ u),w)) = T(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,9728,a(flip),b,9827,a),flip(a)].">
      <j1 rule="hyper" parents="325 9728 9827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      T(x,T(y,(z \ u) * w)) = T(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9706,a(flip),b,9828,a)].">
      <j1 rule="hyper" parents="65 9706 9828"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      T(x,T(y,z * (u \ w))) = T(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9727,a(flip),b,9829,a),flip(a)].">
      <j1 rule="hyper" parents="65 9727 9829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9728,a,b,9830,a)].">
      <j1 rule="hyper" parents="65 9728 9830"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      T(x,T((y * z) \ u,z * (y * w))) = T(x,T(u / (y * z),T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9721,a(flip),b,9831,a),flip(a)].">
      <j1 rule="hyper" parents="65 9721 9831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      T(x,y \ ((a(z,u,w) \ 1) \ v5)) = T(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,7361,a(flip),b,9763,a),flip(a)].">
      <j1 rule="hyper" parents="65 7361 9763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      L((x * K(y,z)) / u,w,v5) \ x = (L(x / u,w,v5) \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(6588(a,1),9818(a,2,1))].">
      <j1 rule="para" parents="6588 9818"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      K(x,y) * T(z * K(u,K(y,x)),u) = T(z * K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(2086(a,2),9819(a,1,2))].">
      <j1 rule="para" parents="2086 9819"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      (x * ((y * K(z,u)) * w)) / w = ((x * (y * w)) / w) * K(z,u)
    ]]></literal>
    <justification jstring="[para(6526(a,1),9822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6526 9822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      ((x * (T(y,z) * u)) / u) * K(z,y) = (x * (y * u)) / u
    ]]></literal>
    <justification jstring="[para(2504(a,1),9836(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2504 9836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) / w = ((x * (y * w)) / w) * K(z,u)
    ]]></literal>
    <justification jstring="[para(9559(a,1),9836(a,1,1,2))].">
      <j1 rule="para" parents="9559 9836"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      ((x * (T(y,z) * T(y,z))) / T(y,z)) * y = x * (y * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,2877,a,b,9837,a(flip))].">
      <j1 rule="hyper" parents="39 2877 9837"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      (x / (T(y,z) \ 1)) * y = x * (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(566(a,1),9839(a,1,1))].">
      <j1 rule="para" parents="566 9839"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      x / (y * (z \ (T(z,u) \ 1))) = (x * (z * T(z,u))) / y
    ]]></literal>
    <justification jstring="[para(9840(a,1),8963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9840 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      (x * (y * T(y,z))) / u = x / (u / (y * T(y,z)))
    ]]></literal>
    <justification jstring="[para(8438(a,1),9841(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8438 9841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      x / (y / (z * T(z,z \ (z \ 1)))) = (x * (z * (1 / (1 / z)))) / y
    ]]></literal>
    <justification jstring="[para(1644(a,1),9842(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1644 9842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      ((x \ 1) / x) * ((x \ 1) \ y) = (x \ (x \ 1)) * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(665(a,1),9824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="665 9824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      ((x \ 1) / x) * ((x \ 1) \ y) = (x * x) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,581,a(flip),b,9844,a),flip(a)].">
      <j1 rule="hyper" parents="325 581 9844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x \ 1) \ y)) = (x * x) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,737,a(flip),b,9845,a)].">
      <j1 rule="hyper" parents="65 737 9845"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      (x \ 1) * (x \ (((x \ 1) \ y) * z)) = ((x * x) \ ((1 / x) \ y)) * z
    ]]></literal>
    <justification jstring="[para(9846(a,1),901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9846 901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      (x \ 1) * (x \ (((x \ 1) \ y) / z)) = ((x * x) \ ((1 / x) \ y)) / z
    ]]></literal>
    <justification jstring="[para(9846(a,1),902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9846 902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w \ 1) * (w \ ((w \ 1) \ v5))))) = R(x,y,z * (u \ (((1 / w) \ v5) / (w * w))))
    ]]></literal>
    <justification jstring="[para(9846(a,2),8746(a,2,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9846 8746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      T(x,T(y \ (z \ u),y * (z * w))) = T(x,T(u / (z * y),T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,7975,a(flip),b,9832,a)].">
      <j1 rule="hyper" parents="65 7975 9832"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) * K(y,w) = L(x / T(y,w),z,u) \ x
    ]]></literal>
    <justification jstring="[para(2855(a,1),9834(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2855 9834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      L((x * y) / T(x,z),u,w) \ (x * y) = ((x * y) / L(y,u,w)) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6591(a,1),9851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6591 9851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      K(x,y) * T(z * K(x,K(y,u)),u) = T(z * K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(3560(a,1),9835(a,1,2,1,2))].">
      <j1 rule="para" parents="3560 9835"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      x / (y / (z * T(z,z \ (z \ 1)))) = (x * ((1 / z) \ z)) / y
    ]]></literal>
    <justification jstring="[para(3288(a,1),9843(a,2,1,2))].">
      <j1 rule="para" parents="3288 9843"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      x / (y / (z * (1 / (1 / z)))) = (x * ((1 / z) \ z)) / y
    ]]></literal>
    <justification jstring="[para(1644(a,1),9854(a,1,2,2,2))].">
      <j1 rule="para" parents="1644 9854"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) / z = x / (z / ((1 / y) \ y))
    ]]></literal>
    <justification jstring="[para(3288(a,1),9855(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3288 9855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) / y = x / (1 / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),9856(a,2,2))].">
      <j1 rule="para" parents="82 9856"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      (x \ 1) * (x \ (((x \ 1) \ y) / z)) = (x * x) \ (((1 / x) \ y) / z)
    ]]></literal>
    <justification jstring="[hyper(325,a,688,a(flip),b,9848,a),flip(a)].">
      <j1 rule="hyper" parents="325 688 9848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9859">
    <literal><![CDATA[
      T(x,T((y \ z) / u,y * w)) = T(x,T(z / (y * u),T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9711,a(flip),b,9850,a)].">
      <j1 rule="hyper" parents="65 9711 9850"/>
    </justification>
  </clause>

  <clause id="9860">
    <literal><![CDATA[
      T(x,T((y \ z) / u,y * w)) = T(x,T(z / (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(325,a,9420,a(flip),b,9859,a),flip(a)].">
      <j1 rule="hyper" parents="325 9420 9859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      T(x,T(((1 / y) \ z) / u,y \ w)) = T(x,T(z / ((1 / y) * u),w))
    ]]></literal>
    <justification jstring="[para(7358(a,1),9860(a,1,2))].">
      <j1 rule="para" parents="7358 9860"/>
    </justification>
  </clause>

  <clause id="9862">
    <literal><![CDATA[
      K(x,y) * T(z * K(x,K(y,u)),u) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,9679,a(flip),b,9853,a),flip(a)].">
      <j1 rule="hyper" parents="325 9679 9853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9863">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u,z) = T(K(x,y) * u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9729,a(flip),b,9862,a)].">
      <j1 rule="hyper" parents="65 9729 9862"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,u)) = K(x,y) * T(z,T(x,u))
    ]]></literal>
    <justification jstring="[para(3122(a,1),9863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3122 9863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      T((x * y) \ T(K(z,y) * y,T(z,x)),x \ 1) = (x * T(y,T(z,x))) \ T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9864(a,2),4307(a,1,1,2))].">
      <j1 rule="para" parents="9864 4307"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      (x * x) \ (((1 / x) \ y) / y) = R(x \ 1,x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8785,a(flip),b,9858,a),flip(a)].">
      <j1 rule="hyper" parents="65 8785 9858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      R(x \ 1,x \ 1,x \ y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1304,a(flip),b,9868,a),flip(a)].">
      <j1 rule="hyper" parents="65 1304 9868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      x \ R(x,x \ 1,x \ y) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,9869,a(flip),b,1079,a),flip(a)].">
      <j1 rule="hyper" parents="137 9869 1079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      T(x,T(((1 / y) \ z) / u,y * w)) = T(x,T(z / ((1 / y) * u),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9714,a(flip),b,9861,a)].">
      <j1 rule="hyper" parents="65 9714 9861"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      T(x,T(L(y,z,z) / ((1 / z) * u),w)) = T(x,T((z * y) / u,z * w))
    ]]></literal>
    <justification jstring="[para(651(a,1),9871(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="651 9871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(9594(a,1),9583(a,1,1))].">
      <j1 rule="para" parents="9594 9583"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      T(x,T(y / (z \ u),u \ (z * w))) = T(x,T(u \ (z * y),w))
    ]]></literal>
    <justification jstring="[para(469(a,1),9732(a,1,2,2))].">
      <j1 rule="para" parents="469 9732"/>
    </justification>
  </clause>

  <clause id="9875">
    <literal><![CDATA[
      T(x,T(y / (z \ u),u * (z * w))) = T(x,T(u \ (z * y),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9714,a(flip),b,9874,a)].">
      <j1 rule="hyper" parents="65 9714 9874"/>
    </justification>
  </clause>

  <clause id="9876">
    <literal><![CDATA[
      T(x,T(y / ((z \ u) \ 1),(u \ z) \ w)) = T(x,T(1 \ ((z \ u) * y),w))
    ]]></literal>
    <justification jstring="[para(8866(a,1),9874(a,1,2))].">
      <j1 rule="para" parents="8866 9874"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      R(x,y,z \ L(u * w,w,w)) = R(x,y,z \ L(w * u,w,w))
    ]]></literal>
    <justification jstring="[para(6319(a,1),9810(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6319 9810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9878">
    <literal><![CDATA[
      T(x,T(L(y,z,z) / ((1 / z) * u),w)) = T(x,T(y / (z \ u),w))
    ]]></literal>
    <justification jstring="[hyper(325,a,9773,a(flip),b,9872,a),flip(a)].">
      <j1 rule="hyper" parents="325 9773 9872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9879">
    <literal><![CDATA[
      T(x,T(y / ((1 / z) * u),w)) = T(x,T(y / (z \ u),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9796,a(flip),b,9878,a)].">
      <j1 rule="hyper" parents="65 9796 9878"/>
    </justification>
  </clause>

  <clause id="9881">
    <literal><![CDATA[
      T(x,T(y * L(z \ u,z,u),w)) = T(x,T(y / (u \ z),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,3266,a,b,9879,a)].">
      <j1 rule="hyper" parents="65 3266 9879"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      T(x,T(y / (z \ u),w)) = T(x,T(y * (u \ z),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8936,a(flip),b,9881,a),flip(a)].">
      <j1 rule="hyper" parents="65 8936 9881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      T(x,T(y * (z \ u),z * (u * w))) = T(x,T(z \ (u * y),w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9875,a(flip),b,9882,a),flip(a)].">
      <j1 rule="hyper" parents="65 9875 9882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9885">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(490,a,9873,a),flip(a)].">
      <j1 rule="hyper" parents="490 9873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,8689,a(flip),b,9885,a),flip(a)].">
      <j1 rule="hyper" parents="325 8689 9885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = K(v5,v6) * R(K(v6,v5) * x,y,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2662,a,b,9886,a),flip(a)].">
      <j1 rule="hyper" parents="325 2662 9886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      R(x,y * z,u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(93(a,1),9886(a,1,2))].">
      <j1 rule="para" parents="93 9886"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      R(x,T(y,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(1583(a,1),9886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1583 9886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      R(x,y / z,u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(1588(a,1),9886(a,1,2))].">
      <j1 rule="para" parents="1588 9886"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      R(x,(y \ z) \ z,u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(2100(a,2),9886(a,1,2))].">
      <j1 rule="para" parents="2100 9886"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[para(2269(a,1),9886(a,1,2))].">
      <j1 rule="para" parents="2269 9886"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      R(x,y \ (K(z,u) * w),v5) = R(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(8303(a,1),9886(a,1,2))].">
      <j1 rule="para" parents="8303 9886"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      (x * T(T(x,y),y)) * (T(y,x) / (x * y)) = R(T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,4192,a,b,9893,a)].">
      <j1 rule="hyper" parents="65 4192 9893"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      R(x,y,z) \ (z * (y * x)) = (x \ (y * x)) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(9893(a,1),8410(a,1,1))].">
      <j1 rule="para" parents="9893 8410"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      R(x,y,z \ R(T(z,u),z,w)) = R(x,y,z * ((w * z) \ w))
    ]]></literal>
    <justification jstring="[para(9893(a,1),9817(a,1,3,2))].">
      <j1 rule="para" parents="9893 9817"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      R(x,y,z) * (((y \ u) \ u) * z) = (x * ((y \ u) \ u)) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,9895,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="136 9895 20"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      R(x,y * (K(z,u) * w),v5) = R(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(2696(a,1),9896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2696 9896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      R(T(x,y),z,(x * z) \ u) \ u = (K(y,x) * z) * ((T(x,y) * (K(y,x) * z)) \ u)
    ]]></literal>
    <justification jstring="[para(9896(a,1),4534(a,1,1))].">
      <j1 rule="para" parents="9896 4534"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      R(x,L(K(y,z) * u,w,v5),v6) = R(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(8549(a,2),9896(a,1,2))].">
      <j1 rule="para" parents="8549 9896"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      R(x,(y * T(z,u)) \ w,v5) = R(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9607(a,1),9896(a,1,2))].">
      <j1 rule="para" parents="9607 9896"/>
    </justification>
  </clause>

  <clause id="9910">
    <literal><![CDATA[
      R(x,(T(y,z) * u) \ w,v5) = R(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(2190(a,1),9898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2190 9898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9911">
    <literal><![CDATA[
      R(x,(K(y,z) * u) * w,v5) = R(x,w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,9891,a,b,9906,a)].">
      <j1 rule="hyper" parents="65 9891 9906"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      R(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(9888(a,2),2723(a,1))].">
      <j1 rule="para" parents="9888 2723"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(9885(a,1),9913(a,1))].">
      <j1 rule="para" parents="9885 9913"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      R(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(2472(a,1),9914(a,1,3))].">
      <j1 rule="para" parents="2472 9914"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      R(x,y,L(K(z,u) * w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(8549(a,2),9914(a,1,3))].">
      <j1 rule="para" parents="8549 9914"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      R(x,y,z) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),9900(a,2,1))].">
      <j1 rule="para" parents="22 9900"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      L(x,y,(T(z,u) * T(w,z * u)) \ (w * (z * u))) = L(x,y,R(u,z,w))
    ]]></literal>
    <justification jstring="[para(9918(a,1),1553(a,1,3,1))].">
      <j1 rule="para" parents="9918 1553"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      R(x,(T(y,z) * T(u,y * z)) \ (u * (y * z)),w) = R(x,R(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(9918(a,1),9895(a,1,2,1))].">
      <j1 rule="para" parents="9918 9895"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      R(x,y,z \ R(z,z,u)) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8700,a(flip),b,9901,a)].">
      <j1 rule="hyper" parents="65 8700 9901"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * u != w * (((y \ z) \ z) * u)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(9905(a,1),46(a,1))].">
      <j1 rule="para" parents="9905 46"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      R(x,y,R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(8753(a,1),9916(a,1))].">
      <j1 rule="para" parents="8753 9916"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      L(x,y,(T(z,u) * w) \ (w * (z * u))) = L(x,y,R(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9638,a(flip),b,9920,a)].">
      <j1 rule="hyper" parents="65 9638 9920"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (z * w))) = L(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8393,a(flip),b,9926,a)].">
      <j1 rule="hyper" parents="65 8393 9926"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      L(x,y,L(K(z,u) * w,u,z)) = L(x,y,R(w,u,z))
    ]]></literal>
    <justification jstring="[para(5238(a,1),9928(a,1,3))].">
      <j1 rule="para" parents="5238 9928"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(8560,a,9930,a),flip(a)].">
      <j1 rule="hyper" parents="8560 9930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9930(a,1),8560(a,1))].">
      <j1 rule="para" parents="9930 8560"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * w) * u)) = L(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,4233,a,b,9931,a)].">
      <j1 rule="hyper" parents="65 4233 9931"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,487,a,b,9931,a)].">
      <j1 rule="hyper" parents="65 487 9931"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      x * L(y,R(z,u,w) \ x,L(z,u,w)) = R(z,u,w) * ((R(z,u,w) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,9931,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="137 9931 101"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      R(x,(T(y,z) * u) \ (u * (y * z)),w) = R(x,R(z,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9909,a(flip),b,9921,a)].">
      <j1 rule="hyper" parents="65 9909 9921"/>
    </justification>
  </clause>

  <clause id="9938">
    <literal><![CDATA[
      R(x,(y * z) \ (z * (y * u)),w) = R(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9910,a(flip),b,9936,a)].">
      <j1 rule="hyper" parents="65 9910 9936"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      R(x,L(K(y,z) * u,z,y),w) = R(x,R(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(5238(a,1),9938(a,1,2))].">
      <j1 rule="para" parents="5238 9938"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      R(x,R(y,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9908,a(flip),b,9940,a),flip(a)].">
      <j1 rule="hyper" parents="65 9908 9940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      (x \ y) * (((y / x) \ 1) \ z) = y * ((((x \ y) \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(2592(a,1),9645(a,1,2,1))].">
      <j1 rule="para" parents="2592 9645"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      (x * y) \ (K(z,u) * (T(x,K(u,z)) * w)) = (x * (K(u,z) * y)) \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2674,a(flip),b,9702,a)].">
      <j1 rule="hyper" parents="65 2674 9702"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      R(x,y,(((1 / z) * u) \ w) * v5) = R(x,y,((z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),9772(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      R(x,y,(((z \ 1) * u) \ w) * v5) = R(x,y,((z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),9945(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 9945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      R(x,y,z \ (u \ (z \ u))) = R(x,y,((z * u) \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8790,a(flip),b,9946,a)].">
      <j1 rule="hyper" parents="65 8790 9946"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      R(x,y,z \ (u \ (z \ u))) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8737,a(flip),b,9947,a),flip(a)].">
      <j1 rule="hyper" parents="325 8737 9947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9949">
    <literal><![CDATA[
      L((x * y) / T(x,z),u,w) \ (x * y) = (y * (L(y,u,w) \ x)) * K(x,z)
    ]]></literal>
    <justification jstring="[para(8357(a,1),9852(a,2,1))].">
      <j1 rule="para" parents="8357 9852"/>
    </justification>
  </clause>

  <clause id="9950">
    <literal><![CDATA[
      T(x,T(y / ((z \ u) \ 1),(u \ z) \ w)) = T(x,T((z \ u) * y,w))
    ]]></literal>
    <justification jstring="[para(67(a,1),9876(a,2,2,1))].">
      <j1 rule="para" parents="67 9876"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      T(x,T(y / ((z \ u) \ 1),z \ (u * w))) = T(x,T((z \ u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8278,a(flip),b,9950,a)].">
      <j1 rule="hyper" parents="65 8278 9950"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      T(x,T(y / ((z \ u) \ 1),z * (u * w))) = T(x,T((z \ u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9714,a(flip),b,9951,a)].">
      <j1 rule="hyper" parents="65 9714 9951"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      T(x,T(y * (z \ u),z * (u * w))) = T(x,T((z \ u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8937,a(flip),b,9952,a)].">
      <j1 rule="hyper" parents="65 8937 9952"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      T(x,T(y \ (z * u),w)) = T(x,T((y \ z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9884,a(flip),b,9953,a)].">
      <j1 rule="hyper" parents="65 9884 9953"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      T(x,T((y \ z) * (u * w),w)) = T(x,w * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,9784,a(flip),b,9954,a),flip(a)].">
      <j1 rule="hyper" parents="65 9784 9954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      T(x,y * (z \ (u * w))) = T(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9733,a(flip),b,9955,a),flip(a)].">
      <j1 rule="hyper" parents="65 9733 9955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      T(x,(y \ z) * ((z \ u) * L((z \ u) \ w,v5,v6))) = T(x,(y \ u) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9219,a,b,9956,a)].">
      <j1 rule="hyper" parents="65 9219 9956"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * w) = (x * u) \ (x * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(9581(a,1),9944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9581 9944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      (x * (K(y,z) * L(u,u,x))) \ (x * w) = (x / (u \ 1)) \ (x * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(1720(a,1),9958(a,2,1))].">
      <j1 rule="para" parents="1720 9958"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      L((x * y) / T(x,z),u,w) \ (x * y) = y * ((L(y,u,w) \ x) * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7899,a(flip),b,9949,a),flip(a)].">
      <j1 rule="hyper" parents="325 7899 9949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      L((x * (y / x)) / T(x,z),u,w) \ (x * (y / x)) = (L(y / x,u,w) \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(1262(a,1),9949(a,2,1))].">
      <j1 rule="para" parents="1262 9949"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      L((x * y) / T(x,z),u,w) \ (x * y) = y * (L(y,u,w) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(6670(a,1),9960(a,2,2))].">
      <j1 rule="para" parents="6670 9960"/>
    </justification>
  </clause>

  <clause id="9963">
    <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(9594(a,1),9584(a,1,2))].">
      <j1 rule="para" parents="9594 9584"/>
    </justification>
  </clause>

  <clause id="9964">
    <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(9559(a,1),9585(a,1,2,1))].">
      <j1 rule="para" parents="9559 9585"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      L(x,x,y * (K(z,u) * x)) = (y * (K(z,u) * (x \ 1))) \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,1547,a(flip),b,9616,a)].">
      <j1 rule="hyper" parents="65 1547 9616"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      L(x,x,y * x) = (y * (K(z,u) * (x \ 1))) \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,3507,a(flip),b,9965,a)].">
      <j1 rule="hyper" parents="65 3507 9965"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      L(x,x,y * x) = ((y * (K(z,u) * (x \ 1))) \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,7916,a(flip),b,9966,a),flip(a)].">
      <j1 rule="hyper" parents="325 7916 9966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      L(x,x,y * x) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,9790,a(flip),b,9967,a),flip(a)].">
      <j1 rule="hyper" parents="325 9790 9967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      ((x / y) * (y \ 1)) \ (x / y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),9969(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 9969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      L((x \ 1) \ 1,x \ 1,x \ y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1554,a,b,9970,a)].">
      <j1 rule="hyper" parents="65 1554 9970"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      (x / (y * y)) \ (x / y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[para(569(a,1),9970(a,1,1))].">
      <j1 rule="para" parents="569 9970"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      L(L(x,x,y) \ z,(y / (x * x)) \ (y / x),y / (x * x)) = (y / x) \ ((y / (x * x)) * z)
    ]]></literal>
    <justification jstring="[para(9972(a,1),469(a,1,1,1))].">
      <j1 rule="para" parents="9972 469"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      L((x * K(y,z)) \ 1,(K(z,y) / x) \ 1,(K(z,y) / x) \ u) = L(K(z,y) / x,K(z,y) / x,u)
    ]]></literal>
    <justification jstring="[para(7526(a,1),9971(a,1,1,1))].">
      <j1 rule="para" parents="7526 9971"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      R(x,y,(z * K(u,z)) * ((u / (z \ 1)) / u)) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(1723(a,1),9821(a,1,3,2))].">
      <j1 rule="para" parents="1723 9821"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      R(x,y,z * (K(u,z) * ((u / (z \ 1)) / u))) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(4578(a,1),9975(a,1,3))].">
      <j1 rule="para" parents="4578 9975"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      R(x,y,z * ((T(u,z) / (z \ 1)) / u)) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(2198(a,1),9976(a,1,3,2))].">
      <j1 rule="para" parents="2198 9976"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      R(x,y,z * (u \ (T(u,z) / (z \ 1)))) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8696,a(flip),b,9977,a)].">
      <j1 rule="hyper" parents="65 8696 9977"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      R(x,y,z * (u \ ((z \ 1) \ T(u,z)))) = R(x,y,z * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8746,a(flip),b,9978,a)].">
      <j1 rule="hyper" parents="65 8746 9978"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      R(x,y,(z \ ((u \ 1) \ z)) * u) = R(x,y,u * ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9757,a(flip),b,9979,a)].">
      <j1 rule="hyper" parents="65 9757 9979"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      (x * L(K(y,z) * u,u,x)) \ (x * w) = (x / (u \ 1)) \ (x * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(8549(a,2),9959(a,1,1,2))].">
      <j1 rule="para" parents="8549 9959"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(709,a,9963,a),flip(a)].">
      <j1 rule="hyper" parents="709 9963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9984">
    <literal><![CDATA[
      a(x,y,K(y,z) * u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(2094(a,2),9983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2094 9983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,626,a(flip),b,9964,a),flip(a)].">
      <j1 rule="hyper" parents="65 626 9964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,2340,a(flip),b,9986,a),flip(a)].">
      <j1 rule="hyper" parents="65 2340 9986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      a(x,T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(1226(a,2),9987(a,1,2))].">
      <j1 rule="para" parents="1226 9987"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2113(a,2),9987(a,1,2))].">
      <j1 rule="para" parents="2113 9987"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      a(x,y * T(z,u),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(2282(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="2282 9987"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      a(x,y * z,u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(2472(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="2472 9987"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      a(x,y / z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(2455(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="2455 9987"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2483(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="2483 9987"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      a(x,(y / z) * u,w) = a(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(2566(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="2566 9987"/>
    </justification>
  </clause>

  <clause id="9999">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(3109(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="3109 9987"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(2696(a,1),9987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2696 9987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10001">
    <literal><![CDATA[
      a(x,T(y,z) \ u,w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(4526(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="4526 9987"/>
    </justification>
  </clause>

  <clause id="10002">
    <literal><![CDATA[
      a(x,(T(y,z) \ u) * w,v5) = a(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(4556(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="4556 9987"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      a(x,(y / z) \ u,w) = a(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4590(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="4590 9987"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      a(x,y \ T(z,u),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(5107(a,1),9987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5107 9987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      a(x,((y \ z) * y) \ u,w) = a(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(6168(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="6168 9987"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      a(x,L(K(y,z) * u,w,v5),v6) = a(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(8549(a,2),9987(a,1,2))].">
      <j1 rule="para" parents="8549 9987"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      a(x,(y * T(z,u)) \ w,v5) = a(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9607(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="9607 9987"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      a(x,y \ (K(z,u) * w),v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(9643(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="9643 9987"/>
    </justification>
  </clause>

  <clause id="10009">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) * v5,v6) = a(x,(y * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(9630(a,1),9987(a,1,2))].">
      <j1 rule="para" parents="9630 9987"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      a(x,T(T(y,z),u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9991,a(flip),b,9991,a),flip(a)].">
      <j1 rule="hyper" parents="325 9991 9991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      a(T(x,y),T(z,u),w) = a(x,z,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1868,a(flip),b,9991,a),flip(a)].">
      <j1 rule="hyper" parents="325 1868 9991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      (x * (T(y,z) * u)) * a(x,y,u) = (x * T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(137,a,9991,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="137 9991 14"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      a(x,((y * y) \ z) * u,w) = a(x,z * (u / (y * y)),w)
    ]]></literal>
    <justification jstring="[para(884(a,1),9991(a,1,2))].">
      <j1 rule="para" parents="884 9991"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      a(x,y * K(y * z,y),u) = a(x,R(y,z,y),u)
    ]]></literal>
    <justification jstring="[para(4667(a,1),9991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4667 9991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      a(x,(T(y,z) * T(u,y * z)) \ (u * (y * z)),w) = a(x,R(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(9918(a,1),9992(a,1,2,1))].">
      <j1 rule="para" parents="9918 9992"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      a(a(x,y,z),u * (w * w),v5) = a(a(x,y,z),u,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,7566,a(flip),b,9995,a),flip(a)].">
      <j1 rule="hyper" parents="325 7566 9995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10020">
    <literal><![CDATA[
      a(x,((y * y) * z) / y,u) = a(x,(1 / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(652(a,1),9996(a,2,2))].">
      <j1 rule="para" parents="652 9996"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      a(x,(y \ z) / (u * u),w) = a(x,(z / (u * u)) / y,w)
    ]]></literal>
    <justification jstring="[para(695(a,2),9996(a,2,2)),flip(a)].">
      <j1 rule="para" parents="695 9996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9983,a(flip),b,9999,a)].">
      <j1 rule="hyper" parents="65 9983 9999"/>
    </justification>
  </clause>

  <clause id="10028">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,y) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,9999,a(flip),b,4034,a)].">
      <j1 rule="hyper" parents="137 9999 4034"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      a(x,y * (z / u),w) = a(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(4004(a,1),9999(a,1,2))].">
      <j1 rule="para" parents="4004 9999"/>
    </justification>
  </clause>

  <clause id="10030">
    <literal><![CDATA[
      a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(6824(a,1),9999(a,1,2))].">
      <j1 rule="para" parents="6824 9999"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5)
    ]]></literal>
    <justification jstring="[para(287(a,2),10027(a,1,3))].">
      <j1 rule="para" parents="287 10027"/>
    </justification>
  </clause>

  <clause id="10037">
    <literal><![CDATA[
      a(x,y,T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1226(a,2),10027(a,1,3))].">
      <j1 rule="para" parents="1226 10027"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2113(a,2),10027(a,1,3))].">
      <j1 rule="para" parents="2113 10027"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      a(x,y,T(z,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(2114(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2114 10027"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5)) = a(x,y,R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(2130(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2130 10027"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(2186(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2186 10027"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(2112(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2112 10027"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      a(x,y,z * T(u,w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2282(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2282 10027"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5) * v6) = a(x,y,L(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(2187(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2187 10027"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      a(x,y,z * u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(2472(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2472 10027"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      a(x,y,z / u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(2455(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2455 10027"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2483(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2483 10027"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(2488(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2488 10027"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(2566(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2566 10027"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(2582(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2582 10027"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * v5) = a(x,y,((u * z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(2727(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2727 10027"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(3109(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="3109 10027"/>
    </justification>
  </clause>

  <clause id="10053">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(2810(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="2810 10027"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(2696(a,1),10027(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2696 10027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(4526(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="4526 10027"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      a(x,y,(z / u) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(4590(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="4590 10027"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      a(x,y,z \ T(u,w)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(5107(a,1),10027(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5107 10027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(6163(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="6163 10027"/>
    </justification>
  </clause>

  <clause id="10061">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * w,v5,v6)) = a(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(8549(a,2),10027(a,1,3))].">
      <j1 rule="para" parents="8549 10027"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      a(x,y,(z \ T(u,w)) \ v5) = a(x,y,(z \ u) \ v5)
    ]]></literal>
    <justification jstring="[para(9609(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="9609 10027"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * v5)) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(9643(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="9643 10027"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5) \ v6) = a(x,y,L(z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(9737(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="9737 10027"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) * v6) = a(x,y,(z * v5) * v6)
    ]]></literal>
    <justification jstring="[para(9630(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="9630 10027"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,7186,a,b,10037,a)].">
      <j1 rule="hyper" parents="325 7186 10037"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      a(x,T(y,z),T(u,w)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,9991,a(flip),b,10037,a),flip(a)].">
      <j1 rule="hyper" parents="325 9991 10037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      a(T(x,y),z,T(u,w)) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1868,a(flip),b,10037,a),flip(a)].">
      <j1 rule="hyper" parents="325 1868 10037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      ((x * y) * T(z,u)) / (x * (y * T(z,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7221,a(flip),b,10037,a)].">
      <j1 rule="hyper" parents="65 7221 10037"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) * a(z,y,x) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(137,a,10037,a(flip),b,1231,a)].">
      <j1 rule="hyper" parents="137 10037 1231"/>
    </justification>
  </clause>

  <clause id="10072">
    <literal><![CDATA[
      (x * (y * T(z,u))) * a(x,y,z) = (x * y) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,10037,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="137 10037 14"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5)) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(252(a,1),10037(a,1,3)),flip(a)].">
      <j1 rule="para" parents="252 10037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(7482,a,10045,a),flip(a)].">
      <j1 rule="hyper" parents="7482 10045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7496,a,b,10045,a)].">
      <j1 rule="hyper" parents="325 7496 10045"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7496,a(flip),b,10045,a),flip(a)].">
      <j1 rule="hyper" parents="325 7496 10045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      a(x,y,z * R(u,u,z)) = a(x,y,(1 / u) \ z)
    ]]></literal>
    <justification jstring="[para(1289(a,1),10045(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1289 10045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,u / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1720(a,1),10045(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1720 10045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      (x * (y * a(z,u,w * v5))) \ (a(z,u,w * v5) * (x * y)) = a(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[para(10045(a,1),7263(a,2,3))].">
      <j1 rule="para" parents="10045 7263"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      a(x,y,(z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(10045(a,1),7482(a,1))].">
      <j1 rule="para" parents="10045 7482"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      a(x,y,z \ (z / (u \ 1))) = a(x,y,(u * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7488,a(flip),b,10046,a),flip(a)].">
      <j1 rule="hyper" parents="65 7488 10046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(7482,a,10047,a)].">
      <j1 rule="hyper" parents="7482 10047"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) * a(x,y,z) = (x * y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,10052,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="137 10052 14"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(4004(a,1),10052(a,1,3))].">
      <j1 rule="para" parents="4004 10052"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      a(x,y,z * (u * K(w,v5))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(6824(a,1),10052(a,1,3))].">
      <j1 rule="para" parents="6824 10052"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      a(x,y,z \ (u \ T(w,v5))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(8302(a,1),10052(a,1,3))].">
      <j1 rule="para" parents="8302 10052"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      a(x,y,z \ (u * T(w,v5))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(8305(a,1),10052(a,1,3))].">
      <j1 rule="para" parents="8305 10052"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) * u)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(8306(a,1),10052(a,1,3))].">
      <j1 rule="para" parents="8306 10052"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(8372(a,1),10052(a,1,3))].">
      <j1 rule="para" parents="8372 10052"/>
    </justification>
  </clause>

  <clause id="10093">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6)) = a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(8545(a,2),10052(a,1,3))].">
      <j1 rule="para" parents="8545 10052"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      a(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(10067(a,1),207(a,1)),flip(b)].">
      <j1 rule="para" parents="10067 207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      a(x,y,(z * (z * u)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(454(a,1),10075(a,1,3))].">
      <j1 rule="para" parents="454 10075"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) * w) * v5) = a(x,y,(u * w) * v5)
    ]]></literal>
    <justification jstring="[para(555(a,1),10075(a,1,3)),flip(a)].">
      <j1 rule="para" parents="555 10075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      a(x,y,(((z * z) / u) * w) * v5) = a(x,y,((1 / u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(769(a,1),10075(a,1,3))].">
      <j1 rule="para" parents="769 10075"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      a(x,y,((((z * z) / u) * w) * v5) * v6) = a(x,y,(((1 / u) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(941(a,1),10075(a,1,3))].">
      <j1 rule="para" parents="941 10075"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,w,v5)) = a(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1311(a,2),10075(a,1,3))].">
      <j1 rule="para" parents="1311 10075"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      a(x,y,z \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(22(a,1),10094(a,1,3))].">
      <j1 rule="para" parents="22 10094"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      a(x,y * T(z,u),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9995,a,b,9993,a),flip(a)].">
      <j1 rule="hyper" parents="325 9995 9993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      a(x,y \ ((z / y) \ u),w) = a(x,y \ ((y \ z) \ u),w)
    ]]></literal>
    <justification jstring="[para(4858(a,1),10001(a,1,2))].">
      <j1 rule="para" parents="4858 10001"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      a(x,y \ (z / u),w) = a(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(115(a,1),10004(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 10004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      a(x,y,(z * K(z * u,z)) * w) = a(x,y,R(z,u,z) * w)
    ]]></literal>
    <justification jstring="[para(4667(a,1),10039(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4667 10039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      a(x,y,z * R(T(u,w),v5,v6)) = a(x,y,z * R(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(27(a,2),10043(a,1,3,2))].">
      <j1 rule="para" parents="27 10043"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) * v5)) = a(x,y,z * (w * (v5 / (u * u))))
    ]]></literal>
    <justification jstring="[para(884(a,1),10043(a,1,3,2))].">
      <j1 rule="para" parents="884 10043"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      a(x,y,T(z,u) \ R(T(z,u),T(z,u),w)) = a(x,y,(w / (T(z,u) * w)) * z)
    ]]></literal>
    <justification jstring="[para(1078(a,2),10043(a,1,3))].">
      <j1 rule="para" parents="1078 10043"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5) \ v6) = a(x,y,L(u \ z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(252(a,1),10056(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="252 10056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(115(a,1),10058(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="115 10058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) \ w)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(114(a,1),10058(a,1,3,2))].">
      <j1 rule="para" parents="114 10058"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10045,a,b,10076,a)].">
      <j1 rule="hyper" parents="65 10045 10076"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(85(a,1),10076(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="85 10076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,w)) = a(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(959(a,1),10076(a,1,3))].">
      <j1 rule="para" parents="959 10076"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      a(x,y,z * a(u,u,z)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(7006(a,1),10077(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7006 10077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      a(x,y,(z * u) * z) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(650(a,1),10113(a,1,3)),flip(a)].">
      <j1 rule="para" parents="650 10113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      a(x,y,z * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(100(a,1),10081(a,1,3))].">
      <j1 rule="para" parents="100 10081"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      a(x,y,(z * (z * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(454(a,1),10081(a,1,3))].">
      <j1 rule="para" parents="454 10081"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      a(x,y,z * (z * L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(L(u,z,z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(412(a,1),10081(a,1,3))].">
      <j1 rule="para" parents="412 10081"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      a(x,y,(z * (u * (z * u))) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(1718(a,1),10081(a,1,3))].">
      <j1 rule="para" parents="1718 10081"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      a(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(7485(a,1),10101(a,1))].">
      <j1 rule="para" parents="7485 10101"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      a(x,y,L((z * u) * z,w,v5)) = a(x,y,L(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(1773(a,2),10116(a,1,3))].">
      <j1 rule="para" parents="1773 10116"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      a(x,(y \ z) * u,w) = a(x,u * (z / y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9995,a,b,9998,a),flip(a)].">
      <j1 rule="hyper" parents="65 9995 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      a(x,y * (z \ T(u,w)),v5) = a(x,y * (z \ u),v5)
    ]]></literal>
    <justification jstring="[para(5107(a,1),10000(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5107 10000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10125">
    <literal><![CDATA[
      a(x,(y \ T(z,u)) * w,v5) = a(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[para(9592(a,1),10000(a,1,2))].">
      <j1 rule="para" parents="9592 10000"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      a(x,(T(y,z) * u) \ w,v5) = a(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(2190(a,1),10008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2190 10008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      a(x,((y / z) \ u) * (z \ y),w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9997,a(flip),b,10029,a),flip(a)].">
      <j1 rule="hyper" parents="65 9997 10029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      a(x,y * (z * (u * (w / u))),v5) = a(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(5897(a,1),10030(a,1,2,2))].">
      <j1 rule="para" parents="5897 10030"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      a(x,y,(((z / u) * w) * v5) * v6) = a(x,y,(((u \ z) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(2810(a,1),10036(a,1,3,1))].">
      <j1 rule="para" parents="2810 10036"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      a(x,y,((z / u) \ w) * v5) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(4590(a,1),10036(a,1,3,1))].">
      <j1 rule="para" parents="4590 10036"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      a(x,y,(z \ T(u,w)) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(5107(a,1),10036(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5107 10036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(10036(a,1),10081(a,1))].">
      <j1 rule="para" parents="10036 10081"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * v5) = v6
    ]]></literal>
    <justification jstring="[para(287(a,2),10133(a,1,3))].">
      <j1 rule="para" parents="287 10133"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(2186(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2186 10133"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      a(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(2472(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2472 10133"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      a(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(2455(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2455 10133"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(2483(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2483 10133"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) * w) = v5
    ]]></literal>
    <justification jstring="[para(2488(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2488 10133"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      a(x,y,(z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(2566(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2566 10133"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      a(x,y,(z \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u / z) * w) = v5
    ]]></literal>
    <justification jstring="[para(2591(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2591 10133"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(3109(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="3109 10133"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,((u \ z) * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(2810(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="2810 10133"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(4526(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="4526 10133"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(8549(a,2),10133(a,1,3))].">
      <j1 rule="para" parents="8549 10133"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * v5) = v6
    ]]></literal>
    <justification jstring="[para(9582(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="9582 10133"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ v5) = v6
    ]]></literal>
    <justification jstring="[para(9643(a,1),10133(a,1,3))].">
      <j1 rule="para" parents="9643 10133"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      a(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(9983(a,2),10133(a,1))].">
      <j1 rule="para" parents="9983 10133"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      a(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(9984(a,1),10133(a,1))].">
      <j1 rule="para" parents="9984 10133"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(114(a,1),10149(a,1,2))].">
      <j1 rule="para" parents="114 10149"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(10112(a,2),10136(a,1))].">
      <j1 rule="para" parents="10112 10136"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      a(x,y,(z * z) * L(z \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1764(a,1),10138(a,1,3,1))].">
      <j1 rule="para" parents="1764 10138"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u * z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(1770(a,1),10138(a,1,3))].">
      <j1 rule="para" parents="1770 10138"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      a(x,y,z * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(4004(a,1),10142(a,1,3))].">
      <j1 rule="para" parents="4004 10142"/>
    </justification>
  </clause>

  <clause id="10155">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(5902(a,1),10142(a,1,3))].">
      <j1 rule="para" parents="5902 10142"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      a(x,y,z \ (u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = v6
    ]]></literal>
    <justification jstring="[para(8305(a,1),10142(a,1,3))].">
      <j1 rule="para" parents="8305 10142"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(8372(a,1),10142(a,1,3))].">
      <j1 rule="para" parents="8372 10142"/>
    </justification>
  </clause>

  <clause id="10158">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(8545(a,2),10142(a,1,3))].">
      <j1 rule="para" parents="8545 10142"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u \ z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(8550(a,1),10142(a,1,3))].">
      <j1 rule="para" parents="8550 10142"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      a(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(93(a,1),10148(a,1,2))].">
      <j1 rule="para" parents="93 10148"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(313(a,1),10148(a,1,2))].">
      <j1 rule="para" parents="313 10148"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      a(x,y * T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,w) = v5
    ]]></literal>
    <justification jstring="[para(1123(a,1),10148(a,1,2))].">
      <j1 rule="para" parents="1123 10148"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      a(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(1588(a,1),10148(a,1,2))].">
      <j1 rule="para" parents="1588 10148"/>
    </justification>
  </clause>

  <clause id="10164">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(2269(a,1),10148(a,1,2))].">
      <j1 rule="para" parents="2269 10148"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      a(x,y \ K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,w) = v5
    ]]></literal>
    <justification jstring="[para(7528(a,1),10148(a,1,2))].">
      <j1 rule="para" parents="7528 10148"/>
    </justification>
  </clause>

  <clause id="10166">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(10136,a,10048,a),flip(a)].">
      <j1 rule="hyper" parents="10136 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      a(x,y,(z * u) * u) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10116,a(flip),b,10048,a),flip(a)].">
      <j1 rule="hyper" parents="325 10116 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10168">
    <literal><![CDATA[
      a(x,y,((z * z) * (u * w)) * v5) = a(x,y,(w * ((z * z) * u)) * v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),10048(a,1,3,1))].">
      <j1 rule="para" parents="33 10048"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      a(x,y,(z / L(u,u,z)) * w) = a(x,y,(u * (z / (u * u))) * w)
    ]]></literal>
    <justification jstring="[para(1635(a,2),10048(a,1,3,1))].">
      <j1 rule="para" parents="1635 10048"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(10048(a,1),10136(a,1))].">
      <j1 rule="para" parents="10048 10136"/>
    </justification>
  </clause>

  <clause id="10171">
    <literal><![CDATA[
      a(x,y,z * (u * z)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(10136,a,10167,a)].">
      <j1 rule="hyper" parents="10136 10167"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      a(x,y,L((z * u) / (w * u),w,w)) = a(x,y,(w * R(w \ z,w,u)) * w)
    ]]></literal>
    <justification jstring="[para(748(a,1),10167(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="748 10167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(10167(a,1),10136(a,1))].">
      <j1 rule="para" parents="10167 10136"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * u) = w
    ]]></literal>
    <justification jstring="[para(10171(a,1),10136(a,1))].">
      <j1 rule="para" parents="10171 10136"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      a(x,y,(((z * u) \ (L(z,w,v5) * v6)) * ((1 / z) * u)) * v7) = a(x,y,(L(1 / z,w,v5) * v6) * v7)
    ]]></literal>
    <justification jstring="[para(9176(a,1),10050(a,1,3,1,1))].">
      <j1 rule="para" parents="9176 10050"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) = a(x,y,z * ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(2566(a,1),10055(a,1,3,2))].">
      <j1 rule="para" parents="2566 10055"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) \ v5)) = a(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[para(4526(a,1),10055(a,1,3,2))].">
      <j1 rule="para" parents="4526 10055"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      a(x,y,z * (u \ T(w,v5))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(5107(a,1),10055(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5107 10055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      a(x,y,z * L(K(u,w) * v5,v6,v7)) = a(x,y,z * L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(8549(a,2),10055(a,1,3,2))].">
      <j1 rule="para" parents="8549 10055"/>
    </justification>
  </clause>

  <clause id="10180">
    <literal><![CDATA[
      a(x,y,(z \ K(u,w)) * v5) = a(x,y,(z \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(9593(a,1),10055(a,1,3))].">
      <j1 rule="para" parents="9593 10055"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      a(x,y,(((z * z) * u) / z) \ w) = a(x,y,((1 / z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(652(a,1),10057(a,2,3,1))].">
      <j1 rule="para" parents="652 10057"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,w)) = a(x,y,(z * w) \ (w * u))
    ]]></literal>
    <justification jstring="[para(102(a,2),10059(a,1,3))].">
      <j1 rule="para" parents="102 10059"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ w) = a(x,y,z \ ((u * u) \ w))
    ]]></literal>
    <justification jstring="[para(393(a,1),10059(a,1,3)),flip(a)].">
      <j1 rule="para" parents="393 10059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u * (w * z))) = a(x,y,L(T(w,z),z,u))
    ]]></literal>
    <justification jstring="[para(240(a,1),10059(a,1,3)),flip(a)].">
      <j1 rule="para" parents="240 10059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      a(x,y,z \ ((T(u,w) * v5) * v6)) = a(x,y,z \ ((u * v5) * v6))
    ]]></literal>
    <justification jstring="[para(2186(a,1),10063(a,1,3,2))].">
      <j1 rule="para" parents="2186 10063"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(2190(a,1),10063(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2190 10063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) * v5)) = a(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(2566(a,1),10063(a,1,3,2))].">
      <j1 rule="para" parents="2566 10063"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) * u) * v5)) = a(x,y,z \ (w * v5))
    ]]></literal>
    <justification jstring="[para(2582(a,1),10063(a,1,3,2))].">
      <j1 rule="para" parents="2582 10063"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(2813(a,1),10063(a,1,3))].">
      <j1 rule="para" parents="2813 10063"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      a(x,y,z \ (u * (K(w,v5) * v6))) = a(x,y,z \ (u * v6))
    ]]></literal>
    <justification jstring="[para(2696(a,1),10063(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2696 10063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      a(x,y,(z * u) \ (K(w,u) * v5)) = a(x,y,(T(u,w) * z) \ v5)
    ]]></literal>
    <justification jstring="[para(4264(a,1),10063(a,1,3))].">
      <j1 rule="para" parents="4264 10063"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) \ v5)) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(4526(a,1),10063(a,1,3,2))].">
      <j1 rule="para" parents="4526 10063"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) \ v5) = a(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(4554(a,1),10063(a,1,3))].">
      <j1 rule="para" parents="4554 10063"/>
    </justification>
  </clause>

  <clause id="10194">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) \ v5)) = a(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(4590(a,1),10063(a,1,3,2))].">
      <j1 rule="para" parents="4590 10063"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) * v5))) = a(x,y,z * ((w * w) * (v5 / u)))
    ]]></literal>
    <justification jstring="[para(556(a,1),10087(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="556 10087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      a(x,y,(z * z) * ((z * u) \ u)) = a(x,y,R(z,z,u))
    ]]></literal>
    <justification jstring="[para(693(a,1),10087(a,1,3)),flip(a)].">
      <j1 rule="para" parents="693 10087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      a(x,y,z * (u * K(w,v5))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10045,a,b,10088,a),flip(a)].">
      <j1 rule="hyper" parents="325 10045 10088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      a(x,y,z * (u * (w / v5))) = a(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(4004(a,1),10088(a,1,3,2))].">
      <j1 rule="para" parents="4004 10088"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ v5) * w))) = a(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[para(8306(a,1),10088(a,1,3,2))].">
      <j1 rule="para" parents="8306 10088"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * v5))) = a(x,y,z * (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(8372(a,1),10088(a,1,3,2))].">
      <j1 rule="para" parents="8372 10088"/>
    </justification>
  </clause>

  <clause id="10201">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) * w) * u)) = a(x,y,z \ L(w,u \ 1,u))
    ]]></literal>
    <justification jstring="[para(389(a,1),10091(a,1,3,2,1))].">
      <j1 rule="para" parents="389 10091"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * (w * u))) = a(x,y,z \ R(w,u,u))
    ]]></literal>
    <justification jstring="[para(573(a,1),10091(a,1,3,2,1))].">
      <j1 rule="para" parents="573 10091"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      a(x,y,z \ (L(u,u,w) * w)) = a(x,y,z \ (w / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(1721(a,2),10091(a,1,3,2,1))].">
      <j1 rule="para" parents="1721 10091"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      a(x,y,z \ ((K(u,w) * (K(w,v5) * v6)) * (v5 * T(w,u)))) = a(x,y,z \ ((w * v5) * v6))
    ]]></literal>
    <justification jstring="[para(9641(a,1),10091(a,1,3,2,1))].">
      <j1 rule="para" parents="9641 10091"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      a(x,y,z \ (L(u,u,w) * (w / (u * u)))) = a(x,y,z \ (w / u))
    ]]></literal>
    <justification jstring="[para(9972(a,1),10091(a,1,3,2,1))].">
      <j1 rule="para" parents="9972 10091"/>
    </justification>
  </clause>

  <clause id="10206">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u * w) * z)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),10092(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 10092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      a(x,y \ T(z / u,w),v5) = a(x,y \ (u \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10004,a,b,10104,a)].">
      <j1 rule="hyper" parents="65 10004 10104"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * w) * v5))) = a(x,y,z \ ((w * w) * (v5 / u)))
    ]]></literal>
    <justification jstring="[para(556(a,1),10110(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="556 10110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ L(u,w,v5))) = a(x,y,z \ L(u \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(1764(a,1),10111(a,1,3,2,1))].">
      <j1 rule="para" parents="1764 10111"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      a(x,((y \ z) \ z) * u,w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[para(82(a,1),10123(a,2,2,2))].">
      <j1 rule="para" parents="82 10123"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      a(x,(y * z) * (y \ 1),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(651(a,1),10128(a,1,2,1))].">
      <j1 rule="para" parents="651 10128"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      a(x,y,((z * u) * (w * w)) * v5) = a(x,y,v5 * ((u * (w * w)) * z))
    ]]></literal>
    <justification jstring="[para(34(a,2),10166(a,1,3,1))].">
      <j1 rule="para" parents="34 10166"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      a(x,y,(K(z,u) * (w * v5)) * v6) = a(x,y,v6 * (v5 * (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[para(287(a,1),10166(a,1,3,1))].">
      <j1 rule="para" parents="287 10166"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      a(x,y,z * (((u \ (w * w)) * v5) * ((w * w) \ u))) = a(x,y,L(v5,u \ (w * w),u) * z)
    ]]></literal>
    <justification jstring="[para(712(a,1),10166(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="712 10166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      a(x,y,((z \ u) * w) * v5) = a(x,y,v5 * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(3272(a,1),10197(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3272 10197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * K(v5,v6)))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[para(7916(a,2),10197(a,1,3,2))].">
      <j1 rule="para" parents="7916 10197"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      a(x,y,z * (u \ (K(w,v5) * v6))) = a(x,y,(u \ v6) * z)
    ]]></literal>
    <justification jstring="[para(8303(a,1),10197(a,1,3,2))].">
      <j1 rule="para" parents="8303 10197"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * T(v5,v6)))) = a(x,y,(u \ (w * v5)) * z)
    ]]></literal>
    <justification jstring="[para(8305(a,1),10197(a,1,3,2))].">
      <j1 rule="para" parents="8305 10197"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * v5) = a(x,y,v5 * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[para(8372(a,1),10197(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8372 10197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      a(x,R(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(10017(a,1),10148(a,1))].">
      <j1 rule="para" parents="10017 10148"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      L(x,y,((z * u) * u) * T(z,u)) = L(x,y,a(z * u,u,z))
    ]]></literal>
    <justification jstring="[para(10028(a,1),1487(a,1,3))].">
      <j1 rule="para" parents="10028 1487"/>
    </justification>
  </clause>

  <clause id="10223">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10046,a(flip),b,10079,a),flip(a)].">
      <j1 rule="hyper" parents="325 10046 10079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10224">
    <literal><![CDATA[
      a(x,(y \ T(T(y,z) / u,u \ 1)) * w,v5) = a(x,(T(y,z) / (T(y,z) * u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(7425(a,1),10002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7425 10002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10225">
    <literal><![CDATA[
      a(x,(y * (z / u)) \ w,v5) = a(x,(y * (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10007(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="115 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10226">
    <literal><![CDATA[
      a(x,(((T(y,z) \ u) * T(y,z)) * y) \ w,v5) = a(x,(u * (u / (u / T(y,z)))) \ w,v5)
    ]]></literal>
    <justification jstring="[para(4028(a,1),10007(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4028 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10227">
    <literal><![CDATA[
      a(x,(y * y) * (z / y),u) = a(x,(1 / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(556(a,1),10020(a,1,2))].">
      <j1 rule="para" parents="556 10020"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      a(x,y,((((z * z) \ u) * z) * w) * v5) = a(x,y,((u * (z \ 1)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(885(a,1),10041(a,1,3,1,1))].">
      <j1 rule="para" parents="885 10041"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) * w) = a(x,y,(z * (z * u)) * w)
    ]]></literal>
    <justification jstring="[para(4516(a,1),10041(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4516 10041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      a(x,y,(z * (u * (u * z))) * w) = a(x,y,(z * (u * (z * u))) * w)
    ]]></literal>
    <justification jstring="[para(4575(a,1),10041(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4575 10041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10231">
    <literal><![CDATA[
      a(x,y,L(z * (K(u,w) * v5),v6,v7)) = a(x,y,L(z * v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(2696(a,1),10061(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2696 10061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10232">
    <literal><![CDATA[
      a(x,y,L(T(z,u) \ w,v5,v6)) = a(x,y,L(z \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(4526(a,1),10061(a,1,3,1))].">
      <j1 rule="para" parents="4526 10061"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      a(x,y,L(z \ T(u,w),v5,v6)) = a(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(5107(a,1),10061(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5107 10061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) \ L(L(K(x,y) * z,u,w),v5,v5) = a(v5,v5,L(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(10061(a,1),7004(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10061 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      a(x,y,(z \ (u / w)) \ v5) = a(x,y,(z \ (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10062(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="115 10062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      a(x,y,z) * (L(z,y,x) * (x * y)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(7226,a,10071,a)].">
      <j1 rule="hyper" parents="7226 10071"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) * a(z,y,x) = (z * y) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,113,a,b,10071,a),flip(a)].">
      <j1 rule="hyper" parents="325 113 10071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      a(x,y,L(z \ ((u * u) * w),v5,v6)) = a(x,y,L((u * u) * (w / z),v5,v6))
    ]]></literal>
    <justification jstring="[para(556(a,1),10073(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="556 10073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ z)) = a(x,y,(u * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10110,a(flip),b,10082,a)].">
      <j1 rule="hyper" parents="65 10110 10082"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      T(x,y) * a(z,u,u \ (z \ x)) = (z * u) * (u \ (z \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(10089(a,1),710(a,1,2))].">
      <j1 rule="para" parents="10089 710"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      a(x,y,z \ (u * (w / v5))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(115(a,1),10090(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="115 10090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (v5 * (v6 \ 1)))) = a(x,y,z \ (v5 * (v6 \ K(u,w))))
    ]]></literal>
    <justification jstring="[para(8457(a,1),10090(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8457 10090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) * K(v5,v6),v7,v8)) = a(x,y,L(L(z,v7,v8),u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),10093(a,2,3))].">
      <j1 rule="para" parents="30 10093"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      a(x,y,L(z * (z * u),w,v5)) = a(x,y,L(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[para(100(a,1),10100(a,1,3,1))].">
      <j1 rule="para" parents="100 10100"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      a(x,y * (z \ (u / w)),v5) = a(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10124(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="115 10124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      a(x,(y \ (z / u)) * w,v5) = a(x,(y \ (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10125(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="115 10125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      a(x,y,(z \ (u / w)) * v5) = a(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10132(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="115 10132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      a(x,y,z * ((((u * u) \ w) * u) \ v5)) = a(x,y,z * ((w * (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[para(885(a,1),10177(a,1,3,2,1))].">
      <j1 rule="para" parents="885 10177"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      a(x,y,z * (u \ (w / v5))) = a(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(115(a,1),10178(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="115 10178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      a(x,y,z * (u \ (((w * w) \ v5) * w))) = a(x,y,z * (u \ (v5 * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(885(a,1),10178(a,1,3,2,2))].">
      <j1 rule="para" parents="885 10178"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      a(x,y,z * (u / (u * (w \ 1)))) = a(x,y,z * (u \ (u / (w \ 1))))
    ]]></literal>
    <justification jstring="[para(7420(a,1),10178(a,1,3,2))].">
      <j1 rule="para" parents="7420 10178"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      a(x,y,(z \ K(u,w)) * v5) = a(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10077,a(flip),b,10180,a),flip(a)].">
      <j1 rule="hyper" parents="325 10077 10180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      a(x,y,(((z * u) * w) \ ((v5 * v5) * K(v6,v7))) * v8) = a(x,y,v8 * ((((v5 * v5) \ z) * u) * w))
    ]]></literal>
    <justification jstring="[para(886(a,1),10253(a,1,3,1))].">
      <j1 rule="para" parents="886 10253"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) \ v5) = a(x,y,(w * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10059,a,b,10186,a),flip(a)].">
      <j1 rule="hyper" parents="325 10059 10186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) \ v5) = a(x,y,(u * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10059,a,b,10186,a)].">
      <j1 rule="hyper" parents="65 10059 10186"/>
    </justification>
  </clause>

  <clause id="10257">
    <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(25(a,2),10186(a,1,3,1,1))].">
      <j1 rule="para" parents="25 10186"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      a(x,y,(z \ ((u / z) \ w)) \ v5) = a(x,y,(z \ ((z \ u) \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(4858(a,1),10193(a,1,3,1))].">
      <j1 rule="para" parents="4858 10193"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      a(x,y / (y * z),u) = a(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(7425(a,1),10207(a,1,2))].">
      <j1 rule="para" parents="7425 10207"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      a(x,(y * z) \ y,u) = a(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(10163,a,10259,a)].">
      <j1 rule="hyper" parents="10163 10259"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      a(x,(y * y) * (y \ z),u) = a(x,(1 / y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10029,a(flip),b,10227,a)].">
      <j1 rule="hyper" parents="65 10029 10227"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      a(x,y,z) \ (z * (x * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(10236(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10236 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      a(x,(y * y) * (y \ z),u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10003,a(flip),b,10261,a),flip(a)].">
      <j1 rule="hyper" parents="325 10003 10261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10266">
    <literal><![CDATA[
      a(x,(y \ z) * (y * y),u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(10160,a,10265,a)].">
      <j1 rule="hyper" parents="10160 10265"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      L(x,y,((T(z,u) * w) * T(z,u)) * w) = L(x,y,a(T(z,u) * w,z,w))
    ]]></literal>
    <justification jstring="[para(10013(a,1),1487(a,1,3))].">
      <j1 rule="para" parents="10013 1487"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      ((x * y) * T(z,z \ u)) / (x * (y * ((z \ u) \ u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),10070(a,1,2,2,2))].">
      <j1 rule="para" parents="114 10070"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      (x * (y * (z * K(y,u)))) * a(x,T(T(y,z),u),z) = (x * T(T(y,z),u)) * T(z,y)
    ]]></literal>
    <justification jstring="[para(4909(a,1),10072(a,1,1,2))].">
      <j1 rule="para" parents="4909 10072"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      a(x,y,z * (u * (u * w))) = a(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10096,a)].">
      <j1 rule="hyper" parents="10136 10096"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      a(x,y,((z * u) * z) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10048,a,b,10096,a)].">
      <j1 rule="hyper" parents="65 10048 10096"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      a(x,y,L(z,z * u,z * u)) = a(x,y,L(u,z,z) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10167,a(flip),b,10096,a)].">
      <j1 rule="hyper" parents="65 10167 10096"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),10096(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * v5) = v6
    ]]></literal>
    <justification jstring="[para(2282(a,1),10134(a,1,3,1))].">
      <j1 rule="para" parents="2282 10134"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      a(x,y,(((z / u) * w) * v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(((u \ z) * w) * v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(2810(a,1),10134(a,1,3,1))].">
      <j1 rule="para" parents="2810 10134"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      a(x,y,((z / u) \ w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,((u \ z) \ w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(4590(a,1),10134(a,1,3,1))].">
      <j1 rule="para" parents="4590 10134"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * ((w \ u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(2566(a,1),10146(a,1,3,2))].">
      <j1 rule="para" parents="2566 10146"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      a(x,y,z * (((u / w) * v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (((w \ u) * v5) * v6)) = v7
    ]]></literal>
    <justification jstring="[para(2810(a,1),10146(a,1,3,2))].">
      <j1 rule="para" parents="2810 10146"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      a(x,y,z * L(K(u,w) * v5,v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * L(v5,v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(8549(a,2),10146(a,1,3,2))].">
      <j1 rule="para" parents="8549 10146"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(2455(a,1),10147(a,1,3,2))].">
      <j1 rule="para" parents="2455 10147"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      a(x,y,z \ (((u / w) * v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (((w \ u) * v5) * v6)) = v7
    ]]></literal>
    <justification jstring="[para(2810(a,1),10147(a,1,3,2))].">
      <j1 rule="para" parents="2810 10147"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ ((w \ u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(4590(a,1),10147(a,1,3,2))].">
      <j1 rule="para" parents="4590 10147"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * u) \ ((u * z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(18(a,2),10157(a,1,3))].">
      <j1 rule="para" parents="18 10157"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,w)) = a(x,y,(z * w) \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10092,a,b,10182,a),flip(a)].">
      <j1 rule="hyper" parents="325 10092 10182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,7493,a(flip),b,10182,a),flip(a)].">
      <j1 rule="hyper" parents="325 7493 10182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10286">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * w) \ (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(10182(a,2),10157(a,1))].">
      <j1 rule="para" parents="10182 10157"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      a(x,y,R(z,z,u)) = a(x,y,(z * u) \ u)
    ]]></literal>
    <justification jstring="[hyper(10081,a,10196,a),flip(a)].">
      <j1 rule="hyper" parents="10081 10196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10059,a,b,10206,a)].">
      <j1 rule="hyper" parents="65 10059 10206"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      a(x,y,L(a(z,u,z * u) \ 1,z * u,z * u) * w) = a(x,y,w * ((z * u) * L(z * u,u,z)))
    ]]></literal>
    <justification jstring="[para(7439(a,1),10270(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="7439 10270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10291">
    <literal><![CDATA[
      a(x,y,a(z * u,z,u)) = a(x,y,L(u,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7489,a(flip),b,10271,a)].">
      <j1 rule="hyper" parents="65 7489 10271"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),L(u,z,z),L(u,z,z)) * w) = a(x,y,(u * L(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[para(822(a,1),10271(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="822 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      a(x,y,a(z * u,z,u)) = a(x,y,u * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10045,a,b,10291,a),flip(a)].">
      <j1 rule="hyper" parents="325 10045 10291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      a(x,y,a(z * u,z,u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,7500,a(flip),b,10293,a),flip(a)].">
      <j1 rule="hyper" parents="325 7500 10293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (w * (u * u))) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(447(a,1),10284(a,1,3)),flip(a)].">
      <j1 rule="para" parents="447 10284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7495,a(flip),b,10289,a),flip(a)].">
      <j1 rule="hyper" parents="65 7495 10289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      a(x,(y * (z / u)) * w,v5) = a(x,(y * (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(2455(a,1),10009(a,1,2,1,2))].">
      <j1 rule="para" parents="2455 10009"/>
    </justification>
  </clause>

  <clause id="10299">
    <literal><![CDATA[
      a(x,(y * (T(z,u) \ w)) * v5,v6) = a(x,(y * (z \ w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(4526(a,1),10009(a,1,2,1,2))].">
      <j1 rule="para" parents="4526 10009"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      a(x,(y * (z \ T(u,w))) * v5,v6) = a(x,(y * (z \ u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5107(a,1),10009(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5107 10009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      a(x,(y * ((z * u) \ w)) * v5,v6) = a(x,(y * ((u * z) \ w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(6163(a,1),10009(a,1,2,1,2))].">
      <j1 rule="para" parents="6163 10009"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      a(x,((y * y) \ z) * u,w) = a(x,z * ((y * y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10029,a(flip),b,10016,a),flip(a)].">
      <j1 rule="hyper" parents="325 10029 10016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      a(x,(y \ z) / (u * u),w) = a(x,z / (y * (u * u)),w)
    ]]></literal>
    <justification jstring="[para(401(a,1),10021(a,2,2))].">
      <j1 rule="para" parents="401 10021"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * v5) = a(x,y,v5 * ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(10136,a,10051,a),flip(a)].">
      <j1 rule="hyper" parents="10136 10051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      a(x,y,((1 / z) * (u * z)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(655(a,1),10064(a,1,3,1))].">
      <j1 rule="para" parents="655 10064"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) * v5) = a(x,y,(z * (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(2455(a,1),10065(a,1,3,1,2))].">
      <j1 rule="para" parents="2455 10065"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      a(x,y,(z * ((u / w) * v5)) * v6) = a(x,y,(z * ((w \ u) * v5)) * v6)
    ]]></literal>
    <justification jstring="[para(2566(a,1),10065(a,1,3,1,2))].">
      <j1 rule="para" parents="2566 10065"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) * v5)) = a(x,y,(w * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10097,a)].">
      <j1 rule="hyper" parents="10136 10097"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10050,a(flip),b,10097,a),flip(a)].">
      <j1 rule="hyper" parents="65 10050 10097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10312">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(10170,a,10311,a)].">
      <j1 rule="hyper" parents="10170 10311"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * w) = a(x,y,(z \ 1) * w)
    ]]></literal>
    <justification jstring="[para(395(a,1),10311(a,1,3,1))].">
      <j1 rule="para" parents="395 10311"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      a(x,y,(z \ (u / (w * w))) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(559(a,1),10311(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="559 10311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      a(x,y,z * R((u * u) * w,v5,v6)) = a(x,y,R(w,v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(1049(a,2),10312(a,1,3,2))].">
      <j1 rule="para" parents="1049 10312"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      a(x,y,z * L((u * u) * w,v5,v6)) = a(x,y,L(w,v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(1311(a,2),10312(a,1,3,2))].">
      <j1 rule="para" parents="1311 10312"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      a(x,y,(a(z,u,z * u) \ 1) * w) = a(x,y,(z * (u * (z * u))) * w)
    ]]></literal>
    <justification jstring="[para(7261(a,1),10313(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="7261 10313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * z) = v5
    ]]></literal>
    <justification jstring="[para(10313(a,2),10151(a,1))].">
      <j1 rule="para" parents="10313 10151"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ (w \ v5)) * v6)) = a(x,y,z * ((w \ (v5 / (u * u))) * v6))
    ]]></literal>
    <justification jstring="[para(695(a,1),10176(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="695 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (w * v5)) = a(x,y,z \ (((u * u) \ w) * v5))
    ]]></literal>
    <justification jstring="[para(391(a,1),10183(a,2,3,2))].">
      <j1 rule="para" parents="391 10183"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z)) = a(x,y,(z \ u) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7501,a,b,10187,a)].">
      <j1 rule="hyper" parents="65 7501 10187"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      a(x,y,z \ ((1 / u) * (u * (u * w)))) = a(x,y,z \ (u * L(w,u \ 1,u)))
    ]]></literal>
    <justification jstring="[para(1341(a,1),10187(a,2,3,2))].">
      <j1 rule="para" parents="1341 10187"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z * w)) \ (u * w)) = a(x,y,a(z \ u,z,w))
    ]]></literal>
    <justification jstring="[para(14(a,2),10188(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * (K(w,v5) * (u * (v6 * u))))) = a(x,y,z \ (L(v6,u \ 1,u) * u))
    ]]></literal>
    <justification jstring="[para(1342(a,1),10190(a,2,3,2))].">
      <j1 rule="para" parents="1342 10190"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      a(x,y,z \ (u * (T(w,v5) * v6))) = a(x,y,z \ (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(2114(a,1),10190(a,1,3,2,2))].">
      <j1 rule="para" parents="2114 10190"/>
    </justification>
  </clause>

  <clause id="10326">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 / w)))) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[para(2587(a,1),10190(a,1,3,2,2))].">
      <j1 rule="para" parents="2587 10190"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      a(x,y,z \ (((u * u) \ (w \ v5)) \ v6)) = a(x,y,z \ ((w \ (v5 / (u * u))) \ v6))
    ]]></literal>
    <justification jstring="[para(695(a,1),10194(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="695 10194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ v5) * w))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ v5) * z) = v6
    ]]></literal>
    <justification jstring="[para(10199(a,2),10136(a,1))].">
      <j1 rule="para" parents="10199 10136"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      a(x,y,z * (u \ (K(w,v5) * (v6 * v7)))) = a(x,y,z * (u \ (v7 * (K(w,v5) * v6))))
    ]]></literal>
    <justification jstring="[para(287(a,1),10200(a,1,3,2,2))].">
      <j1 rule="para" parents="287 10200"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ (w * (v5 * u)))) = a(x,y,z * R(T(v5,u * w),u,w))
    ]]></literal>
    <justification jstring="[para(591(a,1),10200(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="591 10200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * (v5 * v5)) * v6))) = a(x,y,z * ((u \ (v6 * w)) * (v5 * v5)))
    ]]></literal>
    <justification jstring="[para(558(a,1),10200(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="558 10200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * (v5 * v5)) * ((v5 * v5) \ v6)))) = a(x,y,z * (u \ T(v6 * w,v5 * v5)))
    ]]></literal>
    <justification jstring="[para(598(a,1),10200(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="598 10200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) = a(x,y,z * (v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(10170,a,10215,a),flip(a)].">
      <j1 rule="hyper" parents="10170 10215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      a(x,y,(z \ (K(u,w) * v5)) * v6) = a(x,y,v6 * (z \ v5))
    ]]></literal>
    <justification jstring="[para(3073(a,1),10216(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="3073 10216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ K(v5,v6)))) = a(x,y,(u \ (w \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(7528(a,1),10216(a,1,3,2,2))].">
      <j1 rule="para" parents="7528 10216"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) \ v5) * v6) = a(x,y,v6 * ((z * w) \ v5))
    ]]></literal>
    <justification jstring="[para(2190(a,1),10217(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2190 10217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10337">
    <literal><![CDATA[
      a(x,y,(z \ (T(u,w) * v5)) * v6) = a(x,y,v6 * (z \ (u * v5)))
    ]]></literal>
    <justification jstring="[para(2650(a,1),10217(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="2650 10217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * v5) = a(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[para(2493(a,1),10217(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2493 10217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      a(x,y,(z \ (u * (u * ((1 / u) * w)))) * v5) = a(x,y,v5 * (z \ L(w * u,u,u)))
    ]]></literal>
    <justification jstring="[para(9809(a,1),10219(a,2,3,2,2))].">
      <j1 rule="para" parents="9809 10219"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u \ (v5 * w))) = v6
    ]]></literal>
    <justification jstring="[para(10219(a,1),10136(a,1))].">
      <j1 rule="para" parents="10219 10136"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10096,a(flip),b,10229,a),flip(a)].">
      <j1 rule="hyper" parents="325 10096 10229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * w)) = a(x,y,L(u,w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(10170,a,10341,a)].">
      <j1 rule="hyper" parents="10170 10341"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      a(x,y,z * (u * (w * u))) = a(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10341,a)].">
      <j1 rule="hyper" parents="10136 10341"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * ((z * u) * u)) = v5
    ]]></literal>
    <justification jstring="[para(10341(a,1),10170(a,1))].">
      <j1 rule="para" parents="10341 10170"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,L(z,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7494,a(flip),b,10343,a)].">
      <j1 rule="hyper" parents="65 7494 10343"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) = w
    ]]></literal>
    <justification jstring="[para(10343(a,1),10117(a,1))].">
      <j1 rule="para" parents="10343 10117"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,z * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10045,a,b,10345,a),flip(a)].">
      <j1 rule="hyper" parents="325 10045 10345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7500,a(flip),b,10347,a),flip(a)].">
      <j1 rule="hyper" parents="325 7500 10347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      a(x,y,L(z \ (u / w),v5,v6)) = a(x,y,L(z \ (w \ u),v5,v6))
    ]]></literal>
    <justification jstring="[para(115(a,1),10233(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="115 10233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      a(x,y,((z / u) / w) \ v5) = a(x,y,(w \ (u \ z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10057,a,b,10235,a)].">
      <j1 rule="hyper" parents="65 10057 10235"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * w) \ v5))) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,7486,a(flip),b,10241,a),flip(a)].">
      <j1 rule="hyper" parents="65 7486 10241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      a(x,y,(R(z / u,u,z \ (w / v5)) \ (v5 \ w)) * v6) = a(x,y,(u * (z \ (w / v5))) * v6)
    ]]></literal>
    <justification jstring="[para(480(a,1),10247(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="480 10247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      a(x,y,z * (u \ (((w * w) * v5) / w))) = a(x,y,z * (u \ ((1 / w) \ v5)))
    ]]></literal>
    <justification jstring="[para(652(a,1),10249(a,2,3,2,2))].">
      <j1 rule="para" parents="652 10249"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) \ (v5 \ v6)))) = a(x,y,z * (u \ (v5 \ (v6 / (w * w)))))
    ]]></literal>
    <justification jstring="[para(695(a,1),10249(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="695 10249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (u * T(w,u * u))) = a(x,y,z \ (u \ L(w,u,u)))
    ]]></literal>
    <justification jstring="[para(831(a,1),10295(a,1,3,2))].">
      <j1 rule="para" parents="831 10295"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      a(a(x,y,z),u * ((w * w) \ v5),v6) = a(a(x,y,z),u * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,7568,a(flip),b,10302,a),flip(a)].">
      <j1 rule="hyper" parents="65 7568 10302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      a(x,(y \ z) / (u * u),w) = a(x,(y * (u * u)) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9996,a(flip),b,10303,a),flip(a)].">
      <j1 rule="hyper" parents="325 9996 10303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * u) * v5)) = a(x,y,(w * v5) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10304(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      a(x,y,(z \ ((u * u) \ w)) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10247,a(flip),b,10314,a)].">
      <j1 rule="hyper" parents="65 10247 10314"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * (u \ 1))) = a(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[para(650(a,1),10333(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="650 10333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      a(x,y,z \ (((u * u) \ w) * v5)) = a(x,y,z \ (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(10157,a,10351,a)].">
      <j1 rule="hyper" parents="10157 10351"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),10351(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 10351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),10364(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 10364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      a(x,y,(1 / z) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(652(a,1),10364(a,1,3))].">
      <j1 rule="para" parents="652 10364"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      a(x,y,z * R(u,u,z)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10078,a,b,10366,a)].">
      <j1 rule="hyper" parents="65 10078 10366"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10057,a(flip),b,10366,a)].">
      <j1 rule="hyper" parents="65 10057 10366"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10223,a,b,10368,a)].">
      <j1 rule="hyper" parents="65 10223 10368"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      a(x,y,z \ R(z \ 1,u,u)) = a(x,y,a(z \ 1,u,u))
    ]]></literal>
    <justification jstring="[para(1896(a,1),10368(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1896 10368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * L(w,w,u * (z * u))) = a(x,y,w \ (u * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10343,a(flip),b,10369,a)].">
      <j1 rule="hyper" parents="65 10343 10369"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ (w * v5))) = a(x,y,z \ (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10092,a,b,10365,a),flip(a)].">
      <j1 rule="hyper" parents="325 10092 10365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10183,a,b,10365,a)].">
      <j1 rule="hyper" parents="65 10183 10365"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      a(x,y,(z * (u * (w * w))) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(34(a,1),10373(a,1,3,1))].">
      <j1 rule="para" parents="34 10373"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      a(x,(y * (z * z)) \ u,w) = a(x,y \ (u / (z * z)),w)
    ]]></literal>
    <justification jstring="[para(695(a,1),10358(a,1,2)),flip(a)].">
      <j1 rule="para" parents="695 10358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) \ v5))) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10361,a)].">
      <j1 rule="hyper" parents="10136 10361"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * w) * v5))) = a(x,y,z \ (v5 * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),10363(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="9 10363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (w * v5)))) = a(x,y,z \ (L(v5,w,w) * u))
    ]]></literal>
    <justification jstring="[para(18(a,2),10363(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="18 10363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      a(x,y,z \ R(z \ 1,u,u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(1847(a,1),10370(a,2,3))].">
      <j1 rule="para" parents="1847 10370"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * u)) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),10372(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18 10372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      a(x,y,(z * (u / (w * w))) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(12(a,1),10376(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ w) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(221(a,1),10376(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="221 10376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10059,a,b,10384,a)].">
      <j1 rule="hyper" parents="65 10059 10384"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      a(x,y,K(z,u) * ((w * (v5 \ 1)) \ v6)) = a(x,y,(w * v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10027,a,b,10384,a)].">
      <j1 rule="hyper" parents="65 10027 10384"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * (v5 * v5)) = a(x,y,((u \ 1) * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,7481,a,b,10385,a)].">
      <j1 rule="hyper" parents="325 7481 10385"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10189,a,b,10385,a)].">
      <j1 rule="hyper" parents="65 10189 10385"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (z \ L(z,u,w))) \ v5) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(2017(a,1),10385(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2017 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z)) = a(x,y,(u * z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7499,a,b,10388,a)].">
      <j1 rule="hyper" parents="65 7499 10388"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      a(x,(y * (z * z)) \ u,w) = a(x,y \ ((z * z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10104,a(flip),b,10377,a),flip(a)].">
      <j1 rule="hyper" parents="325 10104 10377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      a(x,y,z \ ((T(u,w * w) * v5) * v6)) = a(x,y,z \ (v6 * ((u * (w * w)) * v5)))
    ]]></literal>
    <justification jstring="[para(244(a,1),10379(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="244 10379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      a(x,y,(z * (u * (w \ 1))) \ v5) = a(x,y,(z * (u * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(570(a,1),10383(a,1,3,1,2))].">
      <j1 rule="para" parents="570 10383"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * v5) * z) = v6
    ]]></literal>
    <justification jstring="[para(10045(a,1),10135(a,1))].">
      <j1 rule="para" parents="10045 10135"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      a(x,y,z * (u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * u) * z) = v6
    ]]></literal>
    <justification jstring="[para(10166(a,1),10135(a,1))].">
      <j1 rule="para" parents="10166 10135"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L((u * z) \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(6163(a,1),10145(a,1,3,1))].">
      <j1 rule="para" parents="6163 10145"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u * w) * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(6687(a,1),10158(a,1,3))].">
      <j1 rule="para" parents="6687 10158"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      a(x,y,L(L(z * K(u,w),v5,v6),v7,v8)) != v9
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(L(z,v5,v6),v7,v8)) = v9
    ]]></literal>
    <justification jstring="[para(8545(a,2),10158(a,1,3,1))].">
      <j1 rule="para" parents="8545 10158"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u * (w * z))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10042,a(flip),b,10184,a),flip(a)].">
      <j1 rule="hyper" parents="325 10042 10184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w * z) * u)) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(10157,a,10399,a)].">
      <j1 rule="hyper" parents="10157 10399"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      a(x,y,L(z,z \ u,w)) = a(x,y,((z \ u) * w) \ (w * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10399(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) \ (K(u,w) * (v5 * (v6 * z)))) = a(x,y,L(v6,z,K(u,w) * v5))
    ]]></literal>
    <justification jstring="[para(287(a,1),10399(a,1,3,2))].">
      <j1 rule="para" parents="287 10399"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      a(x,y,(z * (z \ L(u,z,z))) \ (z * T(u,z * z))) = a(x,y,L(z,z,z \ L(u,z,z)))
    ]]></literal>
    <justification jstring="[para(831(a,1),10399(a,1,3,2))].">
      <j1 rule="para" parents="831 10399"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * z)) \ ((u * z) * ((z \ 1) * (z \ 1)))) = a(x,y,L(T(z \ 1,z),z,u))
    ]]></literal>
    <justification jstring="[para(5688(a,1),10399(a,2,3))].">
      <j1 rule="para" parents="5688 10399"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      a(x,y,R(T(z,u * w),u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(591(a,1),10400(a,1,3))].">
      <j1 rule="para" parents="591 10400"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10040,a(flip),b,10406,a)].">
      <j1 rule="hyper" parents="65 10040 10406"/>
    </justification>
  </clause>

  <clause id="10409">
    <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),10407(a,2,3))].">
      <j1 rule="para" parents="30 10407"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      a(x,y,z \ (L(u,u,w) * w)) = a(x,y,z \ ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10110,a(flip),b,10203,a),flip(a)].">
      <j1 rule="hyper" parents="325 10110 10203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      L(x,y,((z * u) * u) * z) = L(x,y,a(z * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2318,a(flip),b,10221,a)].">
      <j1 rule="hyper" parents="65 2318 10221"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,R(z,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2293,a(flip),b,10411,a),flip(a)].">
      <j1 rule="hyper" parents="65 2293 10411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,z * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,2321,a,b,10413,a),flip(a)].">
      <j1 rule="hyper" parents="325 2321 10413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1901,a(flip),b,10414,a),flip(a)].">
      <j1 rule="hyper" parents="325 1901 10414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      a(x,y,((z * u) * u) \ w) = a(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10388,a(flip),b,10305,a)].">
      <j1 rule="hyper" parents="65 10388 10305"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ u)) \ ((z \ u) * u)) = a(x,y,z * a(z \ u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10115,a,b,10402,a),flip(a)].">
      <j1 rule="hyper" parents="65 10115 10402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      a(x,y,(((z * z) / u) * w) * v5) = a(x,y,((u \ 1) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10053,a(flip),b,10098,a),flip(a)].">
      <j1 rule="hyper" parents="325 10053 10098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(10229(a,2),10118(a,1))].">
      <j1 rule="para" parents="10229 10118"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      a(x,y,((z * z) * (u / z)) \ w) = a(x,y,((1 / z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(556(a,1),10181(a,1,3,1))].">
      <j1 rule="para" parents="556 10181"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      a(x,y,z \ (u * (T(w,v5) * v6))) = a(x,y,z \ ((w * v6) * u))
    ]]></literal>
    <justification jstring="[hyper(10157,a,10185,a)].">
      <j1 rule="hyper" parents="10157 10185"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * z) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(10191(a,1),10147(a,1))].">
      <j1 rule="para" parents="10191 10147"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      a(x,y,L((z * (u / z)) * w,v5,v6)) = a(x,y,L(u * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6166(a,1),10231(a,1,3,1))].">
      <j1 rule="para" parents="6166 10231"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) * a(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10237(a,2),292(a,1))].">
      <j1 rule="para" parents="10237 292"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      a(x,y,L(z,z * u,z * u)) = a(x,y,u * (z * L(u,z,z)))
    ]]></literal>
    <justification jstring="[para(8337(a,1),10272(a,2,3))].">
      <j1 rule="para" parents="8337 10272"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      a(x,(y * (T(z,u) \ T(z / w,w \ 1))) * v5,v6) = a(x,(y * (z / (z * w))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(7425(a,1),10299(a,2,2,1,2))].">
      <j1 rule="para" parents="7425 10299"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      a(x,(y * (z \ (u / w))) * v5,v6) = a(x,(y * (z \ (w \ u))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(115(a,1),10300(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 10300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * w)))) = a(x,y,z \ (u * (w * (w * v5))))
    ]]></literal>
    <justification jstring="[para(4516(a,1),10325(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="4516 10325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      a(x,y,z * (u \ (T(w,v5) * v6))) = a(x,y,z * (u \ (w * v6)))
    ]]></literal>
    <justification jstring="[hyper(10136,a,10337,a)].">
      <j1 rule="hyper" parents="10136 10337"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      a(a(x,y,z),u * ((w * w) \ (v5 * v5)),v6) = a(a(x,y,z),u,v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10019,a(flip),b,10357,a),flip(a)].">
      <j1 rule="hyper" parents="325 10019 10357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      a(x,y,(z * (u \ K(w,v5))) \ v6) = a(x,y,(z * u) \ v6)
    ]]></literal>
    <justification jstring="[para(9675(a,1),10386(a,1,3))].">
      <j1 rule="para" parents="9675 10386"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * (v5 \ 1))) \ v6) = a(x,y,(z * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(9629(a,1),10432(a,1,3,1,2))].">
      <j1 rule="para" parents="9629 10432"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(10387(a,1),7482(a,1))].">
      <j1 rule="para" parents="10387 7482"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      a(x,y,z \ (((u \ z) * w) * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w,u \ z,u)) = v5
    ]]></literal>
    <justification jstring="[para(10(a,1),10397(a,1,3,1))].">
      <j1 rule="para" parents="10 10397"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) * w) * v5) = a(x,y,((z \ 1) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10053,a(flip),b,10418,a)].">
      <j1 rule="hyper" parents="65 10053 10418"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(11(a,1),10418(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10437,a)].">
      <j1 rule="hyper" parents="10136 10437"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * u) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(7006(a,1),10437(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="7006 10437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      a(x,y,(z / u) \ ((u * u) \ w)) = a(x,y,((1 / u) \ z) \ w)
    ]]></literal>
    <justification jstring="[para(393(a,1),10420(a,1,3))].">
      <j1 rule="para" parents="393 10420"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w / v5) * v6))) = a(x,y,z * (u \ ((v5 \ w) * v6)))
    ]]></literal>
    <justification jstring="[para(115(a,1),10430(a,1,3,2,2,1)),flip(a)].">
      <j1 rule="para" parents="115 10430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 * w)))) = a(x,y,z * (u \ (w * (w * v5))))
    ]]></literal>
    <justification jstring="[para(4516(a,1),10430(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="4516 10430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      a(a(x,y,z),u * (((w * w) \ v5) * v5),v6) = a(a(x,y,z),u,v6)
    ]]></literal>
    <justification jstring="[para(391(a,1),10431(a,1,2,2))].">
      <j1 rule="para" parents="391 10431"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) \ v6) = a(x,y,(z * v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10393,a(flip),b,10433,a)].">
      <j1 rule="hyper" parents="65 10393 10433"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      a(x,y,(z * ((u / w) * v5)) \ v6) = a(x,y,(z * ((w \ u) * v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(2566(a,1),10445(a,1,3,1,2))].">
      <j1 rule="para" parents="2566 10445"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) * w) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10437,a(flip),b,10436,a),flip(a)].">
      <j1 rule="hyper" parents="325 10437 10436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      a(x,y,(z * (u \ (w * w))) * v5) = a(x,y,(u * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(10139,a,10447,a)].">
      <j1 rule="hyper" parents="10139 10447"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      a(x,y,((1 / z) \ u) \ w) = a(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10365,a(flip),b,10440,a),flip(a)].">
      <j1 rule="hyper" parents="65 10365 10440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      a(x,y,((1 / z) \ u) \ w) = a(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10057,a(flip),b,10449,a),flip(a)].">
      <j1 rule="hyper" parents="325 10057 10449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ w) = a(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[para(82(a,1),10451(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="82 10451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10152,a,10075,a),flip(a)].">
      <j1 rule="hyper" parents="10152 10075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10075(a,1),10152(a,1))].">
      <j1 rule="para" parents="10075 10152"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      a(x,y,(z * z) * L(u \ 1,w,v5)) = a(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10075,a,b,10453,a)].">
      <j1 rule="hyper" parents="65 10075 10453"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),L(z,u,w),w * u)) = a(x,y,(w * (u * z)) \ ((w * u) * 1))
    ]]></literal>
    <justification jstring="[para(477(a,1),10453(a,1,3)),flip(a)].">
      <j1 rule="para" parents="477 10453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10455(a,1),10081(a,1))].">
      <j1 rule="para" parents="10455 10081"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ u) * w) = a(x,y,(z * (u / (z * z))) * w)
    ]]></literal>
    <justification jstring="[hyper(10140,a,10169,a)].">
      <j1 rule="hyper" parents="10140 10169"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      a(x,y,z \ (L(u,u,w) * w)) = a(x,y,z \ (w / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7486,a(flip),b,10205,a)].">
      <j1 rule="hyper" parents="65 7486 10205"/>
    </justification>
  </clause>

  <clause id="10462">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) = a(x,y,z \ (w / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10410,a(flip),b,10460,a)].">
      <j1 rule="hyper" parents="65 10410 10460"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10110,a(flip),b,10462,a),flip(a)].">
      <j1 rule="hyper" parents="325 10110 10462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(10462(a,2),10280(a,1))].">
      <j1 rule="para" parents="10462 10280"/>
    </justification>
  </clause>

  <clause id="10465">
    <literal><![CDATA[
      a(x,y,(z * u) \ u) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10239,a(flip),b,10463,a)].">
      <j1 rule="hyper" parents="65 10239 10463"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      a(x,y,z \ (u \ 1)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10111,a(flip),b,10463,a),flip(a)].">
      <j1 rule="hyper" parents="65 10111 10463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      a(x,y,R(z,z,u)) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10287,a,b,10465,a)].">
      <j1 rule="hyper" parents="65 10287 10465"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      a(x,y,L(L(z,L(z,u,w),v5),u,w)) = a(x,y,v5 \ (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10409,a(flip),b,10467,a)].">
      <j1 rule="hyper" parents="65 10409 10467"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      a(x,y,z \ (x \ z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6879,a(flip),b,10467,a),flip(a)].">
      <j1 rule="hyper" parents="65 6879 10467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10470">
    <literal><![CDATA[
      (x * y) * (y \ (x \ y)) = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(10469(a,1),710(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10469 710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      (x * y) \ (y * a(x,y,x)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(140,a,10470,a)].">
      <j1 rule="hyper" parents="140 10470"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      ((x * y) \ y) * a(x,y,x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7617,a(flip),b,10471,a)].">
      <j1 rule="hyper" parents="65 7617 10471"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      (L(x,y,x) * y) \ y = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7658,a(flip),b,10472,a)].">
      <j1 rule="hyper" parents="65 7658 10472"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      L(x,(y * z) \ z,u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(10472(a,1),7761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10472 7761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      R((x * y) \ y,y,x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9331,a,b,10473,a)].">
      <j1 rule="hyper" parents="65 9331 10473"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      K((x * (y * ((z \ u) \ u))) / ((x * y) * T(z,z \ u)),w) = K(a(x,y,z) \ 1,w)
    ]]></literal>
    <justification jstring="[para(10268(a,1),2281(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10268 2281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ u) * w) = a(x,y,(z * ((z * z) \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10307,a(flip),b,10459,a),flip(a)].">
      <j1 rule="hyper" parents="325 10307 10459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ u) * w) = a(x,y,(z \ L(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[para(874(a,1),10477(a,2,3,1))].">
      <j1 rule="para" parents="874 10477"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      a(x,y,z * (u * (w / (v5 * v5)))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10310,a(flip),b,10107,a),flip(a)].">
      <j1 rule="hyper" parents="65 10310 10107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) \ v5))) = a(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10198,a(flip),b,10479,a)].">
      <j1 rule="hyper" parents="65 10198 10479"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w,u,u))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(874(a,1),10481(a,1,3,2))].">
      <j1 rule="para" parents="874 10481"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      a(x,y,(z \ L(u,z,z)) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10482,a)].">
      <j1 rule="hyper" parents="10136 10482"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10478,a,b,10483,a)].">
      <j1 rule="hyper" parents="65 10478 10483"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * w)) * v5) = a(x,y,(u * u) * ((w * z) * v5))
    ]]></literal>
    <justification jstring="[para(33(a,1),10168(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33 10168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) * v5))) = a(x,y,(v5 / u) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10312,a(flip),b,10195,a),flip(a)].">
      <j1 rule="hyper" parents="325 10312 10195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) * v5))) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10049,a(flip),b,10486,a),flip(a)].">
      <j1 rule="hyper" parents="325 10049 10486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (w * v5)))) = a(x,y,(u \ L(v5,w,w)) * z)
    ]]></literal>
    <justification jstring="[para(100(a,1),10488(a,1,3,2,2))].">
      <j1 rule="para" parents="100 10488"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * v5) * w))) = a(x,y,(u \ L(v5,w,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(10340,a,10489,a)].">
      <j1 rule="hyper" parents="10340 10489"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      a(x,y,(z \ ((u * w) * u)) * v5) = a(x,y,(z \ L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10219,a,b,10489,a)].">
      <j1 rule="hyper" parents="65 10219 10489"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,K(v5,v6) / u)) * v7) = a(x,y,(z \ (L(K(v5,v6) * w,u,u) * (K(v5,v6) / u))) * v7)
    ]]></literal>
    <justification jstring="[para(8624(a,1),10491(a,1,3,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8624 10491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * w) * v5))) = a(x,y,z \ (v5 / u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10364,a(flip),b,10208,a),flip(a)].">
      <j1 rule="hyper" parents="325 10364 10208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * w) * v5))) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10110,a(flip),b,10493,a),flip(a)].">
      <j1 rule="hyper" parents="325 10110 10493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      a(x,y,z \ L(u \ 1,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10365,a(flip),b,10209,a),flip(a)].">
      <j1 rule="hyper" parents="65 10365 10209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10498">
    <literal><![CDATA[
      a(x,y,z \ L(z \ 1,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,7498,a(flip),b,10496,a),flip(a)].">
      <j1 rule="hyper" parents="325 7498 10496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * w)) * v5)) = a(x,y,(v5 * u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10311,a(flip),b,10212,a),flip(a)].">
      <j1 rule="hyper" parents="65 10311 10212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * v6))) = a(x,y,(v6 * u) * z)
    ]]></literal>
    <justification jstring="[hyper(10134,a,10213,a),flip(a)].">
      <j1 rule="hyper" parents="10134 10213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ T(v5,v6)))) = a(x,y,((w \ v5) * u) * z)
    ]]></literal>
    <justification jstring="[para(5164(a,1),10501(a,1,3,2,2))].">
      <j1 rule="para" parents="5164 10501"/>
    </justification>
  </clause>

  <clause id="10504">
    <literal><![CDATA[
      a(x,y,z * ((u * T(w,v5)) * v6)) = a(x,y,(v6 * (u * w)) * z)
    ]]></literal>
    <justification jstring="[para(9586(a,1),10501(a,1,3,2))].">
      <j1 rule="para" parents="9586 10501"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      a(x,y,z * ((T(u,w) / v5) * v6)) = a(x,y,((v5 \ u) * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10333,a,b,10503,a)].">
      <j1 rule="hyper" parents="65 10333 10503"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      a(x,y,z * ((u \ T(w,v5)) * v6)) = a(x,y,((u \ w) * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(10277,a,10505,a)].">
      <j1 rule="hyper" parents="10277 10505"/>
    </justification>
  </clause>

  <clause id="10507">
    <literal><![CDATA[
      a(x,y,L(L(z * K(u,w),v5,v6),v7,v8)) = a(x,y,L(L(z,v7,v8),v5,v6))
    ]]></literal>
    <justification jstring="[para(8545(a,2),10243(a,1,3,1))].">
      <j1 rule="para" parents="8545 10243"/>
    </justification>
  </clause>

  <clause id="10508">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(L(z,v5,v6),u,w)) = v7
    ]]></literal>
    <justification jstring="[para(10243(a,1),10158(a,1))].">
      <j1 rule="para" parents="10243 10158"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ 1)) \ u)) = a(x,y,z * (u \ (u / (w \ 1))))
    ]]></literal>
    <justification jstring="[hyper(10154,a,10251,a)].">
      <j1 rule="hyper" parents="10154 10251"/>
    </justification>
  </clause>

  <clause id="10510">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * w)))) = a(x,y,z \ (L(v5,w,w) * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10380,a(flip),b,10429,a),flip(a)].">
      <j1 rule="hyper" parents="325 10380 10429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 * w)))) = a(x,y,(u \ L(v5,w,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10489,a(flip),b,10443,a),flip(a)].">
      <j1 rule="hyper" parents="325 10489 10443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * w)) * v5) = a(x,y,(w * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10075,a(flip),b,10485,a),flip(a)].">
      <j1 rule="hyper" parents="325 10075 10485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10513">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(10485(a,2),10081(a,1))].">
      <j1 rule="para" parents="10485 10081"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      a(x,y,(z * (u * (u * w))) * v5) = a(x,y,(L(w,u,u) * z) * v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),10512(a,1,3,1,2))].">
      <j1 rule="para" parents="100 10512"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      a(x,y,((((z * z) \ u) * w) * v5) * v6) = a(x,y,(v5 * (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(119(a,1),10512(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="119 10512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10517">
    <literal><![CDATA[
      a(x,y,(z * (u * (u * w))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(L(w,u,u) * z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(100(a,1),10513(a,1,3,1,2))].">
      <j1 rule="para" parents="100 10513"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      a(x,y,(z * (u * (z * u))) * w) = a(x,y,(L(z,u,u) * z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10230,a(flip),b,10515,a)].">
      <j1 rule="hyper" parents="65 10230 10515"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      a(x,y,(z * (u * (z * u))) * w) = a(x,y,(z * L(z,u,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10048,a,b,10518,a),flip(a)].">
      <j1 rule="hyper" parents="325 10048 10518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10520">
    <literal><![CDATA[
      a(x,y,L(L((z \ u) * z,w,v5),v6,v7)) = a(x,y,L(L(u,v6,v7),w,v5))
    ]]></literal>
    <justification jstring="[para(312(a,1),10507(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="312 10507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10521">
    <literal><![CDATA[
      a(x,(T(y,z) * u) \ (u * (y * z)),w) = a(x,R(z,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10007,a(flip),b,10018,a)].">
      <j1 rule="hyper" parents="65 10007 10018"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      a(x,(y * z) \ (z * (y * u)),w) = a(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10126,a(flip),b,10521,a)].">
      <j1 rule="hyper" parents="65 10126 10521"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      a(x,L(K(y,z) * u,z,y),w) = a(x,R(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(5238(a,1),10523(a,1,2))].">
      <j1 rule="para" parents="5238 10523"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      a(x,R(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10006,a(flip),b,10525,a),flip(a)].">
      <j1 rule="hyper" parents="65 10006 10525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      a(R(x,y,z),L(x,y,z),u) \ (((x \ 1) * x) * u) = (R(x,y,z) \ 1) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(10526(a,1),7315(a,1,1))].">
      <j1 rule="para" parents="10526 7315"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      L(x,y,((T(z,u) * w) * z) * w) = L(x,y,a(T(z,u) * w,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9632,a(flip),b,10267,a)].">
      <j1 rule="hyper" parents="65 9632 10267"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      L(x,y,a(T(z,u) * w,z,w)) = L(x,y,w * ((z * w) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4373,a(flip),b,10529,a),flip(a)].">
      <j1 rule="hyper" parents="65 4373 10529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      L(x,y,a(T(z,u) * w,z,w)) = L(x,y,L(w,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2931,a(flip),b,10531,a),flip(a)].">
      <j1 rule="hyper" parents="325 2931 10531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      L(x,y,a(T(z,u) * w,z,w)) = L(x,y,w * L(w,z,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,2321,a,b,10533,a),flip(a)].">
      <j1 rule="hyper" parents="325 2321 10533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      L(x,y,a(T(z,u) * w,z,w)) = L(x,y,a(z,z,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,1639,a(flip),b,10534,a),flip(a)].">
      <j1 rule="hyper" parents="325 1639 10534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      L(x,y,a(z * u,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(112(a,1),10535(a,1,3,1,1))].">
      <j1 rule="para" parents="112 10535"/>
    </justification>
  </clause>

  <clause id="10537">
    <literal><![CDATA[
      L(x,y,a(z,u,u \ z)) = L(x,y,a(u,u,u \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),10536(a,1,3,1))].">
      <j1 rule="para" parents="10 10536"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      L(x,y,a(T(z * u,K(u,w)),u,T(z,T(u,w)))) = L(x,y,a(u,u,T(z,T(u,w))))
    ]]></literal>
    <justification jstring="[para(2904(a,2),10536(a,1,3,1))].">
      <j1 rule="para" parents="2904 10536"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      a(x,y,z * L(u / w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * L(w \ u,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(2455(a,1),10279(a,1,3,2,1))].">
      <j1 rule="para" parents="2455 10279"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      a(x,y,((((z * z) / u) * w) * v5) * v6) = a(x,y,(((u \ 1) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10130,a(flip),b,10099,a),flip(a)].">
      <j1 rule="hyper" parents="325 10130 10099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      a(x,y,R((z * (z \ u)) * z,z,w)) = a(x,y,L((u * w) / (z * w),z,z))
    ]]></literal>
    <justification jstring="[para(4249(a,2),10172(a,2,3)),flip(a)].">
      <j1 rule="para" parents="4249 10172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10544">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) * w) * v5) = a(x,y,(w * (z * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10516,a(flip),b,10228,a),flip(a)].">
      <j1 rule="hyper" parents="65 10516 10228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      a(x,y,(z * (u * (w \ 1))) * v5) = a(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(10139,a,10544,a)].">
      <j1 rule="hyper" parents="10139 10544"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      a(x,y,L(z \ ((u * u) * w),v5,v6)) = a(x,y,L(w / z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,10100,a(flip),b,10238,a),flip(a)].">
      <j1 rule="hyper" parents="325 10100 10238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      a(x,y,L(z \ ((u * u) * w),v5,v6)) = a(x,y,L(z \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,10073,a(flip),b,10547,a),flip(a)].">
      <j1 rule="hyper" parents="325 10073 10547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      a(x,y,L(z \ ((u * u) * w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(10547(a,2),10159(a,1))].">
      <j1 rule="para" parents="10547 10159"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      a(x,y,L(z \ (1 / u),w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(227(a,1),10549(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="227 10549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      a(x,y,L((1 / z) \ u,w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(652(a,1),10549(a,1,3,1))].">
      <j1 rule="para" parents="652 10549"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ 1),w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10349,a(flip),b,10551,a)].">
      <j1 rule="hyper" parents="65 10349 10551"/>
    </justification>
  </clause>

  <clause id="10554">
    <literal><![CDATA[
      a(x,y,L((z \ 1) \ u,w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(82(a,1),10552(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="82 10552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),v5,v6)) = a(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(1531(a,1),10554(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1531 10554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ z,v5,v6)) = a(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(8911(a,1),10554(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="8911 10554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10557">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5,L(z,v6,v7))) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(7699(a,1),10555(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7699 10555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u) \ x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,7715,a(flip),b,10556,a),flip(a)].">
      <j1 rule="hyper" parents="325 7715 10556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10559">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),v5,x) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(54,a,10558,a)].">
      <j1 rule="hyper" parents="54 10558"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      a(x,y,a(z,u,x)) = 1
    ]]></literal>
    <justification jstring="[para(1428(a,2),10558(a,1,3))].">
      <j1 rule="para" parents="1428 10558"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,10560,a)].">
      <j1 rule="hyper" parents="54 10560"/>
    </justification>
  </clause>

  <clause id="10562">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,14,a(flip),b,10561,a),flip(a)].">
      <j1 rule="hyper" parents="325 14 10561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10563">
    <literal><![CDATA[
      (x * y) / a(z,u,x) = x * (y / a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(201,a,10561,a(flip),b,6856,a(flip))].">
      <j1 rule="hyper" parents="201 10561 6856"/>
    </justification>
  </clause>

  <clause id="10565">
    <literal><![CDATA[
      (x * y) * a(z,u,x) = x * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,10561,a(flip),b,4391,a(flip))].">
      <j1 rule="hyper" parents="137 10561 4391"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,10561,a(flip),b,7235,a)].">
      <j1 rule="hyper" parents="136 10561 7235"/>
    </justification>
  </clause>

  <clause id="10567">
    <literal><![CDATA[
      (x \ 1) * a(y,z,x) = x \ a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,10561,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="132 10561 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10568">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(10561(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10561 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,z)
    ]]></literal>
    <literal><![CDATA[
      a(u,w,z) = x
    ]]></literal>
    <justification jstring="[para(10561(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="10561 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,x)) = a(z,u,x) * y
    ]]></literal>
    <justification jstring="[para(10561(a,1),7231(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10561 7231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      (K(x,y) / z) * L(z,u \ 1,u) = K(x,y) / a(u,u \ 1,z)
    ]]></literal>
    <justification jstring="[para(10561(a,1),7543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10561 7543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * z = a(x,y,z) \ z
    ]]></literal>
    <justification jstring="[para(10561(a,1),9013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10561 9013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      R(x / (y \ 1),y \ 1,a(z,u,y)) = (x * a(z,u,y)) / (y \ a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(201,a,10567,a(flip),b,482,a),flip(a)].">
      <j1 rule="hyper" parents="201 10567 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10574">
    <literal><![CDATA[
      x * (a(y,z,x) \ 1) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(8497,a,10572,a)].">
      <j1 rule="hyper" parents="8497 10572"/>
    </justification>
  </clause>

  <clause id="10575">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ ((a(x,y,z) \ z) * u) = a(x,y,z) \ ((a(x,y,z) * z) * u)
    ]]></literal>
    <justification jstring="[para(10572(a,1),4100(a,1,2,1))].">
      <j1 rule="para" parents="10572 4100"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      x / (a(y,z,x) * a(y,z,x)) = a(y,z,x) \ (a(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[para(10572(a,1),8662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10572 8662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) = z * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(7210,a,10563,a)].">
      <j1 rule="hyper" parents="7210 10563"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      R(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(9924,a,10565,a)].">
      <j1 rule="hyper" parents="9924 10565"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,u) = u * (a(x,y,z) * a(w,v5,u))
    ]]></literal>
    <justification jstring="[hyper(7228,a,10565,a)].">
      <j1 rule="hyper" parents="7228 10565"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      x \ (y * a(z,u,x)) = (x \ y) * a(z,u,x)
    ]]></literal>
    <justification jstring="[hyper(547,a,10565,a)].">
      <j1 rule="hyper" parents="547 10565"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      (a(x,y,z) * z) \ (z * (u * a(x,y,z))) = L(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(10565(a,1),7268(a,1,2))].">
      <j1 rule="para" parents="10565 7268"/>
    </justification>
  </clause>

  <clause id="10582">
    <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(10565(a,1),7442(a,1,1))].">
      <j1 rule="para" parents="10565 7442"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(w,v5,x) = L(x,y,z) * (u * a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(10578(a,1),408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10578 408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ z = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(8656,a,10566,a)].">
      <j1 rule="hyper" parents="8656 10566"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      x \ (a(y,z,x) * u) = (x \ u) * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(548,a,10566,a)].">
      <j1 rule="hyper" parents="548 10566"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      x * (a(y,z,x) * (x \ u)) = a(y,z,x) * u
    ]]></literal>
    <justification jstring="[hyper(7219,a,10570,a)].">
      <j1 rule="hyper" parents="7219 10570"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) = z * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7194(a,1),10577(a,2,2))].">
      <j1 rule="para" parents="7194 10577"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      a(x,y,z) * (z \ (a(x,y,z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(132,a,10,a(flip),b,10586,a),flip(a)].">
      <j1 rule="hyper" parents="132 10 10586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      x * (a(y,z,x) \ (y * z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(10262,a,10587,a),flip(a)].">
      <j1 rule="hyper" parents="10262 10587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10590">
    <literal><![CDATA[
      a(x,y,z) \ (z \ u) = z \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(140,a,10588,a)].">
      <j1 rule="hyper" parents="140 10588"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      a(x,y,L(a(z,u,x),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,10568,a)].">
      <j1 rule="hyper" parents="55 10568"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      a(x,y,L(a(z,u,x) \ 1,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(10458,a,10591,a)].">
      <j1 rule="hyper" parents="10458 10591"/>
    </justification>
  </clause>

  <clause id="10593">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),v5,z) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(54,a,10592,a)].">
      <j1 rule="hyper" parents="54 10592"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      L(a(x,y,z),u,z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(10562(a,2),709(a,1))].">
      <j1 rule="para" parents="10562 709"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(152,a,10559,a)].">
      <j1 rule="hyper" parents="152 10559"/>
    </justification>
  </clause>

  <clause id="10597">
    <literal><![CDATA[
      (x / y) * (y / (L(y \ x,z,u) \ (y \ x))) = x / (L(y \ x,z,u) \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(201,a,10596,a(flip),b,6858,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 10596 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) \ x) = x * (y / (L(x,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(201,a,10596,a(flip),b,6856,a(flip))].">
      <j1 rule="hyper" parents="201 10596 6856"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      x * (y * R(L(x,z,u) \ x,x,y)) = ((L(x,z,u) \ x) * x) * y
    ]]></literal>
    <justification jstring="[para(10596(a,1),7830(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10596 7830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * u) = x * (u / (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(7824,a,10598,a)].">
      <j1 rule="hyper" parents="7824 10598"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * u) = x * ((L(x,y,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(7819(a,1),10600(a,2,2))].">
      <j1 rule="para" parents="7819 10600"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(152,a,10593,a)].">
      <j1 rule="hyper" parents="152 10593"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      (K(x,y) / z) * L(z,u \ 1,u) = a(u,u \ 1,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,7194,a(flip),b,10571,a),flip(a)].">
      <j1 rule="hyper" parents="325 7194 10571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      L(x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7473,a(flip),b,10581,a)].">
      <j1 rule="hyper" parents="65 7473 10581"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      L(x,y,z) * ((z * y) * a(z,y,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(10424,a,10583,a),flip(a)].">
      <j1 rule="hyper" parents="10424 10583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10607">
    <literal><![CDATA[
      L(a(x,y,z),u,L(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(455,a,10583,a)].">
      <j1 rule="hyper" parents="455 10583"/>
    </justification>
  </clause>

  <clause id="10608">
    <literal><![CDATA[
      (a(x,y,z) * L(z,u,w)) \ (L(z,u,w) * (v5 * a(x,y,z))) = L(v5,L(z,u,w),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(10583(a,1),7268(a,1,2))].">
      <j1 rule="para" parents="10583 7268"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      L(x,y,z) * (a(u,w,x) * v5) = a(u,w,x) * (L(x,y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(136,a,10607,a(flip),b,8976,a),flip(a)].">
      <j1 rule="hyper" parents="136 10607 8976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      x * L(x \ K(y,z),u \ 1,u) = a(u,u \ 1,x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9174,a(flip),b,10603,a)].">
      <j1 rule="hyper" parents="65 9174 10603"/>
    </justification>
  </clause>

  <clause id="10611">
    <literal><![CDATA[
      a(x,x \ 1,y) \ K(y,z) = y \ L(T(y,z),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2141,a,10610,a),flip(a)].">
      <j1 rule="hyper" parents="2141 10610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5,L(z,v6,v7))) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,7498,a(flip),b,10557,a),flip(a)].">
      <j1 rule="hyper" parents="325 7498 10557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7278,a,10582,a),flip(a)].">
      <j1 rule="hyper" parents="7278 10582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (v5 * v6))) = a(x,y,z \ (v5 * (v6 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(65,a,7502,a(flip),b,10242,a)].">
      <j1 rule="hyper" parents="65 7502 10242"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ K(v5,v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = v7
    ]]></literal>
    <justification jstring="[para(10614(a,1),10147(a,1))].">
      <j1 rule="para" parents="10614 10147"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ ((w * w) * v5))) = a(x,y,z * ((u * (w \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[para(691(a,1),10248(a,1,3,2))].">
      <j1 rule="para" parents="691 10248"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) * (v5 / w)))) = a(x,y,z * (u \ ((1 / w) \ v5)))
    ]]></literal>
    <justification jstring="[para(556(a,1),10353(a,1,3,2,2))].">
      <j1 rule="para" parents="556 10353"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * L(w,w,L(z,u,u))) = a(x,y,w \ (u * (z * u)))
    ]]></literal>
    <justification jstring="[para(2930(a,1),10371(a,1,3,2))].">
      <j1 rule="para" parents="2930 10371"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      a(x,y,L(z,u,u) / (w \ 1)) = a(x,y,w \ (u * (z * u)))
    ]]></literal>
    <justification jstring="[para(1720(a,1),10618(a,1,3))].">
      <j1 rule="para" parents="1720 10618"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ L(u,w,w)) = a(x,y,z \ (w * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(10137,a,10619,a)].">
      <j1 rule="hyper" parents="10137 10619"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * u))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10368,a(flip),b,10620,a),flip(a)].">
      <j1 rule="hyper" parents="65 10368 10620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      a(x,y,(((z \ 1) * u) * w) * v5) = a(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),10542(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10623">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) * w)) * v5) = a(x,y,((u * w) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(10139,a,10622,a)].">
      <j1 rule="hyper" parents="10139 10622"/>
    </justification>
  </clause>

  <clause id="10624">
    <literal><![CDATA[
      a(x,y,((((z * z) / u) * w) * v5) * v6) = a(x,y,((u * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10542,a,b,10622,a)].">
      <j1 rule="hyper" parents="65 10542 10622"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      a(x,y,(z * ((1 / u) * w)) * v5) = a(x,y,((u * w) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10308,a,b,10623,a)].">
      <j1 rule="hyper" parents="65 10308 10623"/>
    </justification>
  </clause>

  <clause id="10626">
    <literal><![CDATA[
      a(x,y,(((z \ (u * u)) * w) * v5) * v6) = a(x,y,((z * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10130,a(flip),b,10624,a)].">
      <j1 rule="hyper" parents="65 10130 10624"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      a(x,y,L((z * u) / (w * u),w,w)) = a(x,y,R(z * w,w,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10543(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      a(x,y,L((z * u) / (w * u),w,w)) = a(x,y,L(z * w,w,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10407,a(flip),b,10627,a),flip(a)].">
      <j1 rule="hyper" parents="325 10407 10627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      a(x,y,L((z * u) \ (w * u),z,z)) = a(x,y,L(w * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(10159,a,10628,a)].">
      <j1 rule="hyper" parents="10159 10628"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ 1)) \ v5)) = a(x,y,((u * w) \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10488,a(flip),b,10616,a),flip(a)].">
      <j1 rule="hyper" parents="65 10488 10616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      a(x,y,z * (u \ (u / (w \ 1)))) = a(x,y,((u * w) \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10509,a(flip),b,10631,a)].">
      <j1 rule="hyper" parents="65 10509 10631"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      a(x,y,((1 * z) \ u) * w) = a(x,y,w * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(7(a,1),10631(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((z * (u \ 1)) * w)) * v5) = a(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),10631(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 10631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[para(7(a,1),10634(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="7 10634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10637">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10045,a,b,10636,a),flip(a)].">
      <j1 rule="hyper" parents="325 10045 10636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      a(x,y,z * (u \ (1 * L(1 \ u,w,v5)))) = a(x,y,(u \ L(u \ 1,w,v5)) * z)
    ]]></literal>
    <justification jstring="[para(1410(a,1),10636(a,1,3,2))].">
      <j1 rule="para" parents="1410 10636"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * w) = a(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(10136,a,10637,a)].">
      <j1 rule="hyper" parents="10136 10637"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      a(x,y,z * (u \ L(u,w,v5))) = a(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1531(a,1),10637(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1531 10637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ w) * z) = v5
    ]]></literal>
    <justification jstring="[para(10637(a,2),10136(a,1))].">
      <j1 rule="para" parents="10637 10136"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ 1) \ u))) = a(x,y,((u * w) \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10249,a(flip),b,10633,a)].">
      <j1 rule="hyper" parents="65 10249 10633"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(10318,a,10635,a),flip(a)].">
      <j1 rule="hyper" parents="10318 10635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(10138,a,10635,a)].">
      <j1 rule="hyper" parents="10138 10635"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * u)) = a(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10362,a(flip),b,10643,a),flip(a)].">
      <j1 rule="hyper" parents="65 10362 10643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,u \ 1) * w) = a(x,y,w * ((z * (u \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10342,a(flip),b,10643,a)].">
      <j1 rule="hyper" parents="65 10342 10643"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      a(x,y,L(z * u,z \ 1,z \ 1) * w) = a(x,y,w * (z * R(u,z,z)))
    ]]></literal>
    <justification jstring="[para(622(a,1),10646(a,2,3,2))].">
      <j1 rule="para" parents="622 10646"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      a(x,y,z * (u \ ((1 / w) \ v5))) = a(x,y,(u \ (v5 / w)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10488,a(flip),b,10617,a),flip(a)].">
      <j1 rule="hyper" parents="65 10488 10617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      a(x,y,z * (u \ ((1 / w) \ v5))) = a(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10247,a(flip),b,10648,a),flip(a)].">
      <j1 rule="hyper" parents="325 10247 10648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      a(x,y,(z \ ((1 / u) \ w)) * v5) = a(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10650,a)].">
      <j1 rule="hyper" parents="10136 10650"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) * w) = a(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[para(85(a,1),10650(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="85 10650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(10136,a,10652,a)].">
      <j1 rule="hyper" parents="10136 10652"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ K(v5,v6)))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10335,a,b,10652,a)].">
      <j1 rule="hyper" parents="65 10335 10652"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10045,a,b,10653,a),flip(a)].">
      <j1 rule="hyper" parents="325 10045 10653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ 1) \ w)) * v5) = a(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),10651(a,1,3,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ 1) \ v5))) = a(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,10656,a)].">
      <j1 rule="hyper" parents="10136 10656"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      a(x,y,(L(z,z,(u \ 1) \ w) \ (u \ w)) * v5) = a(x,y,(z * ((u \ 1) \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10484,a(flip),b,10656,a),flip(a)].">
      <j1 rule="hyper" parents="65 10484 10656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      a(x,y,(z \ ((a(u,u \ 1,w) \ 1) \ w)) * v5) = a(x,y,(z \ L(w,u \ 1,u)) * v5)
    ]]></literal>
    <justification jstring="[para(1781(a,1),10656(a,2,3,1,2))].">
      <j1 rule="para" parents="1781 10656"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * w) = a(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10642,a(flip),b,10657,a)].">
      <j1 rule="hyper" parents="65 10642 10657"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      a(x,y,z * (u \ ((((1 / (w * v5)) * v5) \ 1) \ K(v5,w)))) = a(x,y,(u \ L(w,v5,w * v5)) * z)
    ]]></literal>
    <justification jstring="[para(6565(a,1),10657(a,2,3,1,2))].">
      <j1 rule="para" parents="6565 10657"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * w) = a(x,y,w * ((u * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10338,a(flip),b,10660,a),flip(a)].">
      <j1 rule="hyper" parents="65 10338 10660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * ((z * u) \ (z * R(z \ (z * u),w,v5)))) = a(x,y,R((z * u) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(1404(a,1),10660(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1404 10660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ w)) = a(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(10136,a,10662,a),flip(a)].">
      <j1 rule="hyper" parents="10136 10662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      a(x,y,T(z,u) \ R(T(z,u),z,w)) = a(x,y,(w / (T(z,u) * w)) * z)
    ]]></literal>
    <justification jstring="[para(9893(a,1),10108(a,1,3,2))].">
      <j1 rule="para" parents="9893 10108"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      a(x,y,z \ R(z,z,u)) = a(x,y,(u / (T(z,w) * u)) * z)
    ]]></literal>
    <justification jstring="[para(2228(a,1),10665(a,1,3))].">
      <j1 rule="para" parents="2228 10665"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      a(x,y,(z / (T(u,w) * z)) * u) = a(x,y,u * R(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10114,a(flip),b,10666,a),flip(a)].">
      <j1 rule="hyper" parents="65 10114 10666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) \ w) * z) = a(x,y,z * R(z,z,w))
    ]]></literal>
    <justification jstring="[hyper(10140,a,10668,a)].">
      <j1 rule="hyper" parents="10140 10668"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      a(x,y,z * R(z,z,u)) = a(x,y,z * ((z * u) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10336,a(flip),b,10670,a),flip(a)].">
      <j1 rule="hyper" parents="65 10336 10670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w,u \ 1,u))) = a(x,y,z \ L(u * w,u,u))
    ]]></literal>
    <justification jstring="[para(650(a,1),10322(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="650 10322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ (w * (v5 * u)))) = a(x,y,z * R(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10106,a(flip),b,10330,a),flip(a)].">
      <j1 rule="hyper" parents="325 10106 10330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      a(x,y,z * ((T(u,T(w,v5)) * v6) \ (v6 * T(u * w,K(w,v5))))) = a(x,y,z * R(w,T(u,T(w,v5)),v6))
    ]]></literal>
    <justification jstring="[para(2904(a,2),10673(a,1,3,2,2,2))].">
      <j1 rule="para" parents="2904 10673"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (u * w)) = a(x,y,z \ (u \ L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(10156,a,10356,a)].">
      <j1 rule="hyper" parents="10156 10356"/>
    </justification>
  </clause>

  <clause id="10678">
    <literal><![CDATA[
      a(x,y,z \ (((u * u) \ u) * w)) = a(x,y,z \ (u \ L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10320,a(flip),b,10676,a)].">
      <j1 rule="hyper" parents="65 10320 10676"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,u,u))) = a(x,y,z \ ((1 / u) * w))
    ]]></literal>
    <justification jstring="[para(273(a,1),10678(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="273 10678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,u,u))) = a(x,y,z \ ((u \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10187,a(flip),b,10679,a),flip(a)].">
      <j1 rule="hyper" parents="325 10187 10679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (u * w)) = a(x,y,z \ ((u \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10676,a,b,10680,a)].">
      <j1 rule="hyper" parents="65 10676 10680"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * w)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10373,a(flip),b,10681,a),flip(a)].">
      <j1 rule="hyper" parents="65 10373 10681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ 1))) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(10157,a,10682,a)].">
      <j1 rule="hyper" parents="10157 10682"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z)) = a(x,y,(z \ u) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10321,a,b,10682,a)].">
      <j1 rule="hyper" parents="65 10321 10682"/>
    </justification>
  </clause>

  <clause id="10686">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * u))) = a(x,y,z \ R(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10202,a(flip),b,10682,a),flip(a)].">
      <j1 rule="hyper" parents="65 10202 10682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      a(x,y,z \ (u * ((u \ 1) \ w))) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),10682(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 10682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ v5) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(1515(a,1),10687(a,1,3))].">
      <j1 rule="para" parents="1515 10687"/>
    </justification>
  </clause>

  <clause id="10689">
    <literal><![CDATA[
      a(x,y,z \ (u * (u \ ((u * w) * v5)))) = a(x,y,z \ (((u \ 1) * w) * v5))
    ]]></literal>
    <justification jstring="[para(4100(a,1),10687(a,1,3,2,2))].">
      <j1 rule="para" parents="4100 10687"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      a(x,y,z \ R(u,w,w)) = a(x,y,z \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10621,a(flip),b,10686,a),flip(a)].">
      <j1 rule="hyper" parents="65 10621 10686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      a(x,y,z \ L(z \ 1,u,u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10381,a(flip),b,10690,a),flip(a)].">
      <j1 rule="hyper" parents="65 10381 10690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      a(x,y,z * L(z,u,u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10498,a(flip),b,10691,a)].">
      <j1 rule="hyper" parents="65 10498 10691"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7500,a(flip),b,10692,a),flip(a)].">
      <j1 rule="hyper" parents="65 7500 10692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z * u)) = a(x,y,(u * z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10390,a(flip),b,10685,a),flip(a)].">
      <j1 rule="hyper" parents="65 10390 10685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) * w) * v5)) = a(x,y,z \ ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),10689(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 10689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      a(x,y,z \ L(u,w \ 1,w)) = a(x,y,z \ ((w * u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10201,a(flip),b,10695,a)].">
      <j1 rule="hyper" parents="65 10201 10695"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      a(x,y,z \ L(u,w \ 1,w)) = a(x,y,z \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10382,a(flip),b,10696,a),flip(a)].">
      <j1 rule="hyper" parents="325 10382 10696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      K(x,y) * (K(z \ K(x,y),z) * (u \ w)) = (u * (((z \ K(x,y)) * z) \ 1)) \ w
    ]]></literal>
    <justification jstring="[para(9566(a,1),9673(a,1,2))].">
      <j1 rule="para" parents="9566 9673"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * (u \ ((u \ 1) \ w))) * v5)) = a(x,y,z * (((1 / u) \ (w / (u * u))) * v5))
    ]]></literal>
    <justification jstring="[para(9846(a,2),10319(a,1,3,2,1))].">
      <j1 rule="para" parents="9846 10319"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w / (v5 * v5))) \ v6)) = a(x,y,z \ ((u \ w) \ ((v5 * v5) * v6)))
    ]]></literal>
    <justification jstring="[para(554(a,1),10327(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="554 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (K(v5,v6) * v7)))) = a(x,y,(u \ (v7 * w)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10217,a(flip),b,10329,a),flip(a)].">
      <j1 rule="hyper" parents="65 10217 10329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10704">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ K(v5,v6)) * v7))) = a(x,y,(u \ (v7 * (w \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(9593(a,1),10702(a,1,3,2,2))].">
      <j1 rule="para" parents="9593 10702"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * (v5 * v5)) * v6))) = a(x,y,z * (u \ (v6 * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,7483,a(flip),b,10331,a),flip(a)].">
      <j1 rule="hyper" parents="325 7483 10331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (v5 / (v6 * v6))))) = a(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10378,a(flip),b,10354,a),flip(a)].">
      <j1 rule="hyper" parents="65 10378 10354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (v5 \ 1)))) = a(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[para(271(a,1),10707(a,1,3,2,2,2))].">
      <j1 rule="para" parents="271 10707"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * (v5 * v5)) * v6))) = a(x,y,z \ ((w * v6) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10185,a(flip),b,10392,a),flip(a)].">
      <j1 rule="hyper" parents="65 10185 10392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,a(u,u,T(z,T(u,w))))
    ]]></literal>
    <justification jstring="[para(10069(a,1),10538(a,1,3))].">
      <j1 rule="para" parents="10069 10538"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      L(x,y,a(z,z,T(u,T(z,w)))) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10415,a(flip),b,10712,a),flip(a)].">
      <j1 rule="hyper" parents="65 10415 10712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(10037(a,1),10713(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10037 10713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      a(x,y,(z \ L(z \ 1,u,w)) * v5) = a(x,y,v5 * (z \ (1 * L(z,u,w))))
    ]]></literal>
    <justification jstring="[para(67(a,1),10638(a,1,3,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="67 10638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      a(x,y,(z \ L(z \ 1,u,w)) * v5) = a(x,y,v5 * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(7(a,1),10717(a,2,3,2,2))].">
      <j1 rule="para" parents="7 10717"/>
    </justification>
  </clause>

  <clause id="10719">
    <literal><![CDATA[
      a(x,y,(z \ L(z \ 1,u,w)) * v5) = a(x,y,v5 * (z * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10640,a(flip),b,10718,a),flip(a)].">
      <j1 rule="hyper" parents="325 10640 10718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      (x * (((y \ K(z,u)) * y) \ 1)) \ w = ((y \ K(z,u)) * y) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6159,a(flip),b,10699,a),flip(a)].">
      <j1 rule="hyper" parents="65 6159 10699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      (x * (y * (K(z,u) / y))) \ w = ((y \ K(u,z)) * y) * (x \ w)
    ]]></literal>
    <justification jstring="[para(9787(a,1),10720(a,1,1,2))].">
      <j1 rule="para" parents="9787 10720"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w / (v5 * v5))) \ v6)) = a(x,y,z \ ((u \ w) \ v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,10495,a(flip),b,10701,a),flip(a)].">
      <j1 rule="hyper" parents="325 10495 10701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10724">
    <literal><![CDATA[
      a(x,y,z \ (T(u / w,w \ 1) \ v5)) = a(x,y,z \ (((w \ 1) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(579(a,1),10722(a,1,3,2,1))].">
      <j1 rule="para" parents="579 10722"/>
    </justification>
  </clause>

  <clause id="10725">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) \ w) \ v5)) = a(x,y,z \ ((w / u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10192,a(flip),b,10724,a),flip(a)].">
      <j1 rule="hyper" parents="65 10192 10724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) \ w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(10725(a,2),10282(a,1))].">
      <j1 rule="para" parents="10725 10282"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      (K(x,y) * z) * ((T(y,x) * (K(x,y) * z)) \ u) = z * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8747,a(flip),b,9907,a),flip(a)].">
      <j1 rule="hyper" parents="65 8747 9907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10730">
    <literal><![CDATA[
      (K(x,y) * z) * ((y * z) \ u) = z * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(4515(a,1),10728(a,1,2,1))].">
      <j1 rule="para" parents="4515 10728"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      K(x,y) * (z * ((y * z) \ u)) = z * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(667,a,10730,a)].">
      <j1 rule="hyper" parents="667 10730"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      T(x,y) * (z * ((T(x,y) * z) \ u)) = x * (z * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(137,a,10731,a(flip),b,4507,a)].">
      <j1 rule="hyper" parents="137 10731 4507"/>
    </justification>
  </clause>

  <clause id="10734">
    <literal><![CDATA[
      T(x / y,z) * ((x / (x / y)) * ((T(x / y,z) * (x / (x / y))) \ u)) = (y \ x) * (y * (((x / y) * (x / (x / y))) \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,5272,a(flip),b,10733,a),flip(a)].">
      <j1 rule="hyper" parents="325 5272 10733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10735">
    <literal><![CDATA[
      T(x / y,z) * (y * ((T(x / y,z) * y) \ u)) = (x / y) * (y * (x \ u))
    ]]></literal>
    <justification jstring="[para(12(a,1),10733(a,2,2,2,1))].">
      <j1 rule="para" parents="12 10733"/>
    </justification>
  </clause>

  <clause id="10736">
    <literal><![CDATA[
      T(x,(y \ z) * ((z \ u) * ((z \ u) \ w))) = T(x,(y \ u) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8908,a(flip),b,9957,a)].">
      <j1 rule="hyper" parents="65 8908 9957"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      T(x,(y \ z) * ((z \ u) * w)) = T(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),10736(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      T(x,(y \ (z * u)) * w) = T(x,(y \ z) * (u * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),10737(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 10737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      L((K(x,y) * z) \ L(K(x,y) * z,u,u),w,v5) = a(u,u,L(z,w,v5)) \ 1
    ]]></literal>
    <justification jstring="[hyper(4459,a,10234,a)].">
      <j1 rule="hyper" parents="4459 10234"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      L(a(x,x,K(y,z) * u) \ 1,w,v5) = a(x,x,L(u,w,v5)) \ 1
    ]]></literal>
    <justification jstring="[para(7004(a,2),10740(a,1,1))].">
      <j1 rule="para" parents="7004 10740"/>
    </justification>
  </clause>

  <clause id="10742">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) = a(x,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(4444(a,1),10741(a,1,1,1))].">
      <j1 rule="para" parents="4444 10741"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) != w \ 1
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10742(a,2),50(a,1))].">
      <j1 rule="para" parents="10742 50"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      (x * (y * (z * K(y,u)))) * a(x,y,z) = (x * T(T(y,z),u)) * T(z,y)
    ]]></literal>
    <justification jstring="[para(10011(a,1),10269(a,1,2))].">
      <j1 rule="para" parents="10011 10269"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      (x * T(T(y,z),u)) * T(z,y) = (x * y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10086,a(flip),b,10744,a),flip(a)].">
      <j1 rule="hyper" parents="65 10086 10744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      ((x * y) * (z * K(y,u))) / L(w,w \ T(z,y),x * T(T(y,z),u)) = (x * T(T(y,z),u)) * (T(z,y) / w)
    ]]></literal>
    <justification jstring="[para(10745(a,1),6857(a,1,1))].">
      <j1 rule="para" parents="10745 6857"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      a(x,y,(z * L(z,u,u)) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[para(10607(a,1),10292(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10607 10292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      a(x,y,(z * (u * (z * u))) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10519,a,b,10748,a)].">
      <j1 rule="hyper" parents="65 10519 10748"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (u * z)) = a(x,y,L(u * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(10120,a,10749,a),flip(a)].">
      <j1 rule="hyper" parents="10120 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      a(x,y,(a(z,u,z * u) \ 1) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10317,a,b,10749,a)].">
      <j1 rule="hyper" parents="65 10317 10749"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      a(x,y,z * (u * a(u,u,z))) = a(x,y,L(z * u,u,z))
    ]]></literal>
    <justification jstring="[para(10566(a,1),10751(a,1,3))].">
      <j1 rule="para" parents="10566 10751"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10112,a(flip),b,10752,a)].">
      <j1 rule="hyper" parents="65 10112 10752"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,u,u)) * v5) = a(x,y,v5 * (z \ L(w * u,u,u)))
    ]]></literal>
    <justification jstring="[para(6319(a,1),10339(a,1,3,1,2))].">
      <j1 rule="para" parents="6319 10339"/>
    </justification>
  </clause>

  <clause id="10756">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),L(z,u,w),w * u)) = a(x,y,(w * (u * z)) \ (w * u))
    ]]></literal>
    <justification jstring="[para(8(a,1),10456(a,2,3,2))].">
      <j1 rule="para" parents="8 10456"/>
    </justification>
  </clause>

  <clause id="10757">
    <literal><![CDATA[
      K((x * (y * ((z \ u) \ u))) / ((x * y) * T(z,z \ u)),w) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,8492,a(flip),b,10476,a),flip(a)].">
      <j1 rule="hyper" parents="325 8492 10476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      K(x / (((x * y) * T(z,z \ u)) / (y * ((z \ u) \ u))),w) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,2999,a(flip),b,10757,a)].">
      <j1 rule="hyper" parents="65 2999 10757"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      K(x / R(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[para(8401(a,1),10759(a,1,1,2))].">
      <j1 rule="para" parents="8401 10759"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      K(R(x,y,z) \ x,u) = 1
    ]]></literal>
    <justification jstring="[hyper(3265,a,10760,a)].">
      <j1 rule="hyper" parents="3265 10760"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      T(R(x,y,z) \ x,u) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,10761,a)].">
      <j1 rule="hyper" parents="58 10761"/>
    </justification>
  </clause>

  <clause id="10765">
    <literal><![CDATA[
      T(x,R(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,10762,a)].">
      <j1 rule="hyper" parents="56 10762"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      x * (R(y,z,u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      (R(y,z,u) \ y) * x = w
    ]]></literal>
    <justification jstring="[para(10762(a,1),292(a,1,2))].">
      <j1 rule="para" parents="10762 292"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      (R(x,y,z) \ x) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * (R(x,y,z) \ x) = w
    ]]></literal>
    <justification jstring="[para(10765(a,1),292(a,1,2))].">
      <j1 rule="para" parents="10765 292"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      a(x,y,(L(z,z,u \ w) \ (u \ w)) * v5) = a(x,y,(z * ((u \ 1) \ w)) * v5)
    ]]></literal>
    <justification jstring="[para(5127(a,1),10658(a,1,3,1,1))].">
      <j1 rule="para" parents="5127 10658"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) \ w)) * v5) = a(x,y,(z * (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10484,a(flip),b,10769,a),flip(a)].">
      <j1 rule="hyper" parents="65 10484 10769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) \ w) * v5)) = a(x,y,(v5 * (u \ w)) * z)
    ]]></literal>
    <justification jstring="[hyper(10170,a,10770,a)].">
      <j1 rule="hyper" parents="10170 10770"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,L(u,K(y,z),x),x * K(y,z))
    ]]></literal>
    <justification jstring="[para(9559(a,1),9575(a,1,2))].">
      <j1 rule="para" parents="9559 9575"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      a(T(T(x,y * y) * z,u) \ ((y * y) \ w),v5,v6) = a(((x * (y * y)) * z) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(393(a,1),9684(a,1,1))].">
      <j1 rule="para" parents="393 9684"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * (K(u,z) * (a(w,v5,w) * v6)) = (x * ((y \ 1) * a(w,v5,w))) * v6
    ]]></literal>
    <justification jstring="[para(7598(a,1),9758(a,2,1))].">
      <j1 rule="para" parents="7598 9758"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      T((x * y) \ T(y * K(z,y),T(z,x)),x \ 1) = (x * T(y,T(z,x))) \ T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(2452(a,1),9867(a,1,1,2,1))].">
      <j1 rule="para" parents="2452 9867"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      L((x * (y / x)) / T(x,z),u,w) \ (x * (y / x)) = L(y / T(x,z),u,w) \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,9851,a(flip),b,9961,a),flip(a)].">
      <j1 rule="hyper" parents="325 9851 9961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10777">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ T(y,w)) = L(x / T(y,w),z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,9962,a(flip),b,10776,a)].">
      <j1 rule="hyper" parents="65 9962 10776"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ T(x,w)) = L(y / T(x,w),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,9368,a(flip),b,10777,a)].">
      <j1 rule="hyper" parents="65 9368 10777"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      T((x \ y) * (L(x \ y,z,u) \ x),w) = L(y / T(x,w),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,9797,a,b,10778,a)].">
      <j1 rule="hyper" parents="65 9797 10778"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,w) = L(x / T(y,w),z,u) \ x
    ]]></literal>
    <justification jstring="[para(9369(a,1),10779(a,1,1))].">
      <j1 rule="para" parents="9369 10779"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,T(w,y)) = L(x / T(y,w),z,u) \ x
    ]]></literal>
    <justification jstring="[para(2500(a,1),10780(a,2,1,1,2))].">
      <j1 rule="para" parents="2500 10780"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      T(L(1 / x,y,z) \ 1,u) \ T(x,u) = T(x,u) \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10780(a,2),9342(a,1,1))].">
      <j1 rule="para" parents="10780 9342"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,T(w,y)) = T(L(x / y,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10780,a,b,10781,a),flip(a)].">
      <j1 rule="hyper" parents="325 10780 10781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,w) = v5
    ]]></literal>
    <justification jstring="[para(10783(a,1),3672(a,1))].">
      <j1 rule="para" parents="10783 3672"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      T(L(1 / x,y,z) \ 1,u) \ T(x,u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,8459,a(flip),b,10782,a),flip(a)].">
      <j1 rule="hyper" parents="325 8459 10782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      L(x / T(y,z),u,w) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      T(L(x / y,u,w) \ x,z) = v5
    ]]></literal>
    <justification jstring="[para(10781(a,1),10784(a,1))].">
      <j1 rule="para" parents="10781 10784"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      a(x,y,a(z,u,w * v5)) = a(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(7279,a,10080,a)].">
      <j1 rule="hyper" parents="7279 10080"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      a(x,y,a(z,u,w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(10080(a,1),7279(a,1))].">
      <j1 rule="para" parents="10080 7279"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * ((K(w,v5) * v6) * (v5 * T(w,u))))) = a(x,y,z \ ((w * v5) * v6))
    ]]></literal>
    <justification jstring="[para(287(a,1),10204(a,1,3,2))].">
      <j1 rule="para" parents="287 10204"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      a(x,((T(y,z) * u) \ T(y,z)) * w,v5) = a(x,(y \ T(T(y,z) / u,u \ 1)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,9998,a(flip),b,10224,a)].">
      <j1 rule="hyper" parents="325 9998 10224"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      a(x,(((T(y,z) \ u) * T(y,z)) * y) \ w,v5) = a(x,(u * T(u / (u / y),z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(4629(a,1),10226(a,2,2,1,2))].">
      <j1 rule="para" parents="4629 10226"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      a(x,(y * (T(z,u) \ (z / w))) * v5,v6) = a(x,(y * (z / (z * w))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10300,a(flip),b,10427,a)].">
      <j1 rule="hyper" parents="65 10300 10427"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      a(x,(y * (T(z,u) \ (w \ z))) * v5,v6) = a(x,(y * (z / (z * w))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10428,a(flip),b,10793,a)].">
      <j1 rule="hyper" parents="65 10428 10793"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      a(x,(y * (z / (z * u))) * w,v5) = a(x,(y * (z \ (u \ z))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10299,a(flip),b,10795,a),flip(a)].">
      <j1 rule="hyper" parents="65 10299 10795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      a(x,(y * ((z * u) \ z)) * w,v5) = a(x,(y * (z \ (u \ z))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10298,a(flip),b,10796,a)].">
      <j1 rule="hyper" parents="65 10298 10796"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      a(x,(y * ((z * u) \ u)) * w,v5) = a(x,(y * (u \ (z \ u))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10301,a,b,10797,a)].">
      <j1 rule="hyper" parents="65 10301 10797"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      a(x,(y * (z \ (u \ z))) * L(w,(u * z) \ z,y),v5) = a(x,y * (((u * z) \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),10798(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 10798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      L(x,L(y,K(z,u),w),w * K(z,u)) = L(x,K(z,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,629,a(flip),b,10772,a),flip(a)].">
      <j1 rule="hyper" parents="65 629 10772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w * K(y,z))
    ]]></literal>
    <justification jstring="[para(9558(a,1),10800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9558 10800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2324,a(flip),b,10801,a),flip(a)].">
      <j1 rule="hyper" parents="325 2324 10801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10803">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(10801(a,2),2334(a,1))].">
      <j1 rule="para" parents="10801 2334"/>
    </justification>
  </clause>

  <clause id="10805">
    <literal><![CDATA[
      L(x \ K(y \ z,y),x,z) = ((y * (z / y)) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,6351,a(flip),b,10802,a),flip(a)].">
      <j1 rule="hyper" parents="65 6351 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(1226(a,2),10802(a,1,2))].">
      <j1 rule="para" parents="1226 10802"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(2113(a,2),10802(a,1,2))].">
      <j1 rule="para" parents="2113 10802"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      L(x,T(y,z) * u,w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(2114(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2114 10802"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      L(x,R(T(y,z),u,w),v5) = L(x,R(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(2130(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2130 10802"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w),v5) = L(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(2112(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2112 10802"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      L(x,y * T(z,u),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(2282(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2282 10802"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2454(a,2),10802(a,1,2))].">
      <j1 rule="para" parents="2454 10802"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      L(x,y * z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(2472(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2472 10802"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      L(x,y / z,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(2455(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2455 10802"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2483(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2483 10802"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      L(x,y * (z / y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2587(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2587 10802"/>
    </justification>
  </clause>

  <clause id="10817">
    <literal><![CDATA[
      L(x,(y / z) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(2566(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2566 10802"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      L(x,y * K(z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(3109(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="3109 10802"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(2492(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="2492 10802"/>
    </justification>
  </clause>

  <clause id="10820">
    <literal><![CDATA[
      L(x,y * (K(z,u) * w),v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(2696(a,1),10802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2696 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      L(x,T(y,z) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(4526(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="4526 10802"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      L(x,(T(y,z) \ u) * w,v5) = L(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(4556(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="4556 10802"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(4566(a,1),10802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4566 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      L(x,(y / z) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4590(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="4590 10802"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      L(x,R(T(y,z),u,w) \ v5,v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(4565(a,1),10802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4565 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      L(x,y \ T(z,u),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(5107(a,1),10802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5107 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      L(x,(y * z) \ u,w) = L(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6163(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="6163 10802"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      ((K(x,y) * z) \ 1) \ 1 = K(x,y) * L(z,z,z)
    ]]></literal>
    <justification jstring="[para(10802(a,1),8674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10802 8674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      L(x,(y * K(z,u)) \ w,v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(9566(a,2),10802(a,1,2))].">
      <j1 rule="para" parents="9566 10802"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      L(x,(y * T(z,u)) \ w,v5) = L(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9607(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="9607 10802"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) \ w,v5) = L(x,(y \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9609(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="9609 10802"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(9643(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="9643 10802"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      L(x,(y \ (z * T(u,w))) \ v5,v6) = L(x,(y \ (z * u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(9612(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="9612 10802"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      L(x,(y \ (K(z,u) * w)) * v5,v6) = L(x,(y \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(9649(a,1),10802(a,1,2))].">
      <j1 rule="para" parents="9649 10802"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      (x * ((K(y,z) * u) * u)) / u = (x * K(y,z)) * L(u,u,x)
    ]]></literal>
    <justification jstring="[para(10802(a,1),9617(a,2,2))].">
      <j1 rule="para" parents="10802 9617"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      (x * T(y,z)) \ ((T(y,z) * z) * x) = L(z * K(z * y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7385,a,b,10806,a)].">
      <j1 rule="hyper" parents="65 7385 10806"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      L((x * y) \ (R(x,z,u) * y),x,u * z) = L(a(T(x,y),z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,5387,a(flip),b,10806,a),flip(a)].">
      <j1 rule="hyper" parents="65 5387 10806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      L(T(T(x,y),z) \ u,x,y) = (T(x,z) * y) \ (y * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5244,a(flip),b,10806,a),flip(a)].">
      <j1 rule="hyper" parents="65 5244 10806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      x * L(T(y,z),y,x) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,10806,a(flip),b,1721,a(flip))].">
      <j1 rule="hyper" parents="137 10806 1721"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      (x * T(y,z)) * L(u,y,x) = x * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(137,a,10806,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 10806 18"/>
    </justification>
  </clause>

  <clause id="10845">
    <literal><![CDATA[
      L(x,T(y,z),T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = v5
    ]]></literal>
    <justification jstring="[para(10806(a,2),1574(a,1))].">
      <j1 rule="para" parents="10806 1574"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      L(T(1 / x,x * y) \ z,1 / x,x \ y) = y \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7508,a(flip),b,10807,a),flip(a)].">
      <j1 rule="hyper" parents="65 7508 10807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      L(x,y * (z * z),a(u,w,v5)) = L(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,7561,a(flip),b,10813,a),flip(a)].">
      <j1 rule="hyper" parents="325 7561 10813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      L(x,a(y,z,y) * (u * w),v5) = L(x,w * (a(y,z,y) * u),v5)
    ]]></literal>
    <justification jstring="[para(6210(a,1),10813(a,1,2))].">
      <j1 rule="para" parents="6210 10813"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * w,v5 * v6,v7)) = a(x,y,L(w,v6 * v5,v7))
    ]]></literal>
    <justification jstring="[para(10813(a,1),10061(a,1,3))].">
      <j1 rule="para" parents="10813 10061"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      L(x,y \ z,T(u,w)) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[hyper(1574,a,10814,a),flip(a)].">
      <j1 rule="hyper" parents="1574 10814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      L(T(x / y,z) \ u,y \ x,z) = ((x / y) * z) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5236,a(flip),b,10814,a),flip(a)].">
      <j1 rule="hyper" parents="65 5236 10814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      (x * (y / z)) * L(u,z \ y,x) = x * ((y / z) * u)
    ]]></literal>
    <justification jstring="[hyper(137,a,10814,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 10814 18"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      L(x,y \ ((z * z) * u),w) = L(x,(z * z) * (u / y),w)
    ]]></literal>
    <justification jstring="[para(556(a,1),10814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="556 10814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      L(x,(y * y) \ (z \ u),w) = L(x,z \ (u / (y * y)),w)
    ]]></literal>
    <justification jstring="[para(695(a,1),10814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="695 10814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      L(x,y * (z / u),w) = L(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(4004(a,1),10818(a,1,2))].">
      <j1 rule="para" parents="4004 10818"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      L(x,y \ K(z,u),w) = L(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(7528(a,1),10818(a,1,2))].">
      <j1 rule="para" parents="7528 10818"/>
    </justification>
  </clause>

  <clause id="10866">
    <literal><![CDATA[
      L(x,y \ (z * T(u,w)),v5) = L(x,y \ (z * u),v5)
    ]]></literal>
    <justification jstring="[para(8305(a,1),10818(a,1,2))].">
      <j1 rule="para" parents="8305 10818"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      L(x,y \ ((z \ u) * z),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(8306(a,1),10818(a,1,2))].">
      <j1 rule="para" parents="8306 10818"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      L(x,y \ (z * u),w) = L(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(8372(a,1),10818(a,1,2))].">
      <j1 rule="para" parents="8372 10818"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      R(x,y,L(((1 / z) * u) * w,z * z,v5) * (v5 * (z * T(z,v6)))) = R(x,y,v5 * ((T(z,v6) * u) * w))
    ]]></literal>
    <justification jstring="[para(10811(a,1),8750(a,1,3,1))].">
      <j1 rule="para" parents="10811 8750"/>
    </justification>
  </clause>

  <clause id="10870">
    <literal><![CDATA[
      L(x,y / T(z,u),w) = L(x,z \ y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10814,a,b,10821,a)].">
      <j1 rule="hyper" parents="65 10814 10821"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      L(x,L(y / z,u,w) \ v5,v6) = L(x,L(z \ y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(252(a,1),10821(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="252 10821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10872">
    <literal><![CDATA[
      T(x,y) * L(z,u \ x,u) = u * ((u \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,10826,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="137 10826 101"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      L(x,y \ (z / u),w) = L(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(115(a,1),10826(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 10826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      L(x,y \ ((z * u) * (z \ 1)),w) = L(x,y \ R(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(621(a,1),10826(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="621 10826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      L(x,a(y,y,z) \ T(1,u),w) = L(x,z \ L(z,y,y),w)
    ]]></literal>
    <justification jstring="[para(7004(a,1),10826(a,2,2))].">
      <j1 rule="para" parents="7004 10826"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      L(x,x \ y,z) \ (y * z) = T(z * (T(y,z) / x),x)
    ]]></literal>
    <justification jstring="[para(10826(a,1),8409(a,1,1))].">
      <j1 rule="para" parents="10826 8409"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      L(x,K(y,z) / u,w) = L(x,u \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10814,a,b,10865,a)].">
      <j1 rule="hyper" parents="65 10814 10865"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      L((x \ K(y,z)) \ (u \ w),x \ 1,u) = (u * (x \ K(y,z))) \ w
    ]]></literal>
    <justification jstring="[hyper(65,a,308,a(flip),b,10865,a),flip(a)].">
      <j1 rule="hyper" parents="65 308 10865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      L(x,T(y,z) \ u,w) = L(x,u / T(y,v5),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10821,a,b,10870,a)].">
      <j1 rule="hyper" parents="325 10821 10870"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(846(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="846 10803"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      L(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1226(a,2),10803(a,1,2))].">
      <j1 rule="para" parents="1226 10803"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      L(x,(T(y,z) * u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,(y * u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(2186(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="2186 10803"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      L(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(2472(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="2472 10803"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(2483(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="2483 10803"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      L(x,y * (z / y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(2587(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="2587 10803"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      L(x,(y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(2566(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="2566 10803"/>
    </justification>
  </clause>

  <clause id="10888">
    <literal><![CDATA[
      L(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(3109(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="3109 10803"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u * (z * y),w) = v5
    ]]></literal>
    <justification jstring="[para(2492(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="2492 10803"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      L(x,T(y,z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(4526(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="4526 10803"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      L(x,(y / z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(4590(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="4590 10803"/>
    </justification>
  </clause>

  <clause id="10892">
    <literal><![CDATA[
      L(x,y \ T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(5164(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="5164 10803"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      L(x,(y * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z * y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(6163(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="6163 10803"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      L(x,L(K(y,z) * u,w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(u,w,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(8549(a,2),10803(a,1,2))].">
      <j1 rule="para" parents="8549 10803"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(9643(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="9643 10803"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,u,w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(9737(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="9737 10803"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      L(x,y \ (z * y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(22(a,1),10881(a,1,2))].">
      <j1 rule="para" parents="22 10881"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      L((x * T(y,z)) \ x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L((y * z) \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(5259(a,2),10881(a,1))].">
      <j1 rule="para" parents="5259 10881"/>
    </justification>
  </clause>

  <clause id="10899">
    <literal><![CDATA[
      L(x,y \ (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(7196(a,1),10881(a,1,2))].">
      <j1 rule="para" parents="7196 10881"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = L(y,y,x) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,10843,a),flip(a)].">
      <j1 rule="hyper" parents="373 10843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10901">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),z,w * v5) * w) \ ((w * v5) / (T(z,u) \ 1))) = a(x,y,L(v5,w,L(T(z,u),z,w * v5)))
    ]]></literal>
    <justification jstring="[para(10843(a,1),10206(a,1,3,2))].">
      <j1 rule="para" parents="10843 10206"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      a((T(x,y) \ 1) \ y,z,u) = a(L(x,x,y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(10900(a,1),1870(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10900 1870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      L(x,y \ (z * T(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (z * u),v5) = v6
    ]]></literal>
    <justification jstring="[para(8305(a,1),10888(a,1,2))].">
      <j1 rule="para" parents="8305 10888"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      L(x,y \ (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(8372(a,1),10888(a,1,2))].">
      <j1 rule="para" parents="8372 10888"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      L(x,(((y * y) * z) / y) * u,w) = L(x,((1 / y) \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(652(a,1),10817(a,2,2,1))].">
      <j1 rule="para" parents="652 10817"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      L(x,(y \ 1) * (y \ z),u) = L(x,(y * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(653(a,1),10817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="653 10817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      L(x,((y \ 1) * (y \ ((y \ 1) \ z))) * u,w) = L(x,(((1 / y) \ z) / (y * y)) * u,w)
    ]]></literal>
    <justification jstring="[para(9846(a,2),10817(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9846 10817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      L(x,y * (K(z,u) * w),v5) = L(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10813,a,b,10820,a),flip(a)].">
      <j1 rule="hyper" parents="325 10813 10820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      L(x,y * ((z / u) * w),v5) = L(x,y * ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(2566(a,1),10820(a,1,2,2))].">
      <j1 rule="para" parents="2566 10820"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      L(x,y * (z * (K(u,w) * v5)),v6) = L(x,y * (z * v5),v6)
    ]]></literal>
    <justification jstring="[para(2696(a,1),10820(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2696 10820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      L(x,y * (T(z,u) \ w),v5) = L(x,y * (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(4526(a,1),10820(a,1,2,2))].">
      <j1 rule="para" parents="4526 10820"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) * w,v5) = L(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[para(9592(a,1),10820(a,1,2))].">
      <j1 rule="para" parents="9592 10820"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      L(x,((K(y,z) * u) / (T(y,z) * w)) \ v5,v6) = L(x,((y * w) \ u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2190(a,1),10824(a,2,2,1))].">
      <j1 rule="para" parents="2190 10824"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      L(x,(T(y * z,u) \ ((z * u) * y)) \ w,v5) = L(x,L(u * K(u * z,y),z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(8576(a,1),10824(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8576 10824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      L(x,((y * z) / (y * (y * z))) \ u,w) = L(x,R(T(1 / y,z),y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(9307(a,1),10824(a,2,2,1))].">
      <j1 rule="para" parents="9307 10824"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) = L(x,L(T(u,y),y,z),w)
    ]]></literal>
    <justification jstring="[para(240(a,1),10827(a,1,2)),flip(a)].">
      <j1 rule="para" parents="240 10827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      (x * y) / L(z * K(u,w),z \ y,x) = x * (y / (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(201,a,10830,a(flip),b,6856,a(flip))].">
      <j1 rule="hyper" parents="201 10830 6856"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      L(x,(T(y,z) \ u) \ w,v5) = L(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(4557(a,1),10830(a,1,2,1))].">
      <j1 rule="para" parents="4557 10830"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      L(x,(y * (z * u)) \ w,v5) = L(x,(y * (u * z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(6078(a,1),10830(a,1,2,1))].">
      <j1 rule="para" parents="6078 10830"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      L(x,y \ (T(z,u) * w),v5) = L(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[para(2114(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="2114 10833"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      L(x,y \ ((z * u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(2488(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="2488 10833"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      L(x,y \ ((z / u) * w),v5) = L(x,y \ ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(2566(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="2566 10833"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      L(x,y \ (((z / u) * w) * v5),v6) = L(x,y \ (((u \ z) * w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(2810(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="2810 10833"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) * (w * u)),v5) = L(x,y \ (w * (u * z)),v5)
    ]]></literal>
    <justification jstring="[para(2492(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="2492 10833"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      L(x,y \ (z * (K(u,w) * v5)),v6) = L(x,y \ (z * v5),v6)
    ]]></literal>
    <justification jstring="[para(2696(a,1),10833(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2696 10833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      L(x,y \ (T(z,u) \ w),v5) = L(x,y \ (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(4526(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="4526 10833"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      L(x,y \ ((z / u) \ w),v5) = L(x,y \ ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(4590(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="4590 10833"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      L(x,y \ ((z \ K(u,w)) \ v5),v6) = L(x,y \ ((z \ 1) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(9610(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="9610 10833"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      L(x,y \ (z \ (K(u,w) * v5)),v6) = L(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(9643(a,1),10833(a,1,2,2))].">
      <j1 rule="para" parents="9643 10833"/>
    </justification>
  </clause>

  <clause id="10932">
    <literal><![CDATA[
      L(x,y \ ((z * u) * (1 / z)),w) = L(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(651(a,1),10867(a,1,2,2,1))].">
      <j1 rule="para" parents="651 10867"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      L(x,y \ (z * (u \ a(w,v5,w))),v6) = L(x,y \ ((u \ 1) * z),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,7768,a(flip),b,10868,a),flip(a)].">
      <j1 rule="hyper" parents="325 7768 10868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      L(x,y \ (z * (u / (T(z,w) \ 1))),v5) = L(x,y \ (u * (z * T(z,w))),v5)
    ]]></literal>
    <justification jstring="[para(9840(a,1),10868(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9840 10868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      L(x,y \ (x \ z),y) * (x \ z) = y * ((y \ (z / x)) * x)
    ]]></literal>
    <justification jstring="[para(10873(a,1),8376(a,1,1))].">
      <j1 rule="para" parents="10873 8376"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      L(x,(y / (z * z)) \ (z \ y),u) = L(x,L(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(9972(a,1),10873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9972 10873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10938">
    <literal><![CDATA[
      L(x,T(y,z) \ u,T(w,v5)) = L(x,T(y,v6) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10853,a,b,10879,a)].">
      <j1 rule="hyper" parents="325 10853 10879"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      L(x,(y * z) * u,w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(2472(a,1),10908(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2472 10908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      L(K(x,y) * z,z,z) = ((K(x,y) * z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,8549,a,b,10829,a)].">
      <j1 rule="hyper" parents="325 8549 10829"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      (x * T(T(y,z),u)) * L(w,y,x) = x * (T(T(y,z),u) * w)
    ]]></literal>
    <justification jstring="[para(10806(a,1),10844(a,1,2))].">
      <j1 rule="para" parents="10806 10844"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(114(a,1),10890(a,1,2,1))].">
      <j1 rule="para" parents="114 10890"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      L(x,y \ ((z \ u) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(114(a,1),10892(a,1,2,2))].">
      <j1 rule="para" parents="114 10892"/>
    </justification>
  </clause>

  <clause id="10946">
    <literal><![CDATA[
      L(K(x,y) * z,z,z) = (z \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(2616(a,1),10941(a,2,1))].">
      <j1 rule="para" parents="2616 10941"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      x * (x * (K(y,z) / x)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,8428,a,b,10946,a)].">
      <j1 rule="hyper" parents="65 8428 10946"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      ((x \ K(y,z)) * x) * (x \ u) = ((x \ K(y,z)) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(10947(a,1),10721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10947 10721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      L(x,((y / z) \ u) * w,v5) = L(x,((z \ y) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10822(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="115 10822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10950">
    <literal><![CDATA[
      L(x,(K(y,z) * T((u * z) \ w,v5)) \ v6,v7) = L(x,((u * T(z,y)) \ w) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(9607(a,1),10831(a,2,2,1))].">
      <j1 rule="para" parents="9607 10831"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      L(x,(y \ (z / u)) \ w,v5) = L(x,(y \ (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10832(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="115 10832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      L(x,y \ 1,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(221(a,1),10850(a,1,2)),flip(a)].">
      <j1 rule="para" parents="221 10850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      L(x,y \ (z * z),a(u,w,v5)) = L(x,y \ 1,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(395(a,1),10850(a,1,2))].">
      <j1 rule="para" parents="395 10850"/>
    </justification>
  </clause>

  <clause id="10954">
    <literal><![CDATA[
      L(x,L(y * (z * z),u,w),a(v5,v6,v7)) = L(x,L(y,u,w),a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(1069(a,2),10850(a,1,2))].">
      <j1 rule="para" parents="1069 10850"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,a(x,y,z),a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(10952(a,1),537(a,1))].">
      <j1 rule="para" parents="10952 537"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * T(y,u)) * 1),a(w,v5,v6)) = L(x,(1 / T(y,u)) * z,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(2417(a,2),10952(a,1,2))].">
      <j1 rule="para" parents="2417 10952"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      L(x,R(y,z,u) \ y,a(w,v5,v6)) = L(x,y \ R(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(5794(a,1),10952(a,1,2))].">
      <j1 rule="para" parents="5794 10952"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      L(x,y \ 1,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10952(a,1),10880(a,1))].">
      <j1 rule="para" parents="10952 10880"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      L(x,y \ (z * (u / w)),v5) = L(x,y \ (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),10866(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="115 10866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      L(x,y \ (((z \ a(u,w,u)) \ 1) \ v5),v6) = L(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,7769,a(flip),b,10928,a)].">
      <j1 rule="hyper" parents="65 7769 10928"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      ((x * (y / x)) * z) \ y = (y * z) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,476,a(flip),b,10805,a),flip(a)].">
      <j1 rule="hyper" parents="65 476 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      ((x * y) \ ((z \ x) * z)) * K(u,u \ x) = ((z * (x / z)) * y) \ (u * (x / u))
    ]]></literal>
    <justification jstring="[para(10962(a,1),8304(a,1,1))].">
      <j1 rule="para" parents="10962 8304"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      L(((T(x,y) * z) \ (z * u)) \ (T(T(x,z),y) \ u),w,T(T(x,z),y) \ u) = L(T(T(x,z),y) \ u,x,z) \ (T(T(x,z),y) \ u)
    ]]></literal>
    <justification jstring="[para(10842(a,1),10596(a,1,1,1))].">
      <j1 rule="para" parents="10842 10596"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      (x * (y / (y / z))) * L(u,z,x) = x * ((y / (y / z)) * u)
    ]]></literal>
    <justification jstring="[para(85(a,1),10857(a,1,2,2))].">
      <j1 rule="para" parents="85 10857"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      T(x,y) * z != u * ((u \ T(x,y)) * w)
    ]]></literal>
    <literal><![CDATA[
      L(w,u \ x,u) = z
    ]]></literal>
    <justification jstring="[para(10872(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="10872 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      L(x,(y \ 1) * (y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10906(a,2),10893(a,1))].">
      <j1 rule="para" parents="10906 10893"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      L(x,y \ (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(2455(a,1),10895(a,1,2,2))].">
      <j1 rule="para" parents="2455 10895"/>
    </justification>
  </clause>

  <clause id="10971">
    <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(2488(a,1),10895(a,1,2,2))].">
      <j1 rule="para" parents="2488 10895"/>
    </justification>
  </clause>

  <clause id="10972">
    <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(4590(a,1),10895(a,1,2,2))].">
      <j1 rule="para" parents="4590 10895"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      a(L(x,x,y) * y,z,u) = a(T(x,y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5172,a(flip),b,10902,a),flip(a)].">
      <j1 rule="hyper" parents="65 5172 10902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      a(L(x,x,y) * y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,4562,a(flip),b,10973,a),flip(a)].">
      <j1 rule="hyper" parents="325 4562 10973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      a(L(x,x,y) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(10973(a,2),4563(a,1))].">
      <j1 rule="para" parents="10973 4563"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      a((x \ y) * L(z,z,(x \ 1) \ y),u,w) = a(z \ ((x \ 1) \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(5034,a,10974,a)].">
      <j1 rule="hyper" parents="5034 10974"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      a(L(x,x,y \ ((z \ u) \ w)) * (y \ ((u / z) \ w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ ((u / z) \ w)),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(8395(a,1),10975(a,1,1,1))].">
      <j1 rule="para" parents="8395 10975"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      L(x,((y * y) \ z) \ (y \ z),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(10891,a,10936,a)].">
      <j1 rule="hyper" parents="10891 10936"/>
    </justification>
  </clause>

  <clause id="10980">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,a(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ L(y,z,u),a(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(2015(a,1),10958(a,1,2))].">
      <j1 rule="para" parents="2015 10958"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      L(x,y \ ((z * z) * (z \ y)),u) = L(x,L(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(554(a,1),10979(a,1,2))].">
      <j1 rule="para" parents="554 10979"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      L(x,R(T(y,z),y,y \ z),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(741(a,1),10981(a,1,2))].">
      <j1 rule="para" parents="741 10981"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      L(x,(y \ ((z / u) \ w)) * v5,v6) = L(x,(y \ ((u \ z) \ w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(4590(a,1),10835(a,1,2,1,2))].">
      <j1 rule="para" parents="4590 10835"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      L(x,y \ ((z * z) * u),w) = L(x,(z * z) * (y \ u),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10864,a(flip),b,10859,a),flip(a)].">
      <j1 rule="hyper" parents="325 10864 10859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      L(x,(y \ 1) * (y \ ((y \ 1) \ z)),u) = L(x,(1 / y) \ (z / (y * y)),u)
    ]]></literal>
    <justification jstring="[para(9846(a,2),10860(a,1,2))].">
      <j1 rule="para" parents="9846 10860"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      L(x,(y * y) \ (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ ((y * y) \ u),w) = v5
    ]]></literal>
    <justification jstring="[para(10860(a,2),10970(a,1))].">
      <j1 rule="para" parents="10860 10970"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      L(x,a(y,y,z) \ 1,u) = L(x,z \ L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(10892,a,10875,a)].">
      <j1 rule="hyper" parents="10892 10875"/>
    </justification>
  </clause>

  <clause id="10988">
    <literal><![CDATA[
      L(x,y * (((z \ 1) \ u) * z),w) = L(x,y * (u * (z * z)),w)
    ]]></literal>
    <justification jstring="[para(564(a,1),10909(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="564 10909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      L(x,y * T(z / T(u \ 1,u),u),w) = L(x,y * ((z / u) * (u / (u \ 1))),w)
    ]]></literal>
    <justification jstring="[para(8797(a,2),10909(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8797 10909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      L(x,y * (z * (u / w)),v5) = L(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(2455(a,1),10910(a,1,2,2,2))].">
      <j1 rule="para" parents="2455 10910"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      L(x,y * (z * ((u / w) \ v5)),v6) = L(x,y * (z * ((w \ u) \ v5)),v6)
    ]]></literal>
    <justification jstring="[para(4590(a,1),10910(a,1,2,2,2))].">
      <j1 rule="para" parents="4590 10910"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      L(x,(y * (z * (y \ 1))) \ u,w) = L(x,L(z,y \ 1,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(261(a,1),10921(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="261 10921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10993">
    <literal><![CDATA[
      L(x,(((y * y) \ z) * ((y * y) * u)) \ w,v5) = L(x,T(z * u,y * y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(598(a,1),10921(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="598 10921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      L(x,(y * (K(z,u) * w)) \ v5,v6) = L(x,K(u,z) * ((y * w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(9611(a,1),10921(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9611 10921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      L(x,y \ ((z * u) * w),v5) = L(x,y \ (w * (u * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(10904,a,10923,a),flip(a)].">
      <j1 rule="hyper" parents="10904 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10996">
    <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),10923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      L(x,(y * ((z * z) * (u * w))) \ ((((z * z) * u) * y) * w),v5) = L(x,a(y,(z * z) * u,w),v5)
    ]]></literal>
    <justification jstring="[para(121(a,1),10923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="121 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10998">
    <literal><![CDATA[
      L(x,y \ (((z * T(z,u)) * (T(z,u) \ w)) * v5),v6) = L(x,y \ (T(w / (z \ 1),T(z,u)) * v5),v6)
    ]]></literal>
    <justification jstring="[para(8584(a,1),10923(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8584 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      L(x,y \ ((z * u) * (K(z,w) * v5)),v6) = L(x,y \ ((u * T(z,w)) * v5),v6)
    ]]></literal>
    <justification jstring="[para(9586(a,1),10923(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9586 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11000">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) * (z \ u)),w) = L(x,y \ ((z * z) \ u),w)
    ]]></literal>
    <justification jstring="[para(653(a,1),10924(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="653 10924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      L(x,y \ ((z * (u * (w / u))) * v5),v6) = L(x,y \ ((z * w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(9591(a,1),10927(a,1,2,2))].">
      <j1 rule="para" parents="9591 10927"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      L(x,y \ (z \ ((u / w) \ v5)),v6) = L(x,y \ (z \ ((w \ u) \ v5)),v6)
    ]]></literal>
    <justification jstring="[para(4590(a,1),10931(a,1,2,2,2))].">
      <j1 rule="para" parents="4590 10931"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      L(x,y \ (z \ ((u \ K(w,v5)) \ v6)),v7) = L(x,y \ (z \ ((u \ 1) \ v6)),v7)
    ]]></literal>
    <justification jstring="[para(9610(a,1),10931(a,1,2,2,2))].">
      <j1 rule="para" parents="9610 10931"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      L(x,y \ (z * z),a(u,w,v5)) = L(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10952,a(flip),b,10953,a),flip(a)].">
      <j1 rule="hyper" parents="325 10952 10953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      L(x,(y * y) * (y \ z),u) = L(x,(1 / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(652(a,1),10984(a,1,2)),flip(a)].">
      <j1 rule="para" parents="652 10984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      L(x,(y * y) * (y \ z),u) = L(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10824,a(flip),b,11005,a),flip(a)].">
      <j1 rule="hyper" parents="325 10824 11005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,a(u,w,v5)) = L(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,7561,a(flip),b,11006,a),flip(a)].">
      <j1 rule="hyper" parents="65 7561 11006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      L(x,(y * z) \ ((u * y) * z),w) = L(x,L(K(z,y) * u,y,z),w)
    ]]></literal>
    <justification jstring="[para(5238(a,1),10995(a,2,2))].">
      <j1 rule="para" parents="5238 10995"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),a(w,v5,v6)) = L(x,y * L(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(1531(a,1),11007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1531 11007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(11007(a,1),10944(a,1))].">
      <j1 rule="para" parents="11007 10944"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      (x * ((K(y,z) * u) * u)) / u = x * (K(y,z) * L(u,u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,9559,a(flip),b,10836,a),flip(a)].">
      <j1 rule="hyper" parents="325 9559 10836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      L(x,y * (z * T(u,w)),v5) = L(x,(u * z) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(10883,a,10940,a),flip(a)].">
      <j1 rule="hyper" parents="10883 10940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      L(x,y * (z * T(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,(u * z) * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(10940(a,1),10883(a,1))].">
      <j1 rule="para" parents="10940 10883"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10810,a(flip),b,10918,a),flip(a)].">
      <j1 rule="hyper" parents="325 10810 10918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11017">
    <literal><![CDATA[
      L(x,y \ ((z * u) * (z \ 1)),w) = L(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10959,a(flip),b,10932,a)].">
      <j1 rule="hyper" parents="65 10959 10932"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      L(x,(x \ (y / x)) \ (x \ y),x \ (y / x)) * (x \ y) = (x \ (y / x)) * (x * ((x \ (y / x)) \ (y / x)))
    ]]></literal>
    <justification jstring="[para(324(a,1),10935(a,2,2))].">
      <j1 rule="para" parents="324 10935"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      (x * T(T(x,y),y)) * R(L(z,x,x),u,w) = R(x * (T(T(x,y),y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(10943(a,1),4082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10943 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      (x * (y / (y / z))) * u != x * ((y / (y / z)) * w)
    ]]></literal>
    <literal><![CDATA[
      L(w,z,x) = u
    ]]></literal>
    <justification jstring="[para(10966(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="10966 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      L(x,((y * z) * u) \ ((y * u) * z),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(10893,a,10996,a)].">
      <j1 rule="hyper" parents="10893 10996"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      L(x,(y * (a(z,u,z) * ((w * w) \ v5))) \ (((a(z,u,z) / w) * y) * (w \ v5)),v6) = L(x,a(y,a(z,u,z) / w,w \ v5),v6)
    ]]></literal>
    <justification jstring="[para(6314(a,1),10996(a,1,2,1,2))].">
      <j1 rule="para" parents="6314 10996"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      (x * ((K(y,z) * u) * u)) / u = x * L(K(y,z) * u,u,x)
    ]]></literal>
    <justification jstring="[para(8549(a,2),11011(a,2,2))].">
      <j1 rule="para" parents="8549 11011"/>
    </justification>
  </clause>

  <clause id="11024">
    <literal><![CDATA[
      L(x,y \ R(z,u,u),w) = L(x,y \ L(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10874,a(flip),b,11017,a)].">
      <j1 rule="hyper" parents="65 10874 11017"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      L(x,y \ L(y,z,z),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(1896(a,1),11024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1896 11024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      L(x,a(y,y,z) \ 1,u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10987,a,b,11025,a)].">
      <j1 rule="hyper" parents="65 10987 11025"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(z,z,y),a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(11026(a,1),10958(a,1))].">
      <j1 rule="para" parents="11026 10958"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      (x * (K(y,z) * (u * u))) / u = x * L(K(y,z) * u,u,x)
    ]]></literal>
    <justification jstring="[para(287(a,1),11023(a,1,1,2))].">
      <j1 rule="para" parents="287 11023"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      (x * K(y,z)) / (u / (u * u)) = x * L(K(y,z) * u,u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,697,a(flip),b,11028,a)].">
      <j1 rule="hyper" parents="65 697 11028"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      x * L(K(y,z) * u,u,x) = (x * K(y,z)) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(271(a,1),11029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="271 11029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      x * L(K(y,z) * u,u,x) = x / (u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,8348,a(flip),b,11030,a),flip(a)].">
      <j1 rule="hyper" parents="325 8348 11030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      (x / (y \ 1)) \ (x * (K(z,u) * w)) = (x / (y \ K(z,u))) \ (x * w)
    ]]></literal>
    <justification jstring="[para(11031(a,1),9982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11031 9982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11033">
    <literal><![CDATA[
      L(x,y * (a(z,u,z) * w),v5) = L(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,7759,a(flip),b,10851,a),flip(a)].">
      <j1 rule="hyper" parents="65 7759 10851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      a(x,y,L(z,u * w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,w * u,v5)) = v6
    ]]></literal>
    <justification jstring="[para(10852(a,1),10145(a,1))].">
      <j1 rule="para" parents="10852 10145"/>
    </justification>
  </clause>

  <clause id="11036">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ (z * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(L(w,w,u),w * u,z)) = v5
    ]]></literal>
    <justification jstring="[para(7487(a,1),11035(a,1))].">
      <j1 rule="para" parents="7487 11035"/>
    </justification>
  </clause>

  <clause id="11037">
    <literal><![CDATA[
      L(x,((y * y) * (z / y)) * u,w) = L(x,((1 / y) \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(556(a,1),10905(a,1,2,1))].">
      <j1 rule="para" parents="556 10905"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      L(x,(y * y) * ((z / y) * u),w) = L(x,((1 / y) \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(33(a,1),11037(a,1,2))].">
      <j1 rule="para" parents="33 11037"/>
    </justification>
  </clause>

  <clause id="11039">
    <literal><![CDATA[
      L(x,(y * y) * ((z / y) * u),w) = L(x,((y \ 1) \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10949,a(flip),b,11038,a),flip(a)].">
      <j1 rule="hyper" parents="325 10949 11038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      L(x,(y * y) * ((y \ z) * u),w) = L(x,((y \ 1) \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10909,a(flip),b,11039,a)].">
      <j1 rule="hyper" parents="65 10909 11039"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      L(x,(y \ a(z,u,z)) * (y \ (a(z,u,z) * (((y \ a(z,u,z)) \ w) * v5))),v6) = L(x,(((y \ a(z,u,z)) \ 1) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(7742(a,1),11040(a,1,2))].">
      <j1 rule="para" parents="7742 11040"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ ((T(y,z) * z) * u)),w,v5) = a(x * L(z * K(z * y,u),y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(10840(a,1),6170(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10840 6170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      L(x,y \ (z * (u * w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ ((w * u) * z),v5) = v6
    ]]></literal>
    <justification jstring="[para(10868(a,1),10971(a,1))].">
      <j1 rule="para" parents="10868 10971"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      L(x,(y * y) * (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ ((y * y) * u),w) = v5
    ]]></literal>
    <justification jstring="[para(10984(a,1),10971(a,1))].">
      <j1 rule="para" parents="10984 10971"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      L(x,R(T(y,z * u),z,u),w) = L(x,L(K(u,z) * y,z,u),w)
    ]]></literal>
    <justification jstring="[para(591(a,1),11008(a,1,2))].">
      <j1 rule="para" parents="591 11008"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      L(x,L(K(y,z) * u,z,y),w) = L(x,R(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10809,a(flip),b,11047,a),flip(a)].">
      <j1 rule="hyper" parents="65 10809 11047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11049">
    <literal><![CDATA[
      L(x,R(y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(10894,a,11048,a),flip(a)].">
      <j1 rule="hyper" parents="10894 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11051">
    <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(11048(a,1),10894(a,1))].">
      <j1 rule="para" parents="11048 10894"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      L(x,L(T(y,z),y,y \ z),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10982,a(flip),b,11049,a),flip(a)].">
      <j1 rule="hyper" parents="65 10982 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11054">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,L(x,y,z),x) = (1 / x) * (R((1 / x) \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11049(a,1),4417(a,1,2))].">
      <j1 rule="para" parents="11049 4417"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      L(x,L(y,y,y \ z),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10810,a(flip),b,11053,a)].">
      <j1 rule="hyper" parents="65 10810 11053"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      L(x,L(y,y,y * z),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),11055(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="9 11055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(z,z,y),a(w,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(10715(a,2),11027(a,1))].">
      <j1 rule="para" parents="10715 11027"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      L((x * y) \ (R(x,z,u) * y),x,u * z) = L(a(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(1868(a,1),10841(a,2,1))].">
      <j1 rule="para" parents="1868 10841"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      (x * y) \ (R(x,z,u) * y) = y \ (R(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(43,a,9362,a,b,11060,a),flip(a)].">
      <j1 rule="hyper" parents="43 9362 11060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      L(x \ (R(y,z,u) * (y \ x)),y,u * z) = L(a(y,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),11060(a,1,1,1))].">
      <j1 rule="para" parents="10 11060"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      ((x \ 1) * y) \ (R(x \ 1,z,u) * y) = y \ (R(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,5540,a,b,11061,a)].">
      <j1 rule="hyper" parents="65 5540 11061"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),a(w,v5,v6)) = L(x,L(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(221(a,1),10954(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="221 10954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      L(x,(y * (K(z,u) * w)) \ v5,v6) = L(x,(y * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10802,a(flip),b,10994,a),flip(a)].">
      <j1 rule="hyper" parents="325 10802 10994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      L(x,(y * ((z / u) * w)) \ v5,v6) = L(x,(y * ((u \ z) * w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2566(a,1),11066(a,1,2,1,2))].">
      <j1 rule="para" parents="2566 11066"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      L(x,y \ (((z * (u / z)) * w) * v5),v6) = L(x,y \ ((w * u) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(10971,a,11001,a)].">
      <j1 rule="hyper" parents="10971 11001"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      L(a(x,y,z),x,x \ u) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9362,a(flip),b,11062,a),flip(a)].">
      <j1 rule="hyper" parents="65 9362 11062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x,y,z) \ (R(x,u,w) * (x \ L(x,y,z)))) = K(x,x \ 1) * (R(x \ 1,u,w) * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11064(a,1),8027(a,1,2))].">
      <j1 rule="para" parents="11064 8027"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      L(x,(((y / z) * u) * w) \ v5,v6) = L(x,(w * ((z \ y) * u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10893,a,11068,a)].">
      <j1 rule="hyper" parents="10893 11068"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      L(x,y \ ((T(1 / T(z \ 1,z),z) * u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(8797(a,2),11069(a,1,2,2,1,1))].">
      <j1 rule="para" parents="8797 11069"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      L(x,(((1 / y) * z) * y) \ u,w) = L(x,L(z,y \ 1,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(261(a,1),11072(a,2,2,1))].">
      <j1 rule="para" parents="261 11072"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      L(T(1 / x,x * y) \ z,x \ 1,x \ y) = y \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10814,a(flip),b,10849,a)].">
      <j1 rule="hyper" parents="65 10814 10849"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      a((x \ y) * L(z,z,x \ y),u,w) = a(z \ ((x \ 1) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(5127(a,1),10976(a,1,1,2))].">
      <j1 rule="para" parents="5127 10976"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      a((x \ y) / (z \ 1),u,w) = a(z \ ((x \ 1) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(1720(a,1),11077(a,1,1))].">
      <j1 rule="para" parents="1720 11077"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      a((x \ 1) \ (y \ z),u,w) = a(x \ ((y \ 1) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(2574,a,11078,a)].">
      <j1 rule="hyper" parents="2574 11078"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ z),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5172,a(flip),b,11079,a),flip(a)].">
      <j1 rule="hyper" parents="65 5172 11079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      a(x \ (y / (z \ 1)),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5118,a,b,11080,a)].">
      <j1 rule="hyper" parents="65 5118 11080"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      a(R(x / y,y,x \ ((z \ 1) \ u)) \ (z \ u),w,v5) = a(y * (x \ ((z \ 1) \ u)),w,v5)
    ]]></literal>
    <justification jstring="[para(480(a,1),11080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="480 11080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11083">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(1721(a,2),11081(a,1,1))].">
      <j1 rule="para" parents="1721 11081"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(y \ ((w * w) * (x \ y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,5124,a,b,11083,a),flip(a)].">
      <j1 rule="hyper" parents="325 5124 11083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      a(R(T(x,y),x,x \ y),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(741(a,1),11084(a,2,1)),flip(a)].">
      <j1 rule="para" parents="741 11084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      a(L(T(x,y),x,x \ y),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8679,a(flip),b,11085,a)].">
      <j1 rule="hyper" parents="65 8679 11085"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      a(L(x,x,x \ y),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(1878,a,11086,a)].">
      <j1 rule="hyper" parents="1878 11086"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      L(x,(K(y,z) * (u / (T(y,z) * w))) \ v5,v6) = L(x,((y * w) \ u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(666(a,1),10915(a,1,2,1))].">
      <j1 rule="para" parents="666 10915"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      L(x,y \ (z * (u / (T(z,w) \ 1))),v5) = L(x,(y \ u) * (z * T(z,w)),v5)
    ]]></literal>
    <justification jstring="[para(8468(a,1),10934(a,2,2))].">
      <j1 rule="para" parents="8468 10934"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      L(x,(y \ 1) * (y \ ((y \ 1) \ z)),u) = L(x,y \ T(z,y \ (y \ 1)),u)
    ]]></literal>
    <justification jstring="[para(880(a,1),10985(a,2,2))].">
      <j1 rule="para" parents="880 10985"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      L(x,y \ ((z * T(u,w)) * v5),v6) = L(x,y \ ((u * z) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10927,a(flip),b,10999,a),flip(a)].">
      <j1 rule="hyper" parents="65 10927 10999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      L(x,y \ (z * (T(u,w) * v5)),v6) = L(x,y \ ((u * v5) * z),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10995,a(flip),b,11092,a)].">
      <j1 rule="hyper" parents="65 10995 11092"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      L(x,(y / (T(z,u) * w)) \ (K(u,z) * v5),v6) = L(x,((z * w) \ y) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2674(a,1),11089(a,1,2))].">
      <j1 rule="para" parents="2674 11089"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      L(x,y \ (z * (u / (T(z,w) \ 1))),v5) = L(x,(z * z) * (y \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,11013,a(flip),b,11090,a),flip(a)].">
      <j1 rule="hyper" parents="325 11013 11090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      L(x,y \ (z * ((T(z,u) \ 1) \ w)),v5) = L(x,(z * z) * (y \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10959,a(flip),b,11096,a)].">
      <j1 rule="hyper" parents="65 10959 11096"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      L(x,y \ (((T(z,u) \ 1) \ w) * z),v5) = L(x,(z * z) * (y \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(10904,a,11098,a)].">
      <j1 rule="hyper" parents="10904 11098"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      L(x,(y \ 1) * (y \ ((y \ 1) \ z)),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10826,a(flip),b,11091,a),flip(a)].">
      <j1 rule="hyper" parents="325 10826 11091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      L(x,(y * y) \ ((y \ 1) \ z),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(10969,a,11100,a)].">
      <j1 rule="hyper" parents="10969 11100"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      L(x,(y / (T(z,u) * w)) \ v5,v6) = L(x,((z * w) \ y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10895,a,11095,a)].">
      <j1 rule="hyper" parents="10895 11095"/>
    </justification>
  </clause>

  <clause id="11104">
    <literal><![CDATA[
      L(x,((T(y,z) * u) \ w) \ v5,v6) = L(x,((y * u) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10891,a,11103,a)].">
      <j1 rule="hyper" parents="10891 11103"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      L(x,R(T(y,T(z,u) * w),w,T(z,u)) \ v5,v6) = L(x,((z * w) \ ((y * w) * T(T(z,u),w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(6541(a,1),11104(a,1,2,1))].">
      <j1 rule="para" parents="6541 11104"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      L(x,R(T(1 / y,z),y,z) \ u,w) = L(x,R(1 / y,y,y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(226(a,2),10917(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="226 10917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      (x * T(T(x,y),y)) * L(R(z,u,w),x,x) = R(x * (T(T(x,y),y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(29(a,1),11019(a,1,2))].">
      <j1 rule="para" parents="29 11019"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      R(x * (T(T(x,y),y) * z),u,w) = x * (T(T(x,y),y) * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10943,a(flip),b,11108,a),flip(a)].">
      <j1 rule="hyper" parents="65 10943 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      R(x * (T(T(x,K(y,z)),K(y,z)) * u),w,v5) = x * (x * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(3619(a,1),11109(a,2,2,1))].">
      <j1 rule="para" parents="3619 11109"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      R(x * (x * y),z,u) = x * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2838(a,1),11110(a,1,1,2,1))].">
      <j1 rule="para" parents="2838 11110"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      x * (x * R(T(y,x),z,u)) = R(x * (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),11111(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 11111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      L(x,T((y * z) \ u,w) \ (K(z,v5) * v6),v7) = L(x,((y * T(z,v5)) \ u) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(2674(a,1),10950(a,1,2))].">
      <j1 rule="para" parents="2674 10950"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      ((x * (y / x)) * z) \ (x * (y / x)) = (y * z) \ ((x \ y) * T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8305,a(flip),b,10963,a),flip(a)].">
      <j1 rule="hyper" parents="65 8305 10963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11115">
    <literal><![CDATA[
      ((x * (y / x)) * z) \ (x * (y / x)) = (y * z) \ y
    ]]></literal>
    <justification jstring="[para(231(a,1),11114(a,2,2))].">
      <j1 rule="para" parents="231 11114"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      L(x,y * T(z / T(u \ 1,u),u),w) = L(x,y * ((z / u) * ((u \ 1) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10990,a(flip),b,10989,a),flip(a)].">
      <j1 rule="hyper" parents="325 10990 10989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      L(x,(((y * y) \ z) * ((y * y) * u)) \ w,v5) = L(x,(z * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10821,a(flip),b,10993,a),flip(a)].">
      <j1 rule="hyper" parents="325 10821 10993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      L(x,(y * ((z * z) * u)) \ ((z * z) * w),v5) = L(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(691(a,1),11117(a,1,2))].">
      <j1 rule="para" parents="691 11117"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      L(x,(y * y) * ((z * ((y * y) * u)) \ w),v5) = L(x,(z * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10984,a(flip),b,11119,a)].">
      <j1 rule="hyper" parents="65 10984 11119"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) \ w,v5) = L(x,(z * z) * ((y * u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),11120(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,x,L(x,y,z)) = (1 / x) * (R((1 / x) \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(7460(a,1),11054(a,1,2))].">
      <j1 rule="para" parents="7460 11054"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      L(x,y \ ((T((z \ 1) \ 1,z) * u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(1363(a,1),11073(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="1363 11073"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      L(x,y \ ((((z \ 1) \ 1) * u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(323(a,1),11123(a,1,2,2,1,1))].">
      <j1 rule="para" parents="323 11123"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      L(x,T((y * z) \ u,w) \ v5,v6) = L(x,((y * T(z,v7)) \ u) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10895,a,11113,a)].">
      <j1 rule="hyper" parents="10895 11113"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      L(x,((y * T(z,u)) \ w) \ v5,v6) = L(x,((y * z) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10890,a,11125,a),flip(a)].">
      <j1 rule="hyper" parents="10890 11125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      L(x,y * T(z / T(u \ 1,u),u),w) = L(x,y * ((z / u) * (u * u)),w)
    ]]></literal>
    <justification jstring="[para(272(a,1),11116(a,2,2,2,2))].">
      <j1 rule="para" parents="272 11116"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      L(x,y * T(z / T(u \ 1,u),u),w) = L(x,y * ((u \ z) * (u * u)),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10909,a(flip),b,11128,a),flip(a)].">
      <j1 rule="hyper" parents="325 10909 11128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      L(x,y * (z / T(u \ 1,u)),w) = L(x,y * ((u \ z) * (u * u)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10811,a(flip),b,11129,a)].">
      <j1 rule="hyper" parents="65 10811 11129"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      L(x,y * (T(z \ 1,z) \ u),w) = L(x,y * ((z \ u) * (z * z)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10864,a(flip),b,11130,a)].">
      <j1 rule="hyper" parents="65 10864 11130"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      L(x,y * ((z \ u) * (z * z)),w) = L(x,y * ((z \ 1) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10911,a(flip),b,11132,a),flip(a)].">
      <j1 rule="hyper" parents="65 10911 11132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,x,L(x,y,z)) = (1 / x) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(85(a,1),11122(a,2,2,1,1))].">
      <j1 rule="para" parents="85 11122"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ R(x \ R(x,y,z),x,z * y)) * L(u,x \ R(x,y,z),a(x,y,z)) = (1 / (x \ R(x,y,z))) * (R(x \ R(x,y,z),x,z * y) * u)
    ]]></literal>
    <justification jstring="[para(2326(a,2),11135(a,1,2,3))].">
      <j1 rule="para" parents="2326 11135"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      a(T(T(x,y * y) * z,u) \ w,v5,v6) = a(((x * (y * y)) * z) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,5122,a(flip),b,10773,a)].">
      <j1 rule="hyper" parents="65 5122 10773"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      a((T(x,y * y) * z) \ u,w,v5) = a(((x * (y * y)) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(4563,a,11137,a)].">
      <j1 rule="hyper" parents="4563 11137"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      a(((x * (y * y)) * z) \ u,w,v5) = a((x * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8397,a(flip),b,11138,a),flip(a)].">
      <j1 rule="hyper" parents="65 8397 11138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      a(L(x,y * (z * z),u),w,v5) = a((y * u) \ (u * (x * y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,9167,a(flip),b,11140,a)].">
      <j1 rule="hyper" parents="65 9167 11140"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      a(L(x,y * (z * z),u),w,v5) = a(L(x,y,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,8577,a(flip),b,11142,a),flip(a)].">
      <j1 rule="hyper" parents="325 8577 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      a(L(x,y \ 1,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(221(a,1),11144(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="221 11144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      a(L(x,(y * y) \ z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(10815(a,1),11144(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10815 11144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      a((x * y) \ (((z / ((y \ 1) * x)) * (y \ 1)) * x),u,w) = a(L((x * (y \ 1)) \ z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8681,a,b,11145,a)].">
      <j1 rule="hyper" parents="65 8681 11145"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      a(L(x,(y * y) \ z,u),w,v5) = a(L(x,z \ (y * y),u),w,v5)
    ]]></literal>
    <justification jstring="[para(434(a,1),11145(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="434 11145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      a(L(x,L(y \ z,y,z),u),w,v5) = a(L(x,(1 / z) * y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(700(a,2),11145(a,1,1,2))].">
      <j1 rule="para" parents="700 11145"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      a(L(x,(y \ 1) \ z,u),w,v5) = a(L(x,y \ z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(11101(a,1),11146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11101 11146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      a(L(x,y \ (z * z),u),w,v5) = a(L(x,y,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11146,a(flip),b,11148,a),flip(a)].">
      <j1 rule="hyper" parents="65 11146 11148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      a(L(x,L(y \ z,y,z),u),w,v5) = a(L(x,z * y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(102(a,2),11151(a,1,1,2))].">
      <j1 rule="para" parents="102 11151"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      a(L(x,L(y \ z,y,z),u),w,v5) = a(L(x,(z \ 1) * y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(10817(a,1),11149(a,2,1))].">
      <j1 rule="para" parents="10817 11149"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      a(L(x,L(y \ z,y,z),u),w,v5) = a(L(x,y * (z \ 1),u),w,v5)
    ]]></literal>
    <justification jstring="[para(10813(a,1),11154(a,2,1))].">
      <j1 rule="para" parents="10813 11154"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      a(L(x,y * (z \ 1),u),w,v5) = a(L(x,z * y,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11153,a(flip),b,11155,a),flip(a)].">
      <j1 rule="hyper" parents="65 11153 11155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * (K(u,z) * (a(w,v5,w) * v6)) = (x * (y \ a(w,v5,w))) * v6
    ]]></literal>
    <justification jstring="[para(7600(a,1),10774(a,2,1,2))].">
      <j1 rule="para" parents="7600 10774"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      (x * (y \ 1)) * (a(z,u,z) * w) = (x * (y \ a(z,u,z))) * w
    ]]></literal>
    <justification jstring="[hyper(65,a,9669,a(flip),b,11157,a)].">
      <j1 rule="hyper" parents="65 9669 11157"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      L(x,(y * (z \ a(u,w,u))) * v5,v6) = L(x,v5 * (y * (z \ 1)),v6)
    ]]></literal>
    <justification jstring="[para(11158(a,1),11033(a,1,2))].">
      <j1 rule="para" parents="11158 11033"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      T((x * y) \ T(y,K(z,x)),x \ 1) = (x * T(y,T(z,x))) \ T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(3844(a,1),10775(a,1,1,2))].">
      <j1 rule="para" parents="3844 10775"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ T(y,T(z,x)) = (x * y) \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(42,a,2785,a,b,11160,a)].">
      <j1 rule="hyper" parents="42 2785 11160"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (K(w,v5) * (v6 * (v5 * T(w,u)))))) = a(x,y,z \ ((w * v5) * v6))
    ]]></literal>
    <justification jstring="[para(287(a,1),10790(a,1,3,2,2))].">
      <j1 rule="para" parents="287 10790"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      a(x,(y \ T(T(y,z) / u,u \ 1)) * w,v5) = a(x,((y * u) \ y) * w,v5)
    ]]></literal>
    <justification jstring="[para(2264(a,1),10791(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2264 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      a(x,(y \ (T(y,z) / u)) * w,v5) = a(x,((y * u) \ y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10125,a(flip),b,11163,a)].">
      <j1 rule="hyper" parents="65 10125 11163"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      a(x,(y \ (z \ T(y,u))) * w,v5) = a(x,((y * z) \ y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10246,a(flip),b,11164,a)].">
      <j1 rule="hyper" parents="65 10246 11164"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      a(x,((y * z) \ y) * u,w) = a(x,(y \ (z \ y)) * u,w)
    ]]></literal>
    <justification jstring="[para(112(a,1),11167(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="112 11167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      a(x,(y \ ((y \ z) \ y)) * u,w) = a(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11168(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      a(x,(((T(y,z) \ u) * T(y,z)) * y) \ w,v5) = a(x,(u * (u / (u / y))) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10007,a(flip),b,10792,a),flip(a)].">
      <j1 rule="hyper" parents="325 10007 10792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      a(x,(((T(y,z) \ u) * T(y,z)) * y) \ w,v5) = a(x,(u * ((u / y) \ u)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10225,a(flip),b,11170,a),flip(a)].">
      <j1 rule="hyper" parents="325 10225 11170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      a(x,(((T(y,z) \ u) * T(y,z)) * y) \ w,v5) = a(x,(u * y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(85(a,1),11172(a,2,2,1,2))].">
      <j1 rule="para" parents="85 11172"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      a(x,(((T(y,z) \ u) * y) * T(y,z)) \ w,v5) = a(x,(u * y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(1131(a,1),11173(a,1,2,1))].">
      <j1 rule="para" parents="1131 11173"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      a(x,(((T(y,z) \ u) * y) * y) \ w,v5) = a(x,(u * y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10007,a(flip),b,11175,a)].">
      <j1 rule="hyper" parents="65 10007 11175"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      L(x,((y \ 1) * (y \ ((y \ 1) \ z))) * u,w) = L(x,((1 / y) \ (z / (y * y))) * u,w)
    ]]></literal>
    <justification jstring="[para(695(a,1),10907(a,2,2,1))].">
      <j1 rule="para" parents="695 10907"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      L(x,(y * z) \ (y * T(y,u)),a(w,v5,v6)) = L(x,(1 / T(y,u)) * z,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(8(a,1),10956(a,1,2,2))].">
      <j1 rule="para" parents="8 10956"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      L(x,(y * z) \ (y * y),a(u,w,v5)) = L(x,(1 / T(y,v6)) * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10903,a,11179,a)].">
      <j1 rule="hyper" parents="10903 11179"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      L(x,(1 / T(y,z)) * u,a(w,v5,v6)) = L(x,y * u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,11004,a(flip),b,11180,a),flip(a)].">
      <j1 rule="hyper" parents="65 11004 11180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      L(x,(y \ 1) * z,a(u,w,v5)) = L(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(268(a,1),11182(a,1,2,1))].">
      <j1 rule="para" parents="268 11182"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (v5 * (v6 * T(w,u))))) = a(x,y,z \ ((w * v6) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10190,a(flip),b,11162,a)].">
      <j1 rule="hyper" parents="65 10190 11162"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * T(v5,v6)))) = a(x,y,z \ ((v5 * w) * u))
    ]]></literal>
    <justification jstring="[hyper(10147,a,11185,a)].">
      <j1 rule="hyper" parents="10147 11185"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5)) * v6)) = a(x,y,z \ ((w * u) * v6))
    ]]></literal>
    <justification jstring="[hyper(10157,a,11186,a)].">
      <j1 rule="hyper" parents="10157 11186"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      L(x,((y \ 1) * (y \ ((y \ 1) \ z))) * u,w) = L(x,(y \ T(z,y \ (y \ 1))) * u,w)
    ]]></literal>
    <justification jstring="[para(880(a,1),11178(a,2,2,1))].">
      <j1 rule="para" parents="880 11178"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      L(x,((y \ 1) * (y \ ((y \ 1) \ z))) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10912,a(flip),b,11191,a),flip(a)].">
      <j1 rule="hyper" parents="325 10912 11191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      L(x,((y * y) \ ((1 / y) \ z)) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(9846(a,1),11192(a,1,2,1))].">
      <j1 rule="para" parents="9846 11192"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      a(x,y,(((z \ (u * u)) * w) * z) * v5) = a(x,y,L(w,z \ (u * u),z) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10481,a(flip),b,10214,a)].">
      <j1 rule="hyper" parents="65 10481 10214"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      a(x,y,L(z,u \ (w * w),u) * v5) = a(x,y,((u * z) * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10626,a(flip),b,11195,a),flip(a)].">
      <j1 rule="hyper" parents="65 10626 11195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      a(x,y,L(z,u \ (w * w),u) * v5) = a(x,y,L(z,u,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10271,a(flip),b,11197,a),flip(a)].">
      <j1 rule="hyper" parents="325 10271 11197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,u) * w) = a(x,y,L(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(7(a,1),11199(a,1,3,1,2,2))].">
      <j1 rule="para" parents="7 11199"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      a(x,y,z \ ((u \ K(w,v5)) * (u * (v6 * u)))) = a(x,y,z \ (L(v6,u \ 1,u) * u))
    ]]></literal>
    <justification jstring="[para(9593(a,1),10324(a,1,3,2))].">
      <j1 rule="para" parents="9593 10324"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,w) * (w \ K(v5,v6)))) = a(x,y,z \ (L(u,w \ 1,w) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10510,a(flip),b,11201,a)].">
      <j1 rule="hyper" parents="65 10510 11201"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ 1,w) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,w) * w)) = v5
    ]]></literal>
    <justification jstring="[para(11202(a,1),10615(a,1))].">
      <j1 rule="para" parents="11202 10615"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      a(x,y,(R(z / u,u,z \ (w \ v5)) \ (w \ v5)) * v6) = a(x,y,(u * (z \ (v5 / w))) * v6)
    ]]></literal>
    <justification jstring="[para(8717(a,1),10352(a,1,3,1,1))].">
      <j1 rule="para" parents="8717 10352"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      a(x,y,(T(z,K(u,w)) * v5) \ (v5 * (v6 * z))) = a(x,y,L(v6,z,K(u,w) * v5))
    ]]></literal>
    <justification jstring="[para(9703(a,1),10403(a,1,3))].">
      <j1 rule="para" parents="9703 10403"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      a(x,y,(T(z / (u * u),K(w,v5)) * v6) \ (v6 * (v7 * z))) = a(x,y,L(v7,z / (u * u),K(w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,7503,a(flip),b,11205,a)].">
      <j1 rule="hyper" parents="65 7503 11205"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      a(x,y,L(z,u,u) \ (u * T(z,u * u))) = a(x,y,L(u,u,u \ L(z,u,u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),10404(a,1,3,1))].">
      <j1 rule="para" parents="10 10404"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      a(x,y,L(z,z,z \ L(u,z,z))) = a(x,y,L(u,z,z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(10156,a,11207,a),flip(a)].">
      <j1 rule="hyper" parents="10156 11207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      a(x,y,L(z,u,u) \ (u * z)) = a(x,y,L(u,u,u * z))
    ]]></literal>
    <justification jstring="[para(2361(a,1),11208(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2361 11208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) \ (((x \ 1) * x) * u) = (R(x,y,z) \ 1) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(8679(a,1),10528(a,1,1))].">
      <j1 rule="para" parents="8679 10528"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,y)) = L(x,a(w,v5,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7473,a(flip),b,10608,a),flip(a)].">
      <j1 rule="hyper" parents="65 7473 10608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      a(x,(y * (z \ (u \ z))) * L(w,z \ (u \ z),y),v5) = a(x,y * (((u * z) \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(10474(a,1),10799(a,1,2,2))].">
      <j1 rule="para" parents="10474 10799"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      L(x,(T(y * z,u) \ ((z * u) * y)) \ w,v5) = L(x,K(y,u * z) * (L(u,z,y) \ w),v5)
    ]]></literal>
    <justification jstring="[para(9613(a,1),10916(a,2,2))].">
      <j1 rule="para" parents="9613 10916"/>
    </justification>
  </clause>

  <clause id="11216">
    <literal><![CDATA[
      a(R(x / y,y,x \ (z \ u)) \ (z \ u),w,v5) = a(y * (x \ ((z \ 1) \ u)),w,v5)
    ]]></literal>
    <justification jstring="[para(8991(a,1),11082(a,1,1,1))].">
      <j1 rule="para" parents="8991 11082"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      a(x * (y \ ((z \ 1) \ u)),w,v5) = a(x * (y \ (z \ u)),w,v5)
    ]]></literal>
    <justification jstring="[para(480(a,1),11216(a,1,1)),flip(a)].">
      <j1 rule="para" parents="480 11216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      a(L(x,x,y \ ((z \ 1) \ u)) * (y \ (z \ u)),w,v5) = a(x \ (y \ ((z \ 1) \ u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(10975,a,11217,a),flip(a)].">
      <j1 rule="hyper" parents="10975 11217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11219">
    <literal><![CDATA[
      a((x \ ((y \ 1) \ z)) * u,w,v5) = a(u * (x \ (y \ z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(2363,a,11217,a)].">
      <j1 rule="hyper" parents="2363 11217"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      a((x \ ((y \ 1) \ T(y / z,z \ 1))) * u,w,v5) = a(u * (x \ (y / (y * z))),w,v5)
    ]]></literal>
    <justification jstring="[para(7425(a,1),11219(a,2,1,2,2))].">
      <j1 rule="para" parents="7425 11219"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      a(x * (y \ ((z \ 1) \ (z / u))),w,v5) = a(x * (y \ (z / (z * u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8450,a(flip),b,11220,a)].">
      <j1 rule="hyper" parents="65 8450 11220"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      a(x * (y \ (z / (z * u))),w,v5) = a(x * (y \ (z \ (z / u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11217,a(flip),b,11221,a),flip(a)].">
      <j1 rule="hyper" parents="65 11217 11221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      a(x * (y \ ((z * u) \ z)),w,v5) = a(x * (y \ (z \ (z / u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,5171,a(flip),b,11223,a)].">
      <j1 rule="hyper" parents="65 5171 11223"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      a(x * (y \ ((z * u) \ u)),w,v5) = a(x * (y \ (u \ (u / z))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8455,a,b,11224,a)].">
      <j1 rule="hyper" parents="65 8455 11224"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      a(x * (y \ ((z * u) \ u)),w,v5) = a(x * (y \ (u \ (z \ u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,8661,a(flip),b,11225,a),flip(a)].">
      <j1 rule="hyper" parents="325 8661 11225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      a(x,y,(z * (u \ (w / v5))) * v6) = a(x,y,(z * (u \ (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[para(480(a,1),11204(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="480 11204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      a(x,y * (((z * u) \ u) * w),v5) = a(x,y * ((u \ (z \ u)) * w),v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),11214(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 11214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      a(x,K(y,z) * (((u * w) \ w) * v5),v6) = a(x,(w \ (u \ w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,9987,a(flip),b,11228,a),flip(a)].">
      <j1 rule="hyper" parents="325 9987 11228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      a(x,((y * z) \ z) * u,w) = a(x,(z \ (y \ z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(10164,a,11229,a)].">
      <j1 rule="hyper" parents="10164 11229"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      L(x,(T(y * z,u) \ ((z * u) * y)) \ w,v5) = L(x,L(u,z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10802,a(flip),b,11215,a),flip(a)].">
      <j1 rule="hyper" parents="325 10802 11215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      L(x,((y * z) \ ((z * u) * y)) \ w,v5) = L(x,L(u,z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10920,a(flip),b,11231,a)].">
      <j1 rule="hyper" parents="65 10920 11231"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      a(L(x,x,y \ (z \ u)) * (y \ (z \ u)),w,v5) = a(x \ (y \ ((z \ 1) \ u)),w,v5)
    ]]></literal>
    <justification jstring="[para(8593(a,1),11218(a,1,1,1))].">
      <j1 rule="para" parents="8593 11218"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      a(x \ (y \ ((z \ 1) \ u)),w,v5) = a(x \ (y \ (z \ u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(10975,a,11235,a),flip(a)].">
      <j1 rule="hyper" parents="10975 11235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11237">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),y / (x * x)) = (y / x) \ ((y / (x * x)) * z)
    ]]></literal>
    <justification jstring="[para(9972(a,1),9973(a,1,2))].">
      <j1 rule="para" parents="9972 9973"/>
    </justification>
  </clause>

  <clause id="11238">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),y) = (y / x) \ ((y / (x * x)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1555,a(flip),b,11237,a)].">
      <j1 rule="hyper" parents="65 1555 11237"/>
    </justification>
  </clause>

  <clause id="11240">
    <literal><![CDATA[
      (x / y) \ ((x / (y * y)) * z) = (x / (y \ 1)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1724,a(flip),b,11238,a),flip(a)].">
      <j1 rule="hyper" parents="65 1724 11238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      a(x,y,(((z * u) * w) \ (v5 * v5)) * v6) = a(x,y,v6 * ((((v5 * v5) \ z) * u) * w))
    ]]></literal>
    <justification jstring="[para(93(a,1),10254(a,1,3,1,2))].">
      <j1 rule="para" parents="93 10254"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      a(x,y,z * ((((u * u) \ w) * v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * ((w * v5) * v6)) = v7
    ]]></literal>
    <justification jstring="[para(11241(a,1),10318(a,1))].">
      <j1 rule="para" parents="11241 10318"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * (v5 * v5)) * ((v5 * v5) \ v6)))) = a(x,y,z * (u \ (v6 * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10178,a(flip),b,10332,a),flip(a)].">
      <j1 rule="hyper" parents="325 10178 10332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      a(x,y,z * (u \ (((w * w) \ v5) * v6))) = a(x,y,z * (u \ (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10705,a(flip),b,11243,a)].">
      <j1 rule="hyper" parents="65 10705 11243"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 \ 1)))) = a(x,y,z * (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10250,a(flip),b,11245,a)].">
      <j1 rule="hyper" parents="65 10250 11245"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ 1) * v5))) = a(x,y,z * (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(10340,a,11247,a)].">
      <j1 rule="hyper" parents="10340 11247"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w \ 1))) * v5) = a(x,y,v5 * (z \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(10136,a,11247,a)].">
      <j1 rule="hyper" parents="10136 11247"/>
    </justification>
  </clause>

  <clause id="11251">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ K(v5,v6)) * v7))) = a(x,y,z * (u \ (v7 * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10704,a,b,11249,a)].">
      <j1 rule="hyper" parents="65 10704 11249"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 \ K(v6,v7))))) = a(x,y,z * (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(10340,a,11251,a)].">
      <j1 rule="hyper" parents="10340 11251"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      a(x,y,z * (u \ (T(w,v5) * (v6 \ K(v7,v8))))) = a(x,y,z * (u \ (w * v6)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10430,a(flip),b,11252,a),flip(a)].">
      <j1 rule="hyper" parents="325 10430 11252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      a(x,y,z * (u \ (T(w,v5) * ((v6 \ v7) \ 1)))) = a(x,y,z * (u \ (w * (v7 / v6))))
    ]]></literal>
    <justification jstring="[para(2453(a,1),11253(a,1,3,2,2,2))].">
      <j1 rule="para" parents="2453 11253"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      a(x,y,z * (u \ (T(w,v5) * (v6 \ v7)))) = a(x,y,z * (u \ (w * (v7 / v6))))
    ]]></literal>
    <justification jstring="[hyper(65,a,11247,a(flip),b,11254,a)].">
      <j1 rule="hyper" parents="65 11247 11254"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 / v6)))) = a(x,y,z * (u \ (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[hyper(65,a,10430,a(flip),b,11255,a),flip(a)].">
      <j1 rule="hyper" parents="65 10430 11255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      a(x * (y \ ((z * y) \ T(y,K(u,z)))),w,v5) = a(x * L(z * y,z * y,y),w,v5)
    ]]></literal>
    <justification jstring="[para(11161(a,1),9683(a,1,1,2,2))].">
      <j1 rule="para" parents="11161 9683"/>
    </justification>
  </clause>

  <clause id="11258">
    <literal><![CDATA[
      a(x * L(y * z,y * z,z),u,w) = a(x * (z \ ((y * z) \ z)),u,w)
    ]]></literal>
    <justification jstring="[para(2119(a,1),11257(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2119 11257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      a(x * L(y * z,y * z,z),u,w) = a(x * (z \ (z \ (y \ z))),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11226,a(flip),b,11258,a),flip(a)].">
      <j1 rule="hyper" parents="325 11226 11258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * z)) \ ((u * z) * ((z \ 1) / z))) = a(x,y,L(T(z \ 1,z),z,u))
    ]]></literal>
    <justification jstring="[para(420(a,1),10405(a,1,3,2,2))].">
      <j1 rule="para" parents="420 10405"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * z)) \ (u * (z * ((z \ 1) / z)))) = a(x,y,L(T(z \ 1,z),z,u))
    ]]></literal>
    <justification jstring="[para(8736(a,1),11260(a,1,3,2))].">
      <j1 rule="para" parents="8736 11260"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * z)) \ (u * (z \ 1))) = a(x,y,L(T(z \ 1,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10326,a(flip),b,11261,a)].">
      <j1 rule="hyper" parents="65 10326 11261"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * z)) \ (z * u)) = a(x,y,L(T(z \ 1,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10683,a(flip),b,11262,a)].">
      <j1 rule="hyper" parents="65 10683 11262"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      a(x,y,((z * u) * u) \ (u * z)) = a(x,y,L(T(u \ 1,u),u,z))
    ]]></literal>
    <justification jstring="[hyper(10434,a,11264,a)].">
      <j1 rule="hyper" parents="10434 11264"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      a(x,y,L(T(z \ 1,z),z,u)) = a(x,y,L(u,z,z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10416,a(flip),b,11265,a),flip(a)].">
      <j1 rule="hyper" parents="65 10416 11265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      a(x,y,L(T(z \ 1,z),z,u)) = a(x,y,L(z,z,z * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,11211,a(flip),b,11266,a),flip(a)].">
      <j1 rule="hyper" parents="325 11211 11266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u)) = a(x,y,L(z,z,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10042,a(flip),b,11267,a)].">
      <j1 rule="hyper" parents="65 10042 11267"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      a(x,y,L(z,z,z * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(10454,a,11268,a),flip(a)].">
      <j1 rule="hyper" parents="10454 11268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      a(x,y,L(z,z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11268(a,1),10454(a,1))].">
      <j1 rule="para" parents="11268 10454"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,u * w)) * v5) = a(x,y,v5 * (z \ (((1 / (u * w)) * w) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10654,a(flip),b,10661,a),flip(a)].">
      <j1 rule="hyper" parents="65 10654 10661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,u * w)) * v5) = a(x,y,v5 * (z \ ((1 / (u * w)) * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10653,a(flip),b,11272,a),flip(a)].">
      <j1 rule="hyper" parents="325 10653 11272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,u * w)) * v5) = a(x,y,v5 * (z \ (((u * w) \ 1) * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10442,a(flip),b,11274,a),flip(a)].">
      <j1 rule="hyper" parents="325 10442 11274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11276">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,u * w)) * v5) = a(x,y,v5 * (z \ (w * (u * w))))
    ]]></literal>
    <justification jstring="[hyper(325,a,11248,a(flip),b,11275,a),flip(a)].">
      <j1 rule="hyper" parents="325 11248 11275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11277">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,u * w)) * v5) = a(x,y,(z \ L(u,w,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10511,a(flip),b,11276,a),flip(a)].">
      <j1 rule="hyper" parents="325 10511 11276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11278">
    <literal><![CDATA[
      L(x,(y * ((z * z) * (u * w))) \ (((z * z) * (u * y)) * w),v5) = L(x,a(y,(z * z) * u,w),v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),10997(a,1,2,2,1))].">
      <j1 rule="para" parents="33 10997"/>
    </justification>
  </clause>

  <clause id="11279">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ ((T(y,z) * z) * u)),w,v5) = a(x * L(z,y,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,8553,a(flip),b,11043,a),flip(a)].">
      <j1 rule="hyper" parents="325 8553 11043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      a(x * ((y * z) \ ((y * u) * z)),w,v5) = a(x * L(u,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(2266(a,1),11279(a,1,1,2))].">
      <j1 rule="para" parents="2266 11279"/>
    </justification>
  </clause>

  <clause id="11282">
    <literal><![CDATA[
      a(x * R(y,z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,2440,a(flip),b,11281,a)].">
      <j1 rule="hyper" parents="65 2440 11281"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      a(((x * y) / x) * R(x,z,u),w,v5) = a(L(x,z,u) * y,w,v5)
    ]]></literal>
    <justification jstring="[para(8340(a,1),11282(a,2,1))].">
      <j1 rule="para" parents="8340 11282"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      a(R(x,y,z) * u,w,v5) = a(L(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3054(a,1),11284(a,1,1))].">
      <j1 rule="para" parents="3054 11284"/>
    </justification>
  </clause>

  <clause id="11286">
    <literal><![CDATA[
      a((x * y) \ (((z / ((y \ 1) * x)) * (y \ 1)) * x),u,w) = a(L((x * y) \ z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9055,a(flip),b,11147,a),flip(a)].">
      <j1 rule="hyper" parents="325 9055 11147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      L(x,(y * ((z * z) * (u * w))) \ ((z * z) * ((u * y) * w)),v5) = L(x,a(y,(z * z) * u,w),v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),11278(a,1,2,2))].">
      <j1 rule="para" parents="33 11278"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      L(x,a(y,(z * z) * u,w),v5) = L(x,(y * (u * w)) \ ((u * y) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11119,a(flip),b,11287,a),flip(a)].">
      <j1 rule="hyper" parents="65 11119 11287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      L(x,a(y,(z * z) * u,w),v5) = L(x,a(y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10996,a(flip),b,11288,a),flip(a)].">
      <j1 rule="hyper" parents="325 10996 11288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      L(x,a(y,R(z,z,z),u),w) = L(x,a(y,z \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(568(a,1),11290(a,1,2,2))].">
      <j1 rule="para" parents="568 11290"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      L(x,a(y,T(z * u,w \ (w \ 1)),v5),v6) = L(x,a(y,z * (u / (w * w)),v5),v6)
    ]]></literal>
    <justification jstring="[para(879(a,1),11290(a,1,2,2))].">
      <j1 rule="para" parents="879 11290"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      L(x,a(y,z * (((u * u) \ (u * w)) / z),v5),v6) = L(x,a(y,u * (u * (z * ((u \ w) / z))),v5),v6)
    ]]></literal>
    <justification jstring="[para(5442(a,1),11290(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5442 11290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11294">
    <literal><![CDATA[
      L(x,a(y,z \ 1,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(7775(a,1),11291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7775 11291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      L(x,a(y,z * (u / (w * w)),v5),v6) = L(x,a(y,z * u,v5),v6)
    ]]></literal>
    <justification jstring="[para(9991(a,1),11292(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9991 11292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11298">
    <literal><![CDATA[
      L(x,a(y,z * ((u * u) \ w),v5),v6) = L(x,a(y,z * w,v5),v6)
    ]]></literal>
    <justification jstring="[para(10029(a,1),11296(a,1,2))].">
      <j1 rule="para" parents="10029 11296"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      R(x,y,T(z * (u * (w \ 1)),v5) \ ((w * w) \ v6)) = R(x,y,T(z * (u * w),w \ (w \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[para(393(a,1),9686(a,1,3))].">
      <j1 rule="para" parents="393 9686"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w \ 1) * (w \ ((w \ 1) \ v5))))) = R(x,y,z * (u \ ((1 / w) \ (v5 / (w * w)))))
    ]]></literal>
    <justification jstring="[para(695(a,1),9849(a,2,3,2,2))].">
      <j1 rule="para" parents="695 9849"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      L(K(x,y) * (z \ 1),(K(x,y) / z) \ 1,(K(x,y) / z) \ u) = L(K(x,y) / z,K(x,y) / z,u)
    ]]></literal>
    <justification jstring="[para(9566(a,1),9974(a,1,1))].">
      <j1 rule="para" parents="9566 9974"/>
    </justification>
  </clause>

  <clause id="11302">
    <literal><![CDATA[
      a(x,y,((z * u) * ((z * u) \ (L(z,w,v5) * v6))) * v7) = a(x,y,(L(1 / z,w,v5) * v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(65,a,10625,a(flip),b,10175,a)].">
      <j1 rule="hyper" parents="65 10625 10175"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      a(x,y,(L(1 / z,u,w) * v5) * v6) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),11302(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 11302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,u,w) * v5) * v6) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(82(a,1),11303(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 11303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11306">
    <literal><![CDATA[
      a(x,y,z * (u * L(w \ 1,v5,v6))) = a(x,y,(L(w,v5,v6) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(10170,a,11305,a)].">
      <j1 rule="hyper" parents="10170 11305"/>
    </justification>
  </clause>

  <clause id="11307">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * ((z * u) \ (z * R(z \ (z * u),w,v5)))) = a(x,y,L((z * u) \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10407,a(flip),b,10663,a),flip(a)].">
      <j1 rule="hyper" parents="325 10407 10663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11308">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * (u \ ((u \ 1) \ w))) * v5)) = a(x,y,z * ((u \ T(w,u \ (u \ 1))) * v5))
    ]]></literal>
    <justification jstring="[para(880(a,1),10700(a,2,3,2,1))].">
      <j1 rule="para" parents="880 10700"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      L(x,y \ (((z * T(z,u)) * (T(z,u) \ w)) * v5),v6) = L(x,y \ ((w / (z \ 1)) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10922,a(flip),b,10998,a),flip(a)].">
      <j1 rule="hyper" parents="325 10922 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11311">
    <literal><![CDATA[
      L(x,y \ (((z * T(z,u)) * (T(z,u) \ w)) * v5),v6) = L(x,y \ (((z \ 1) \ w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10924,a(flip),b,11309,a),flip(a)].">
      <j1 rule="hyper" parents="325 10924 11309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      L(x,a(y,z * (((u * u) \ (u * w)) / z),v5),v6) = L(x,a(y,u * (u * (u \ w)),v5),v6)
    ]]></literal>
    <justification jstring="[para(10129(a,1),11293(a,2,2))].">
      <j1 rule="para" parents="10129 11293"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      L(x,a(y,z * (((u * u) \ (u * w)) / z),v5),v6) = L(x,a(y,u * w,v5),v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),11312(a,2,2,2,2))].">
      <j1 rule="para" parents="10 11312"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      L(x,a(y,z * (((1 / u) * w) / z),v5),v6) = L(x,a(y,u * w,v5),v6)
    ]]></literal>
    <justification jstring="[para(647(a,1),11313(a,1,2,2,2,1))].">
      <j1 rule="para" parents="647 11313"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      L(x,a(y,z * (z \ ((1 / u) * w)),v5),v6) = L(x,a(y,u * w,v5),v6)
    ]]></literal>
    <justification jstring="[para(10029(a,1),11316(a,1,2))].">
      <j1 rule="para" parents="10029 11316"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      L(x,a(y,(z \ 1) * u,w),v5) = L(x,a(y,z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(333(a,1),11317(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="333 11317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11319">
    <literal><![CDATA[
      R(x,y,T(z * (u * (w \ 1)),v5) \ v6) = R(x,y,T(z * (u * w),w \ (w \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,8734,a(flip),b,11299,a)].">
      <j1 rule="hyper" parents="65 8734 11299"/>
    </justification>
  </clause>

  <clause id="11321">
    <literal><![CDATA[
      R(x,y,T(z * (u * w),w \ (w \ 1)) \ v5) = R(x,y,(z * (u * (w \ 1))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8698,a(flip),b,11319,a),flip(a)].">
      <j1 rule="hyper" parents="65 8698 11319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      R(x,y,(z * (u * (w \ 1))) \ v5) = R(x,y,(z * (u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,8698,a(flip),b,11321,a),flip(a)].">
      <j1 rule="hyper" parents="65 8698 11321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11324">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w \ 1) * (w \ ((w \ 1) \ v5))))) = R(x,y,z * (u \ (w \ T(v5,w \ (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(880(a,1),11300(a,2,3,2,2))].">
      <j1 rule="para" parents="880 11300"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      L(K(x,y) * (z \ 1),z * K(y,x),(K(x,y) / z) \ u) = L(K(x,y) / z,K(x,y) / z,u)
    ]]></literal>
    <justification jstring="[para(7526(a,1),11301(a,1,2))].">
      <j1 rule="para" parents="7526 11301"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      L(K(x,y) * (z \ 1),z * K(y,x),(z \ K(x,y)) \ u) = L(K(x,y) / z,K(x,y) / z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,4603,a(flip),b,11325,a)].">
      <j1 rule="hyper" parents="65 4603 11325"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      L(K(x,y) * (z \ 1),z * K(y,x),z \ u) = L(K(x,y) / z,K(x,y) / z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,9687,a(flip),b,11326,a)].">
      <j1 rule="hyper" parents="65 9687 11326"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      L(K(x,y) / z,K(x,y) / z,u) = L(K(x,y) * (z \ 1),z,z \ u)
    ]]></literal>
    <justification jstring="[hyper(10888,a,11327,a),flip(a)].">
      <j1 rule="hyper" parents="10888 11327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11331">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * ((z * u) \ (z * R(u,w,v5)))) = a(x,y,L((z * u) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),11307(a,1,3,2,2,2,1))].">
      <j1 rule="para" parents="9 11307"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (z \ (R(u,w,v5) * (u \ z)))) = a(x,y,L((z * u) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(9359(a,1),11331(a,1,3,2))].">
      <j1 rule="para" parents="9359 11331"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      a(x,y,R(z \ (u \ z),w,v5)) = a(x,y,L((z * u) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(1407(a,1),11332(a,1,3))].">
      <j1 rule="para" parents="1407 11332"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      a(x,y,L((z * u) \ z,w,v5)) = a(x,y,L(z \ (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10407,a(flip),b,11333,a),flip(a)].">
      <j1 rule="hyper" parents="65 10407 11333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11335">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * (u \ ((u \ 1) \ w))) * v5)) = a(x,y,((u \ w) * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10506,a(flip),b,11308,a),flip(a)].">
      <j1 rule="hyper" parents="325 10506 11308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ ((1 / u) \ w)) * v5)) = a(x,y,((u \ w) * v5) * z)
    ]]></literal>
    <justification jstring="[para(9846(a,1),11335(a,1,3,2,1))].">
      <j1 rule="para" parents="9846 11335"/>
    </justification>
  </clause>

  <clause id="11338">
    <literal><![CDATA[
      a(x,y,(((1 / z) \ u) * w) * v5) = a(x,y,((z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10310,a(flip),b,11337,a)].">
      <j1 rule="hyper" parents="65 10310 11337"/>
    </justification>
  </clause>

  <clause id="11340">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w \ 1) * (w \ ((w \ 1) \ v5))))) = R(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,9757,a(flip),b,11324,a),flip(a)].">
      <j1 rule="hyper" parents="325 9757 11324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11342">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w * w) \ ((1 / w) \ v5)))) = R(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[para(9846(a,1),11340(a,1,3,2,2))].">
      <j1 rule="para" parents="9846 11340"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      R(x,y,(z \ ((1 / u) \ w)) * v5) = R(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,9771,a(flip),b,11342,a)].">
      <j1 rule="hyper" parents="65 9771 11342"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      R(x,y,(z \ ((u \ 1) \ w)) * v5) = R(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,9769,a(flip),b,11343,a)].">
      <j1 rule="hyper" parents="65 9769 11343"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      R(x,y,(z \ (u \ z)) * u) = R(x,y,u * ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9980,a(flip),b,11345,a),flip(a)].">
      <j1 rule="hyper" parents="65 9980 11345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      a(x,y,((T(z,T(u,w)) * v5) \ (v5 * (z * u))) * v6) = a(x,y,v6 * R(u,T(z,T(u,w)),v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10218,a(flip),b,10675,a)].">
      <j1 rule="hyper" parents="65 10218 10675"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      a(x,y,z * R(u,T(w,T(u,v5)),v6)) = a(x,y,z * ((w * v6) \ (v6 * (w * u))))
    ]]></literal>
    <justification jstring="[hyper(65,a,10336,a(flip),b,11347,a),flip(a)].">
      <j1 rule="hyper" parents="65 10336 11347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      a(x,y,z * R(u,T(w,T(u,v5)),v6)) = a(x,y,z * L(K(v6,w) * u,w,v6))
    ]]></literal>
    <justification jstring="[para(5238(a,1),11349(a,2,3,2))].">
      <j1 rule="para" parents="5238 11349"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      a(x,y,z * R(u,T(w,T(u,v5)),v6)) = a(x,y,z * L(u,w,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,10179,a(flip),b,11351,a),flip(a)].">
      <j1 rule="hyper" parents="325 10179 11351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      a(x,y,z * R(u,w,v5)) = a(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9893(a,1),11352(a,1,3,2))].">
      <j1 rule="para" parents="9893 11352"/>
    </justification>
  </clause>

  <clause id="11355">
    <literal><![CDATA[
      a(x,y,z * L((u * u) * w,v5,v6)) = a(x,y,R(w,v5,v6) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10315,a(flip),b,11354,a),flip(a)].">
      <j1 rule="hyper" parents="65 10315 11354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      a(x,y,(z * u) * R(L(w,u,z),v5,v6)) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(412(a,1),11354(a,2,3))].">
      <j1 rule="para" parents="412 11354"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      a(x,y,R(z,z,R(u,w,v5)) * L(u,w,v5)) = a(x,y,(1 / z) \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1289(a,1),11354(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1289 11354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10316,a(flip),b,11355,a),flip(a)].">
      <j1 rule="hyper" parents="65 10316 11355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      a(x,y,(z * K(z * u,z)) * w) = a(x,y,L(z,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10105,a,b,11359,a)].">
      <j1 rule="hyper" parents="65 10105 11359"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      a(x,y,z * (K(z * u,z) * w)) = a(x,y,L(z,u,z) * w)
    ]]></literal>
    <justification jstring="[para(4578(a,1),11360(a,1,3))].">
      <j1 rule="para" parents="4578 11360"/>
    </justification>
  </clause>

  <clause id="11362">
    <literal><![CDATA[
      a(x,y,L(z,u,z) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(10146,a,11361,a),flip(a)].">
      <j1 rule="hyper" parents="10146 11361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      a(x,y,z * L(u,w,u)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,11362,a)].">
      <j1 rule="hyper" parents="10136 11362"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      a(x,y,z * (u * R(w,v5,v6))) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(413(a,1),11356(a,1,3))].">
      <j1 rule="para" parents="413 11356"/>
    </justification>
  </clause>

  <clause id="11366">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * v6) = a(x,y,v6 * (v5 * R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10166,a,b,11365,a)].">
      <j1 rule="hyper" parents="325 10166 11365"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      a(x,y,z * (u * R(w \ 1,v5,v6))) = a(x,y,(L(w,v5,v6) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,11306,a(flip),b,11365,a),flip(a)].">
      <j1 rule="hyper" parents="325 11306 11365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11368">
    <literal><![CDATA[
      a(x,y,L(z * u,z \ 1,z \ 1) * w) = a(x,y,w * (z * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10647,a,b,11365,a)].">
      <j1 rule="hyper" parents="65 10647 11365"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * v6) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10166,a,b,11366,a)].">
      <j1 rule="hyper" parents="325 10166 11366"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      a(x,y,z * (u * R(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(11366(a,1),10170(a,1))].">
      <j1 rule="para" parents="11366 10170"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * v6) = a(x,y,v6 * (R(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(10136,a,11369,a),flip(a)].">
      <j1 rule="hyper" parents="10136 11369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11372">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * v6) = a(x,y,v6 * (R(u,w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(10139,a,11371,a)].">
      <j1 rule="hyper" parents="10139 11371"/>
    </justification>
  </clause>

  <clause id="11373">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * v6)) = a(x,y,z * (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(10136,a,11371,a),flip(a)].">
      <j1 rule="hyper" parents="10136 11371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11374">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (L(u,w,v5) * v6)) = v7
    ]]></literal>
    <justification jstring="[para(11371(a,1),10136(a,1))].">
      <j1 rule="para" parents="11371 10136"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) * v6) = a(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10166,a,b,11372,a)].">
      <j1 rule="hyper" parents="325 10166 11372"/>
    </justification>
  </clause>

  <clause id="11376">
    <literal><![CDATA[
      a(x,y,R(z,z,R(u,w,v5) * v6) * (L(u,w,v5) * v6)) = a(x,y,(1 / z) \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(1289(a,1),11373(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1289 11373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      a(x,y,(z * L(u / w,w,w)) * v5) = a(x,y,(z * (u * (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[para(572(a,1),11375(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="572 11375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11378">
    <literal><![CDATA[
      a(x,y,(z * R(z \ (u / z),w,v5)) * v6) = a(x,y,(L(u,w,v5) / z) * v6)
    ]]></literal>
    <justification jstring="[para(1748(a,1),11375(a,2,3,1))].">
      <j1 rule="para" parents="1748 11375"/>
    </justification>
  </clause>

  <clause id="11379">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * R(z \ 1,u,w)) * v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(7482,a,11367,a),flip(a)].">
      <j1 rule="hyper" parents="7482 11367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      a(x,y,(z * L(u / w,w,w)) * v5) = a(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10545,a(flip),b,11377,a),flip(a)].">
      <j1 rule="hyper" parents="325 10545 11377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      a(x,y,R(z,z,R(u,w,v5)) * L(u,w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10366,a(flip),b,11357,a),flip(a)].">
      <j1 rule="hyper" parents="325 10366 11357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      a(x,y,R(z,z,L(u,w,v5)) * L(u,w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(8754(a,1),11381(a,1,3,1))].">
      <j1 rule="para" parents="8754 11381"/>
    </justification>
  </clause>

  <clause id="11383">
    <literal><![CDATA[
      a(x,y,(1 / z) \ L(u,w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1289(a,1),11382(a,1,3))].">
      <j1 rule="para" parents="1289 11382"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      a(x,y,z \ R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10366,a(flip),b,11383,a),flip(a)].">
      <j1 rule="hyper" parents="65 10366 11383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      a(x,y,x \ R(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,7700,a(flip),b,11384,a),flip(a)].">
      <j1 rule="hyper" parents="325 7700 11384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      a(x,y,z \ R(L(u,w,v5),v6,v7)) = a(x,y,z \ L(L(u,v6,v7),w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),11384(a,2,3,2))].">
      <j1 rule="para" parents="30 11384"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,11385,a)].">
      <j1 rule="hyper" parents="54 11385"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      a(x,y,L(z * u,z \ 1,z) * w) = a(x,y,w * (z * L(u,z,z)))
    ]]></literal>
    <justification jstring="[para(1499(a,1),11368(a,1,3,1))].">
      <j1 rule="para" parents="1499 11368"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) * w) = a(x,y,w * (z * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11200,a(flip),b,11389,a)].">
      <j1 rule="hyper" parents="65 11200 11389"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) / v5) * v6) = a(x,y,(L(z,u,w) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(2935(a,1),11378(a,1,3,1))].">
      <j1 rule="para" parents="2935 11378"/>
    </justification>
  </clause>

  <clause id="11392">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) / v5) * v6) = a(x,y,(v5 \ R(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(10140,a,11391,a),flip(a)].">
      <j1 rule="hyper" parents="10140 11391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      a(x,y,(z \ R(u,w,v5)) * v6) = a(x,y,(z \ L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(10140,a,11392,a),flip(a)].">
      <j1 rule="hyper" parents="10140 11392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11394">
    <literal><![CDATA[
      a(x,y,(z \ R(z \ 1,u,w)) * v5) = a(x,y,v5 * (z * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10719,a(flip),b,11393,a),flip(a)].">
      <j1 rule="hyper" parents="325 10719 11393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11395">
    <literal><![CDATA[
      a(x,y,R(z,z,R(u,w,v5) * v6) * (L(u,w,v5) * v6)) = a(x,y,z \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,10366,a(flip),b,11376,a),flip(a)].">
      <j1 rule="hyper" parents="325 10366 11376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      R(x,y,L(((1 / z) * u) * w,z * z,v5) * (v5 * (z * z))) = R(x,y,v5 * ((T(z,v6) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8724,a(flip),b,10869,a)].">
      <j1 rule="hyper" parents="65 8724 10869"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      R(x,y,L(((1 / z) * u) * w,z * z,v5) * v5) = R(x,y,v5 * ((T(z,v6) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1004,a(flip),b,11396,a)].">
      <j1 rule="hyper" parents="65 1004 11396"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      R(x,y,(((1 / z) * u) * w) * v5) = R(x,y,v5 * ((T(z,v6) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8767,a(flip),b,11399,a)].">
      <j1 rule="hyper" parents="65 8767 11399"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      R(x,y,(((1 / z) * u) * w) * v5) = R(x,y,v5 * (w * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8771,a(flip),b,11401,a),flip(a)].">
      <j1 rule="hyper" parents="325 8771 11401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      R(x,y,z * (u * L(w / v5,v5,v5))) = R(x,y,z * (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8957,a,b,11402,a)].">
      <j1 rule="hyper" parents="65 8957 11402"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * T(T(y,w),z))) \ v5,v6) = L(x,R(T(u,T(y,w) * z),z,y) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(7907(a,1),11106(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7907 11106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * T(T(y,w),z))) \ v5,v6) = L(x,R(u,z,y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10825,a(flip),b,11405,a),flip(a)].">
      <j1 rule="hyper" parents="325 10825 11405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * T(y,w))) \ v5,v6) = L(x,R(u,z,y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10834,a(flip),b,11406,a)].">
      <j1 rule="hyper" parents="65 10834 11406"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ w,v5) = L(x,R(u,z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10834,a(flip),b,11409,a)].">
      <j1 rule="hyper" parents="65 10834 11409"/>
    </justification>
  </clause>

  <clause id="11412">
    <literal><![CDATA[
      L(x,((1 / y) * (y \ ((z * y) * y))) \ u,w) = L(x,R(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(653(a,2),11411(a,1,2,1))].">
      <j1 rule="para" parents="653 11411"/>
    </justification>
  </clause>

  <clause id="11413">
    <literal><![CDATA[
      L(x,((y * (z * K(u,z))) \ ((T(u,z) * z) * y)) \ w,v5) = L(x,R(u,z * K(u,z),y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(3973(a,1),11411(a,1,2,1,2,1))].">
      <j1 rule="para" parents="3973 11411"/>
    </justification>
  </clause>

  <clause id="11414">
    <literal><![CDATA[
      L(x,((1 / y) * T(z * y,y)) \ u,w) = L(x,R(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),11412(a,1,2,1,2))].">
      <j1 rule="para" parents="22 11412"/>
    </justification>
  </clause>

  <clause id="11415">
    <literal><![CDATA[
      L(x,T(((1 / y) * z) * y,y) \ u,w) = L(x,R(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6718(a,2),11414(a,1,2,1))].">
      <j1 rule="para" parents="6718 11414"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      L(x,(((1 / y) * z) * y) \ u,w) = L(x,R(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(10890,a,11415,a)].">
      <j1 rule="hyper" parents="10890 11415"/>
    </justification>
  </clause>

  <clause id="11418">
    <literal><![CDATA[
      L(x,L(y,z \ 1,z) \ u,w) = L(x,R(y,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11074,a(flip),b,11416,a)].">
      <j1 rule="hyper" parents="65 11074 11416"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      L(x,(K(y,z) * ((u * y) \ ((T(z,y) * y) * u))) \ w,v5) = L(x,R(z,y * K(z,y),u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9611(a,1),11413(a,1,2,1))].">
      <j1 rule="para" parents="9611 11413"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      L(x,(T(y * z,K(u,z)) \ ((u * z) * y)) \ w,v5) = L(x,R(u,z * K(u,z),y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9670(a,1),11419(a,1,2,1))].">
      <j1 rule="para" parents="9670 11419"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      L(x,(T(y * z,K(z,u)) \ ((u * z) * y)) \ w,v5) = L(x,R(u,z * K(u,z),y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(3617(a,1),11420(a,1,2,1,1))].">
      <j1 rule="para" parents="3617 11420"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      L(x,(K(y,z) * ((u * z) \ ((z * y) * u))) \ w,v5) = L(x,R(y,z * K(y,z),u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9671(a,1),11421(a,1,2,1))].">
      <j1 rule="para" parents="9671 11421"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      L(x,((y * T(z,u)) \ ((z * u) * y)) \ w,v5) = L(x,R(u,z * K(u,z),y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9607(a,1),11422(a,1,2,1))].">
      <j1 rule="para" parents="9607 11422"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      L(x,R(y,z * K(y,z),u) \ w,v5) = L(x,((u * z) \ ((z * y) * u)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11126,a(flip),b,11423,a),flip(a)].">
      <j1 rule="hyper" parents="65 11126 11423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      L(x,R(y,z * K(y,z),u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,11233,a(flip),b,11424,a),flip(a)].">
      <j1 rule="hyper" parents="325 11233 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      L(x,R(y,z,u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9886(a,1),11426(a,1,2,1))].">
      <j1 rule="para" parents="9886 11426"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      L(x,L(y,z \ 1,z) \ u,w) = L(x,L(y,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11418,a,b,11427,a)].">
      <j1 rule="hyper" parents="65 11418 11427"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      L(x,R(T(1 / y,z),y,z) \ u,w) = L(x,L(1 / y,y,y * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11107,a,b,11427,a)].">
      <j1 rule="hyper" parents="65 11107 11427"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,a(w,v5,v6)) = L(x,y \ R(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,10957,a(flip),b,11427,a),flip(a)].">
      <j1 rule="hyper" parents="65 10957 11427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      x * L(y,L(z,u,w) \ x,L(z,u,w)) = R(z,u,w) * ((R(z,u,w) \ x) * y)
    ]]></literal>
    <justification jstring="[para(11427(a,1),9935(a,1,2))].">
      <j1 rule="para" parents="11427 9935"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      L(x,(y * (z * (y \ 1))) \ u,w) = L(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10992,a,b,11428,a)].">
      <j1 rule="hyper" parents="65 10992 11428"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      L(x,(y * (z * (y \ 1))) \ z,u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(824(a,1),11434(a,2,2))].">
      <j1 rule="para" parents="824 11434"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),a(w,v5,v6)) = L(x,y \ L(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(10980,a,11430,a),flip(a)].">
      <j1 rule="hyper" parents="10980 11430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),a(y,z,u)) = L(x,a(y,z,u),y * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7544,a(flip),b,11436,a),flip(a)].">
      <j1 rule="hyper" parents="65 7544 11436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      L(x,y * L(y,z,u),a(y,z,u)) = L(x,a(y,z,u),y * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11009,a(flip),b,11437,a)].">
      <j1 rule="hyper" parents="65 11009 11437"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      L(x,R(T(1 / y,z),y,z) \ u,w) = L(x,L(y \ 1,y,y * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10871,a(flip),b,11429,a),flip(a)].">
      <j1 rule="hyper" parents="325 10871 11429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      L(x,L(T(1 / y,z),y,z) \ u,w) = L(x,L(y \ 1,y,y * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11427,a(flip),b,11439,a)].">
      <j1 rule="hyper" parents="65 11427 11439"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      L(x,L(y \ 1,y,y * z) \ u,w) = L(x,L(1 / y,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(10896,a,11440,a),flip(a)].">
      <j1 rule="hyper" parents="10896 11440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      L(x,L(y \ 1,y,y * z) \ u,w) = L(x,L(y \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10871,a(flip),b,11441,a),flip(a)].">
      <j1 rule="hyper" parents="325 10871 11441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) \ u) * w) = L(x,y,z) * ((L(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,414,a(flip),b,11433,a),flip(a)].">
      <j1 rule="hyper" parents="65 414 11433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11444">
    <literal><![CDATA[
      R(x,y,y) * ((a(x,y,y) \ 1) * z) = L(x,y,y) * ((L(x,y,y) \ x) * z)
    ]]></literal>
    <justification jstring="[para(5798(a,1),11443(a,1,2,1))].">
      <j1 rule="para" parents="5798 11443"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      a(x,y,L(z,u / (w * w),K(v5,v6) * v7)) = a(x,y,(v7 * (u / (w * w))) \ (v7 * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(10422,a,11206,a),flip(a)].">
      <j1 rule="hyper" parents="10422 11206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      a(x,y,L(z,u / (w * w),K(v5,v6) * v7)) = a(x,y,(v7 * u) \ (v7 * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10383,a(flip),b,11445,a),flip(a)].">
      <j1 rule="hyper" parents="325 10383 11445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      a(x,y,L(T(z,u),u,w)) = a(x,y,L(z,u / (v5 * v5),K(v6,v7) * w))
    ]]></literal>
    <justification jstring="[para(240(a,1),11447(a,2,3)),flip(a)].">
      <j1 rule="para" parents="240 11447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      a(x,y,L(z,u / (w * w),K(v5,v6) * v7)) = a(x,y,L(z,u,v7))
    ]]></literal>
    <justification jstring="[hyper(65,a,10042,a(flip),b,11449,a),flip(a)].">
      <j1 rule="hyper" parents="65 10042 11449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11452">
    <literal><![CDATA[
      a(x,y,L(z,u / (w * w),v5)) = a(x,y,L(z,u,v5))
    ]]></literal>
    <justification jstring="[para(1541(a,1),11450(a,1,3))].">
      <j1 rule="para" parents="1541 11450"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) * w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(10812(a,1),11452(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10812 11452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) \ w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(10814(a,1),11452(a,1,3))].">
      <j1 rule="para" parents="10814 11452"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      a(x,y,L(z,(u \ 1) \ w,v5)) = a(x,y,L(z,u \ w,v5))
    ]]></literal>
    <justification jstring="[para(11006(a,1),11453(a,1,3))].">
      <j1 rule="para" parents="11006 11453"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      a(L(x,x,y \ ((z \ u) \ w)) * (y \ ((z \ u) \ w)),v5,v6) = a(x \ (y \ ((u / z) \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10978,a,8454,a),flip(a)].">
      <j1 rule="hyper" parents="10978 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      a(x \ (y \ ((z / u) \ w)),v5,v6) = a(x \ (y \ ((u \ z) \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10975,a,11456,a),flip(a)].">
      <j1 rule="hyper" parents="10975 11456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      ((x * y) * (z * K(y,u))) / L(w,w \ T(z,y),x * T(y,z)) = (x * T(T(y,z),u)) * (T(z,y) / w)
    ]]></literal>
    <justification jstring="[para(2318(a,1),10747(a,1,2))].">
      <j1 rule="para" parents="2318 10747"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      ((x * y) * (z * K(y,u))) / L(w,w \ T(z,y),x * y) = (x * T(T(y,z),u)) * (T(z,y) / w)
    ]]></literal>
    <justification jstring="[para(2318(a,1),11458(a,1,2))].">
      <j1 rule="para" parents="2318 11458"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      ((x * y) * (z * K(y,u))) / L(w,w \ z,x * y) = (x * T(T(y,z),u)) * (T(z,y) / w)
    ]]></literal>
    <justification jstring="[para(10826(a,1),11459(a,1,2))].">
      <j1 rule="para" parents="10826 11459"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      ((x * y) * z) / (L(u,u \ z,x * y) * K(w,y)) = (x * T(T(y,z),w)) * (T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8349,a(flip),b,11462,a)].">
      <j1 rule="hyper" parents="65 8349 11462"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      ((x * y) * z) / L(u * K(w,y),u \ z,x * y) = (x * T(T(y,z),w)) * (T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(8545(a,2),11463(a,1,2))].">
      <j1 rule="para" parents="8545 11463"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      (x * T(T(y,z),u)) * (T(z,y) / w) = (x * y) * (z / (w * K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10919,a(flip),b,11465,a),flip(a)].">
      <j1 rule="hyper" parents="65 10919 11465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      (x * x) * (y / ((x * y) * K(y,x))) = R(T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9899,a(flip),b,11466,a),flip(a)].">
      <j1 rule="hyper" parents="65 9899 11466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      (x * x) * (y / (y * x)) = R(T(x,y),x,y)
    ]]></literal>
    <justification jstring="[para(93(a,1),11467(a,1,2,2))].">
      <j1 rule="para" parents="93 11467"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      (R(T(x,y \ L(y,z,u)),x,y \ L(y,z,u)) * (y \ L(y,z,u))) * x = (y \ L(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[para(11468(a,1),8653(a,1,1,1))].">
      <j1 rule="para" parents="11468 8653"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      (R(x,x,y \ L(y,z,u)) * (y \ L(y,z,u))) * x = (y \ L(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[para(8475(a,1),11469(a,1,1,1,1))].">
      <j1 rule="para" parents="8475 11469"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      (R(x,x,y * L(y,z,u)) * (y \ L(y,z,u))) * x = (y \ L(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[para(1039(a,1),11470(a,1,1,1))].">
      <j1 rule="para" parents="1039 11470"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * y = (x \ L(x,z,u)) * (y * y)
    ]]></literal>
    <justification jstring="[para(9218(a,1),11471(a,1,1))].">
      <j1 rule="para" parents="9218 11471"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (u \ 1) = (x / u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,564,a,b,11472,a)].">
      <j1 rule="hyper" parents="37 564 11472"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,u,x * L(x,y,z)) = (x / u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1789,a,b,11473,a)].">
      <j1 rule="hyper" parents="65 1789 11473"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      R(x,x,y * L(y,z,u)) = L(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,9215,a,b,11474,a)].">
      <j1 rule="hyper" parents="36 9215 11474"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),z,w * v5) * w) \ ((T(z,u) \ 1) \ (w * v5))) = a(x,y,L(v5,w,L(T(z,u),z,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(10280,a,10901,a)].">
      <j1 rule="hyper" parents="10280 10901"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      L(x,(x \ (x \ y)) \ (x \ y),x \ (y / x)) * (x \ y) = (x \ (y / x)) * (x * ((x \ (y / x)) \ (y / x)))
    ]]></literal>
    <justification jstring="[para(10951(a,1),11018(a,1,1))].">
      <j1 rule="para" parents="10951 11018"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),z,w * v5) * w) \ (T(z,u) \ (w * v5))) = a(x,y,L(v5,w,L(T(z,u),z,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(10464,a,11476,a)].">
      <j1 rule="hyper" parents="10464 11476"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),z,w * v5) * w) \ (z \ (w * v5))) = a(x,y,L(v5,w,L(T(z,u),z,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10192,a(flip),b,11478,a)].">
      <j1 rule="hyper" parents="65 10192 11478"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      a(x,y,L(z,u,L(T(w,v5),w,u * z))) = a(x,y,(L(w,w,u * z) * u) \ (w \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10257,a(flip),b,11479,a),flip(a)].">
      <j1 rule="hyper" parents="65 10257 11479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      a(x,y,(L(z,z,u * w) * u) \ (z \ (u * w))) = a(x,y,L(w,u,L(z,z,u * w)))
    ]]></literal>
    <justification jstring="[para(112(a,1),11481(a,1,3,3,1)),flip(a)].">
      <j1 rule="para" parents="112 11481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      (x \ (y / x)) * (x * ((x \ (y / x)) \ (y / x))) = L(x,x,x \ (y / x)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(10807(a,1),11477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10807 11477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      (x \ (y / x)) * (x * ((x \ (y / x)) \ (y / x))) = L(x,x,x * (y / x)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2368(a,1),11484(a,2,1))].">
      <j1 rule="para" parents="2368 11484"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      (x \ (y / x)) * (x * ((x \ (y / x)) \ (y / x))) = L(x,x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2323(a,1),11485(a,2,1))].">
      <j1 rule="para" parents="2323 11485"/>
    </justification>
  </clause>

  <clause id="11488">
    <literal><![CDATA[
      (x \ (y / x)) * (x * ((x \ (y / x)) \ (y / x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(325,a,8385,a(flip),b,11487,a),flip(a)].">
      <j1 rule="hyper" parents="325 8385 11487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      (x \ (y / x)) * (x * T(x,x \ (y / x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[para(114(a,2),11488(a,1,2,2))].">
      <j1 rule="para" parents="114 11488"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      (x \ (y / x)) * (x * T(x,x \ (x \ y))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[para(4969(a,1),11490(a,1,2,2))].">
      <j1 rule="para" parents="4969 11490"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      L(x,(y * y) * (y \ (z / y)),u) = L(x,(z / (y \ 1)) / y,u)
    ]]></literal>
    <justification jstring="[para(11490(a,1),11013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11490 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      a(x,y,L((z \ (u / z)) \ w,z \ (u / z),z * T(z,z \ (z \ u)))) = a(x,y,((u / (z \ 1)) / z) \ ((z * T(z,z \ (z \ u))) * w))
    ]]></literal>
    <justification jstring="[para(11491(a,1),10182(a,2,3,1))].">
      <j1 rule="para" parents="11491 10182"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      L(x,(y / (z \ 1)) / z,u) = L(x,(z \ 1) \ (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11006,a(flip),b,11492,a),flip(a)].">
      <j1 rule="hyper" parents="65 11006 11492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11495">
    <literal><![CDATA[
      L(x,(y / (z \ 1)) / z,u) = L(x,(z \ 1) \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10873,a(flip),b,11494,a),flip(a)].">
      <j1 rule="hyper" parents="325 10873 11494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      L(x,(y \ 1) \ (y \ z),u) = L(x,y \ (z / (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10814,a(flip),b,11495,a),flip(a)].">
      <j1 rule="hyper" parents="65 10814 11495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      L(x,(y \ 1) \ (y \ z),u) = L(x,y \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10873,a(flip),b,11496,a),flip(a)].">
      <j1 rule="hyper" parents="325 10873 11496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      L(x,y \ ((y \ 1) \ (z * ((u * y) / u))),w) = L(x,(y \ 1) \ T(z * K(u,y),y),w)
    ]]></literal>
    <justification jstring="[para(4030(a,1),11497(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4030 11497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      a(L(x,y \ ((y \ 1) \ z),u),w,v5) = a(L(x,y \ (y \ z),u),w,v5)
    ]]></literal>
    <justification jstring="[para(11497(a,1),11150(a,1,1))].">
      <j1 rule="para" parents="11497 11150"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      L(x,y \ ((y \ 1) \ (z * ((u * y) / u))),w) = L(x,((y \ 1) \ T(z,y)) * K(u,y),w)
    ]]></literal>
    <justification jstring="[para(8299(a,1),11498(a,2,2))].">
      <j1 rule="para" parents="8299 11498"/>
    </justification>
  </clause>

  <clause id="11501">
    <literal><![CDATA[
      L(x,y \ ((y \ 1) \ (z * ((u * y) / u))),w) = L(x,(y \ 1) \ T(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10818,a(flip),b,11500,a),flip(a)].">
      <j1 rule="hyper" parents="325 10818 11500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      L(x,y \ ((y \ 1) \ (z * ((u * y) / u))),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(y \ 1) \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(11501(a,2),10892(a,1))].">
      <j1 rule="para" parents="11501 10892"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      K(x,x \ 1) * (R(x \ 1,y,z) * L(x,u,w)) = (x \ L(x,u,w)) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(8516(a,1),11071(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8516 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      K(x,x \ 1) * (R(x \ 1,y,z) * L(x,u,w)) = R(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1347,a(flip),b,11504,a),flip(a)].">
      <j1 rule="hyper" parents="325 1347 11504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      R(1 / x,y,z) * L(x,u,w) = R(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1061,a(flip),b,11505,a)].">
      <j1 rule="hyper" parents="65 1061 11505"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,K(v5,v6) / u)) * v7) = a(x,y,(z \ (K(v5,v6) * (L(w,u,u) * (K(v5,v6) / u)))) * v7)
    ]]></literal>
    <justification jstring="[para(8557(a,1),10492(a,2,3,1,2))].">
      <j1 rule="para" parents="8557 10492"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      T(x / y,z) * (((x / y) \ x) * ((T(x / y,z) * ((x / y) \ x)) \ u)) = (y \ x) * (y * (((x / y) * (x / (x / y))) \ u))
    ]]></literal>
    <justification jstring="[para(9825(a,1),10734(a,1,2))].">
      <j1 rule="para" parents="9825 10734"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) \ (a(w,v5,w) \ (((a(w,v5,w) / z) * y) * (z \ u))),v6) = L(x,a(y,a(w,v5,w) / z,z \ u),v6)
    ]]></literal>
    <justification jstring="[para(7628(a,1),11022(a,1,2))].">
      <j1 rule="para" parents="7628 11022"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      L(x,(y \ a(z,u,z)) * (y \ (((y \ 1) \ w) * v5)),v6) = L(x,(((y \ a(z,u,z)) \ 1) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(9317(a,1),11041(a,1,2,2,2))].">
      <j1 rule="para" parents="9317 11041"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      L(x,(((y \ a(z,u,z)) \ 1) \ w) * v5,v6) = L(x,(y \ 1) * (y \ (((y \ 1) \ w) * v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,7764,a(flip),b,11511,a),flip(a)].">
      <j1 rule="hyper" parents="65 7764 11511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      L(x,(((y \ a(z,u,z)) \ 1) \ w) * v5,v6) = L(x,((y * y) \ ((1 / y) \ w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(9847(a,1),11512(a,2,2))].">
      <j1 rule="para" parents="9847 11512"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      L(x,(((y \ a(z,u,z)) \ 1) \ w) * v5,v6) = L(x,(y \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,11194,a(flip),b,11515,a),flip(a)].">
      <j1 rule="hyper" parents="325 11194 11515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,K(v5,v6) / u)) * v7) = a(x,y,v7 * (z \ (L(w,u,u) * (K(v5,v6) / u))))
    ]]></literal>
    <justification jstring="[hyper(325,a,10334,a(flip),b,11508,a),flip(a)].">
      <j1 rule="hyper" parents="325 10334 11508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11519">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,K(v5,v6) / u)) * v7) = a(x,y,v7 * (z \ (L(w,u,u) * (u \ K(v5,v6)))))
    ]]></literal>
    <justification jstring="[hyper(325,a,11256,a(flip),b,11517,a),flip(a)].">
      <j1 rule="hyper" parents="325 11256 11517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,K(v5,v6) / u)) * v7) = a(x,y,v7 * (z \ (L(w,u,u) * u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,11252,a(flip),b,11519,a),flip(a)].">
      <j1 rule="hyper" parents="325 11252 11519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      T(x / y,z) * (y * ((T(x / y,z) * ((x / y) \ x)) \ u)) = (y \ x) * (y * (((x / y) * (x / (x / y))) \ u))
    ]]></literal>
    <justification jstring="[para(85(a,1),11509(a,1,2,1))].">
      <j1 rule="para" parents="85 11509"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      T(x / y,z) * (y * ((T(x / y,z) * y) \ u)) = (y \ x) * (y * (((x / y) * (x / (x / y))) \ u))
    ]]></literal>
    <justification jstring="[para(85(a,1),11522(a,1,2,2,1,2))].">
      <j1 rule="para" parents="85 11522"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      (x \ y) * (x * (((y / x) * (y / (y / x))) \ z)) = (y / x) * (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10735,a(flip),b,11523,a),flip(a)].">
      <j1 rule="hyper" parents="65 10735 11523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      (x \ y) * (x * (((x \ y) * x) \ z)) = (y / x) * (x * (y \ z))
    ]]></literal>
    <justification jstring="[para(4027(a,1),11524(a,1,2,2,1))].">
      <j1 rule="para" parents="4027 11524"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) \ (((a(w,v5,w) / z) * y) * (a(w,v5,w) \ (z \ u))),v6) = L(x,a(y,a(w,v5,w) / z,z \ u),v6)
    ]]></literal>
    <justification jstring="[para(7626(a,1),11510(a,1,2,2))].">
      <j1 rule="para" parents="7626 11510"/>
    </justification>
  </clause>

  <clause id="11528">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,w \ v5),v6) = L(x,(y * ((w * w) \ v5)) \ (((1 / w) * y) * (w \ v5)),v6)
    ]]></literal>
    <justification jstring="[para(7875(a,1),11527(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7875 11527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11529">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,w \ v5),v6) = L(x,(y * ((w * w) \ v5)) \ (((w \ 1) * y) * (w \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10925,a(flip),b,11528,a),flip(a)].">
      <j1 rule="hyper" parents="325 10925 11528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      L(x,y,z) * R(K(y * x,z) * (((z * y) \ ((y * x) * z)) \ 1),u,w) = ((z * y) \ ((y * x) * z)) \ R((z * y) \ ((y * x) * z),u,w)
    ]]></literal>
    <justification jstring="[para(1057(a,2),9811(a,1,2))].">
      <j1 rule="para" parents="1057 9811"/>
    </justification>
  </clause>

  <clause id="11532">
    <literal><![CDATA[
      a(x,y,((z / (u \ 1)) / u) \ ((u * T(u,u \ (u \ z))) * w)) = a(x,y,(u \ (z / u)) \ w)
    ]]></literal>
    <justification jstring="[para(2237(a,1),11493(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2237 11493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11533">
    <literal><![CDATA[
      a(x,y,((z / (u \ 1)) / u) \ ((u * T(u,u \ (u \ z))) * w)) = a(x,y,(u \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10235,a(flip),b,11532,a),flip(a)].">
      <j1 rule="hyper" parents="325 10235 11532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      a(x,y,((z / (u \ 1)) / u) \ ((u * u) * w)) = a(x,y,(u \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11189,a(flip),b,11533,a)].">
      <j1 rule="hyper" parents="65 11189 11533"/>
    </justification>
  </clause>

  <clause id="11537">
    <literal><![CDATA[
      a(x,y,((z / (u \ 1)) / u) \ w) = a(x,y,(u \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10364,a(flip),b,11535,a)].">
      <j1 rule="hyper" parents="65 10364 11535"/>
    </justification>
  </clause>

  <clause id="11539">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ 1) \ u)) \ w) = a(x,y,(z \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10350,a(flip),b,11537,a)].">
      <j1 rule="hyper" parents="65 10350 11537"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      ((x * y) \ ((y * z) * x)) \ R((x * y) \ ((y * z) * x),u,w) = L(z,y,x) * R(((x * y) \ ((y * z) * T(x,y * z))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(9612(a,1),11531(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9612 11531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      ((x * y) \ ((y * z) * x)) \ R((x * y) \ ((y * z) * x),u,w) = L(z,y,x) * R(((x * y) \ (x * (y * z))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(113(a,1),11540(a,2,2,1,1,2))].">
      <j1 rule="para" parents="113 11540"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      ((x * y) \ ((y * z) * x)) \ R((x * y) \ ((y * z) * x),u,w) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),11541(a,2,2,1,1))].">
      <j1 rule="para" parents="18 11541"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      ((x * y) \ ((y * z) * x)) \ R((x * y) \ ((y * z) * x),u,w) = L(z,y,x) \ R(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1077,a(flip),b,11542,a),flip(a)].">
      <j1 rule="hyper" parents="325 1077 11542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      ((x * y) \ ((y * z) * x)) \ R((x * y) \ ((y * z) * x),u,w) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),11543(a,2,2))].">
      <j1 rule="para" parents="29 11543"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      (x * y) \ (((y * z) * x) * R(((y * z) * x) \ (x * y),u,w)) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(1406,a,11544,a)].">
      <j1 rule="hyper" parents="1406 11544"/>
    </justification>
  </clause>

  <clause id="11546">
    <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(5390(a,1),11545(a,1,2))].">
      <j1 rule="para" parents="5390 11545"/>
    </justification>
  </clause>

  <clause id="11547">
    <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(1084(a,1),11546(a,1,2,2))].">
      <j1 rule="para" parents="1084 11546"/>
    </justification>
  </clause>

  <clause id="11548">
    <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(456,a,11547,a),flip(a)].">
      <j1 rule="hyper" parents="456 11547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      L(x,y,z) * L(x \ R(x,u,w),y,z) = L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,18,a,b,11547,a(flip))].">
      <j1 rule="hyper" parents="137 18 11547"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      L(x \ R(x,y,y),z,u) = a(L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(1902,a,11548,a),flip(a)].">
      <j1 rule="hyper" parents="1902 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      L(x,y,x) \ L(R(x,z,u),y,x) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,11387,a(flip),b,11548,a),flip(a)].">
      <j1 rule="hyper" parents="325 11387 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      ((1 / (x * y)) * y) \ (K(y,x) * R(K(y,x) \ ((1 / (x * y)) * y),z,u)) = L(x \ R(x,z,u),y,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,7046,a,b,11548,a)].">
      <j1 rule="hyper" parents="65 7046 11548"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u * x) = (1 / (u * x)) * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4488,a(flip),b,11548,a),flip(a)].">
      <j1 rule="hyper" parents="65 4488 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11554">
    <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),11548(a,1,2))].">
      <j1 rule="para" parents="29 11548"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      L(L(x,y,z) \ L(R(x,u,w),y,z),v5,v6) = L(L(x \ R(x,u,w),v5,v6),y,z)
    ]]></literal>
    <justification jstring="[para(11548(a,2),30(a,1,1))].">
      <j1 rule="para" parents="11548 30"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ L(R(T(y,x),z,u),x,x) = L(T(y,x) \ R(T(y,x),z,u),x,x)
    ]]></literal>
    <justification jstring="[para(655(a,1),11548(a,1,1))].">
      <j1 rule="para" parents="655 11548"/>
    </justification>
  </clause>

  <clause id="11557">
    <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(11548(a,1),5804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11548 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      L(x,y,x) \ L(R(x,z,u),y,L(x,w,v5)) = L(x \ R(x,z,u),y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(7063(a,1),11548(a,1,1))].">
      <j1 rule="para" parents="7063 11548"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      x \ (R(y,z,z) * (y \ x)) = a(L(y,y,x),z,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9360,a(flip),b,11550,a)].">
      <j1 rule="hyper" parents="65 9360 11550"/>
    </justification>
  </clause>

  <clause id="11560">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = L(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(1896(a,1),11550(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1896 11550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      a(L(x,y,z),z,z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10561,a(flip),b,11560,a),flip(a)].">
      <j1 rule="hyper" parents="325 10561 11560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      L(x,y,z) != a(L(u,y,z),w,w)
    ]]></literal>
    <literal><![CDATA[
      a(u,w,w) = x
    ]]></literal>
    <justification jstring="[para(11560(a,2),52(a,1)),flip(a)].">
      <j1 rule="para" parents="11560 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      a(L(x,x,y),x \ y,x \ y) = a(x,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11087,a(flip),b,11561,a)].">
      <j1 rule="hyper" parents="65 11087 11561"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      L(L(x,y,z) \ R(L(x,y,z),u,w),v5,v6) = L(L(x \ R(x,u,w),v5,v6),y,z)
    ]]></literal>
    <justification jstring="[para(11554(a,2),30(a,1,1))].">
      <j1 rule="para" parents="11554 30"/>
    </justification>
  </clause>

  <clause id="11565">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z,v5,v6),u,w)) = a(x,y,L(z \ R(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(11554(a,1),11386(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11554 11386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,L(x,w,v5)) = L(x,u,x) \ L(R(x,y,z),u,x)
    ]]></literal>
    <justification jstring="[para(7068(a,1),11558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7068 11558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,L(x,w,v5)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,11551,a(flip),b,11566,a),flip(a)].">
      <j1 rule="hyper" parents="325 11551 11566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      L(L(x,y,z) \ R(L(x,y,z),u,w),v5,L(x,v6,v7)) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(11567(a,1),11564(a,2,1))].">
      <j1 rule="para" parents="11567 11564"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      a(x,y,L(z \ R(z,u,w),v5,v6)) = a(x,y,L(z \ L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(4460(a,1),11565(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4460 11565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11572">
    <literal><![CDATA[
      a(x,y,L(z \ R(z,u,w),v5,v6)) = a(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(325,a,10555,a(flip),b,11571,a),flip(a)].">
      <j1 rule="hyper" parents="325 10555 11571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,w * u)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(2326(a,2),11572(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2326 11572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      a(x,y,a(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,7715,a(flip),b,11573,a),flip(a)].">
      <j1 rule="hyper" parents="65 7715 11573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((z * u) * (w * (w * L(w,u,z))))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),11573(a,1,3))].">
      <j1 rule="para" parents="18 11573"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      a(x * y,z,a(x,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,10294,a(flip),b,11574,a)].">
      <j1 rule="hyper" parents="65 10294 11574"/>
    </justification>
  </clause>

  <clause id="11577">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,11574,a)].">
      <j1 rule="hyper" parents="54 11574"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      L(a(x,x,y),z,x * y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,11576,a)].">
      <j1 rule="hyper" parents="54 11576"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = a(L(x,w,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,6897,a,b,11577,a),flip(a)].">
      <j1 rule="hyper" parents="325 6897 11577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      L(a(x,y,z),x,a(u,w,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10605,a(flip),b,11577,a)].">
      <j1 rule="hyper" parents="65 10605 11577"/>
    </justification>
  </clause>

  <clause id="11581">
    <literal><![CDATA[
      (x * (y / a(x,z,u))) \ (x * y) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,6856,a(flip),b,11577,a)].">
      <j1 rule="hyper" parents="65 6856 11577"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = x * (y * a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,11577,a(flip),b,4391,a(flip))].">
      <j1 rule="hyper" parents="137 11577 4391"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = x * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,11577,a(flip),b,7235,a)].">
      <j1 rule="hyper" parents="136 11577 7235"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,x) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(11577(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11577 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      (x * y) * L(a(x,z,u),w,v5) = x * (y * L(a(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(11577(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="11577 412"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,x) = (a(x,y,z) \ a(x,y,z)) * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(11577(a,1),1316(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11577 1316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * a(x,y,z)) = L(z,y,x) * L(L(z,y,x) \ z,u,x)
    ]]></literal>
    <justification jstring="[para(11577(a,1),5775(a,1,2,2))].">
      <j1 rule="para" parents="11577 5775"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      L(K(x,y) * a(z,u,w),v5,z) = K(x,y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(11577(a,1),8549(a,2,2))].">
      <j1 rule="para" parents="11577 8549"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * x = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(11577(a,1),9013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11577 9013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      x \ R(x,x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(1908,a,11578,a)].">
      <j1 rule="hyper" parents="1908 11578"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      a(x,x,y) * ((x * y) * z) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,11578,a(flip),b,8976,a)].">
      <j1 rule="hyper" parents="136 11578 8976"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      x \ (y * R(y \ x,x \ y,z)) = a(x \ y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(1406,a,11590,a)].">
      <j1 rule="hyper" parents="1406 11590"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      a(x,x,x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(1090,a,11590,a),flip(a)].">
      <j1 rule="hyper" parents="1090 11590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      (x / (y * x)) * y = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(1083,a,11590,a)].">
      <j1 rule="hyper" parents="1083 11590"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      x * a(x,x,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(148,a,11590,a)].">
      <j1 rule="hyper" parents="148 11590"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      (x \ 1) * R(x,x \ 1,y) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8766,a(flip),b,11590,a)].">
      <j1 rule="hyper" parents="65 8766 11590"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      a(x \ y,x \ y,x) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6563,a(flip),b,11590,a),flip(a)].">
      <j1 rule="hyper" parents="65 6563 11590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      R(1 / x,x,y) = a(x,x,y) / x
    ]]></literal>
    <justification jstring="[hyper(135,a,11590,a(flip),b,1080,a),flip(a)].">
      <j1 rule="hyper" parents="135 11590 1080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      a(x,x,y) / x = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(135,a,11590,a(flip),b,1078,a(flip))].">
      <j1 rule="hyper" parents="135 11590 1078"/>
    </justification>
  </clause>

  <clause id="11600">
    <literal><![CDATA[
      (x * y) \ (x * R(y,y,z)) = L(a(y,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(11590(a,1),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11590 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      a(x \ 1,x \ 1,y) * x = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(11590(a,1),1469(a,1,1))].">
      <j1 rule="para" parents="11590 1469"/>
    </justification>
  </clause>

  <clause id="11602">
    <literal><![CDATA[
      x \ L(x,x,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7682(a,1),11590(a,1,2))].">
      <j1 rule="para" parents="7682 11590"/>
    </justification>
  </clause>

  <clause id="11603">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),a(x,y,z),u) = a(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9010(a,1),11590(a,1,2))].">
      <j1 rule="para" parents="9010 11590"/>
    </justification>
  </clause>

  <clause id="11604">
    <literal><![CDATA[
      R(x,y,z * ((u * z) \ u)) = R(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(11590(a,1),9922(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11590 9922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11605">
    <literal><![CDATA[
      a(x,y,z * R(z,z,u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(11590(a,1),10114(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11590 10114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      L(x,y,z) * L(a(x,x,u),y,z) = L(R(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(11590(a,1),11549(a,1,2,1))].">
      <j1 rule="para" parents="11590 11549"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      R(x,x,y) * L(z,a(x,x,y),x) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,11595,a(flip),b,193,a)].">
      <j1 rule="hyper" parents="136 11595 193"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      R(x,x \ y,a(y,y,z)) = R(y,y,z) / ((x \ y) * a(y,y,z))
    ]]></literal>
    <justification jstring="[para(11595(a,1),106(a,2,1))].">
      <j1 rule="para" parents="11595 106"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      x / L(a(y,y,z),y,R(y,y,z) \ x) = (x / (y * a(y,y,z))) * y
    ]]></literal>
    <justification jstring="[para(11595(a,1),1579(a,1,2,3,1))].">
      <j1 rule="para" parents="11595 1579"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) = a(x,y,z * R(u,u,z))
    ]]></literal>
    <justification jstring="[para(11595(a,1),10753(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="11595 10753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      L(x,y,z * ((z * u) \ u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(11594(a,1),2325(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11594 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      (a(x,x,y) / x) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(195,a,11599,a(flip))].">
      <j1 rule="hyper" parents="195 11599"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      (a(x,x,y) / x) * T(x,y) = (y / (y * x)) * x
    ]]></literal>
    <justification jstring="[para(11599(a,2),6578(a,1,1))].">
      <j1 rule="para" parents="11599 6578"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      a(x,(y \ a(y,y,z)) * u,w) = a(x,(z / (y * z)) * u,w)
    ]]></literal>
    <justification jstring="[para(11599(a,1),9998(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11599 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      x * T(x \ R(1 / (1 / x),1 / x,y),z) = T(a(1 / x,1 / x,y),z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(11598(a,2),5135(a,1,2,1,2))].">
      <j1 rule="para" parents="11598 5135"/>
    </justification>
  </clause>

  <clause id="11616">
    <literal><![CDATA[
      (x * y) \ ((x * x) * (x \ y)) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,90,a,b,11593,a)].">
      <j1 rule="hyper" parents="65 90 11593"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      a(L(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(11579(a,1),351(a,1)),flip(b)].">
      <j1 rule="para" parents="11579 351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ ((a(x,y,z) \ x) * u) = a(x,y,z) \ ((a(x,y,z) * x) * u)
    ]]></literal>
    <justification jstring="[para(11589(a,1),4100(a,1,2,1))].">
      <j1 rule="para" parents="11589 4100"/>
    </justification>
  </clause>

  <clause id="11619">
    <literal><![CDATA[
      L(a(x,y,z),u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(11579(a,2),11617(a,1))].">
      <j1 rule="para" parents="11579 11617"/>
    </justification>
  </clause>

  <clause id="11620">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ u)) \ ((z \ u) * u)) = a(x,y,z * ((z / u) * (u / z)))
    ]]></literal>
    <justification jstring="[para(11597(a,1),10417(a,2,3,2))].">
      <j1 rule="para" parents="11597 10417"/>
    </justification>
  </clause>

  <clause id="11621">
    <literal><![CDATA[
      (x * (a(x,y,z) \ u)) \ (x * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(7194(a,1),11581(a,1,1,2))].">
      <j1 rule="para" parents="7194 11581"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      R(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(9924,a,11582,a)].">
      <j1 rule="hyper" parents="9924 11582"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      x \ ((x * y) * (y \ z)) = z * a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(815,a,11582,a)].">
      <j1 rule="hyper" parents="815 11582"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      x \ ((x * y) * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(550,a,11582,a)].">
      <j1 rule="hyper" parents="550 11582"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      x \ (y * a(x,z,u)) = (x \ y) * a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(547,a,11582,a)].">
      <j1 rule="hyper" parents="547 11582"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      x * ((y * z) * a(x,y,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(297,a,11582,a),flip(a)].">
      <j1 rule="hyper" parents="297 11582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      x * ((y * z) * a(x,z,y)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10028,a(flip),b,11582,a),flip(a)].">
      <j1 rule="hyper" parents="65 10028 11582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11628">
    <literal><![CDATA[
      ((x * (y * a(x,z,u))) \ (x * y)) * (a(x,z,u) * a(x,z,u)) = L(a(x,z,u),a(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(11582(a,1),560(a,1,1,1))].">
      <j1 rule="para" parents="11582 560"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      (x * a(x,y,z)) \ (x * (u * a(x,y,z))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11582(a,1),7320(a,1,2))].">
      <j1 rule="para" parents="11582 7320"/>
    </justification>
  </clause>

  <clause id="11630">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(x,w,v5) = L(x,y,z) * (u * a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(11622(a,1),408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11622 408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(x,w,v5)) = x \ R(R(x,u,a(x,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(11622(a,1),9229(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11622 9229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11632">
    <literal><![CDATA[
      (x * y) \ ((z / x) \ (z * y)) = a(x \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(2953,a,11624,a)].">
      <j1 rule="hyper" parents="2953 11624"/>
    </justification>
  </clause>

  <clause id="11633">
    <literal><![CDATA[
      a(x,y,z) = (y * z) \ (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(533,a,11624,a),flip(a)].">
      <j1 rule="hyper" parents="533 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11634">
    <literal><![CDATA[
      x \ ((x * y) * z) = a(x,y,z) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7190,a,b,11624,a),flip(a)].">
      <j1 rule="hyper" parents="325 7190 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11635">
    <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(325,a,10579,a(flip),b,11624,a),flip(a)].">
      <j1 rule="hyper" parents="325 10579 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      K(x,y) * (z \ ((z * y) * x)) = (x * y) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,11624,a,b,2499,a)].">
      <j1 rule="hyper" parents="137 11624 2499"/>
    </justification>
  </clause>

  <clause id="11637">
    <literal><![CDATA[
      (x * y) \ (z \ ((z * y) * x)) = K(y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,11624,a,b,6155,a)].">
      <j1 rule="hyper" parents="132 11624 6155"/>
    </justification>
  </clause>

  <clause id="11638">
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,652,a(flip),b,11624,a(flip))].">
      <j1 rule="hyper" parents="132 652 11624"/>
    </justification>
  </clause>

  <clause id="11639">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,307,a(flip),b,11624,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 307 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11640">
    <literal><![CDATA[
      ((x \ y) * z) * a(x,x \ y,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11624(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      (x * L(y,z,x)) * a(z,x,L(y,z,x)) = z \ (x * (T(z,x) * y))
    ]]></literal>
    <justification jstring="[para(5232(a,1),11624(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5232 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11642">
    <literal><![CDATA[
      (a(x,y,z) * y) \ (x \ ((x * y) * z)) = L(z,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11624(a,2),7268(a,1,2))].">
      <j1 rule="para" parents="11624 7268"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      (x \ ((x * y) * z)) \ (y * z) = (y * z) \ (a(x,y,z) \ (y * z))
    ]]></literal>
    <justification jstring="[para(11624(a,2),8532(a,1,1))].">
      <j1 rule="para" parents="11624 8532"/>
    </justification>
  </clause>

  <clause id="11644">
    <literal><![CDATA[
      L(L(x,y,a(z,y,x)),y * a(z,y,x),z) = (z * (y * a(z,y,x))) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(11626(a,1),7328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11626 7328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      ((x \ K(y,z)) * u) \ ((w / x) \ ((w * (x \ (x \ K(y,z)))) * u)) = a(w / x,x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8406(a,1),11633(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8406 11633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      K(x,x \ (y \ (z \ ((z * y) * x)))) * a(z,y,x) = L((y \ (z \ ((z * y) * x))) / x,x,y)
    ]]></literal>
    <justification jstring="[para(11633(a,2),9672(a,1,2))].">
      <j1 rule="para" parents="11633 9672"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      ((1 / x) \ y) / (x * y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,652,a(flip),b,11634,a(flip))].">
      <j1 rule="hyper" parents="135 652 11634"/>
    </justification>
  </clause>

  <clause id="11648">
    <literal><![CDATA[
      a(x,x \ y,z) * ((x \ y) * z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11634(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      R(T(a(x,x,y),(x * y) * z),x * y,z) = ((x * y) * z) \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[para(11647(a,1),825(a,1,1,1))].">
      <j1 rule="para" parents="11647 825"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,v5) * x) = x * (a(u,w,v5) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(7219,a,11583,a)].">
      <j1 rule="hyper" parents="7219 11583"/>
    </justification>
  </clause>

  <clause id="11651">
    <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(11583(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11583 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      x * a(x,x \ 1,y) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(7291,a,11601,a)].">
      <j1 rule="hyper" parents="7291 11601"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      x \ R(x,x \ 1,y) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,11601,a(flip),b,7281,a(flip))].">
      <j1 rule="hyper" parents="132 11601 7281"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      a(x,x \ 1,x \ y) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,9870,a(flip),b,11653,a),flip(a)].">
      <j1 rule="hyper" parents="65 9870 11653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11655">
    <literal><![CDATA[
      x * ((x \ y) / y) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1296,a(flip),b,11653,a)].">
      <j1 rule="hyper" parents="65 1296 11653"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = x \ a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,11653,a(flip),b,1298,a),flip(a)].">
      <j1 rule="hyper" parents="132 11653 1298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      a(x,y * (z \ (y \ z)),u) = a(x,a(y,y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(11655(a,1),10029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11655 10029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11658">
    <literal><![CDATA[
      a(x,y,z * ((z * u) \ u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10671,a(flip),b,11605,a)].">
      <j1 rule="hyper" parents="65 10671 11605"/>
    </justification>
  </clause>

  <clause id="11659">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) = x * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(41,a,7205,a,b,11621,a)].">
      <j1 rule="hyper" parents="41 7205 11621"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      (x \ ((a(x,y,z) \ 1) * u)) * a(x,y,z) = x \ L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(7469(a,1),11625(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7469 11625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      a(x,x \ 1,x \ (x \ y)) = x \ R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1298,a(flip),b,11654,a),flip(a)].">
      <j1 rule="hyper" parents="325 1298 11654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      (x / y) * (a(x / y,z,u) \ y) = a(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(12(a,1),11659(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 11659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      x * (y * (a(y,z,x) \ z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(11659(a,1),10589(a,1,2))].">
      <j1 rule="para" parents="11659 10589"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      R(x,y,((z * u) \ z) * u) = R(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(9915,a,11604,a)].">
      <j1 rule="hyper" parents="9915 11604"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      R(x,y,(z \ (u \ z)) * u) = R(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11346,a,b,11604,a)].">
      <j1 rule="hyper" parents="65 11346 11604"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      R(x,y,z \ (u \ (z \ u))) = R(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9948,a,b,11604,a)].">
      <j1 rule="hyper" parents="65 9948 11604"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      L(x,y,z * L(z,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,6313,a,b,11611,a)].">
      <j1 rule="hyper" parents="65 6313 11611"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      L(((x \ y) * (y \ x)) \ z,x \ y,a(x \ y,x \ y,x)) = (x \ y) * (L(x \ y,x \ y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9374,a(flip),b,11668,a),flip(a)].">
      <j1 rule="hyper" parents="65 9374 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11670">
    <literal><![CDATA[
      L(x,y,a(x,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,9160,a(flip),b,11668,a),flip(a)].">
      <j1 rule="hyper" parents="65 9160 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      L((x \ L(x,x,y)) \ z,x,a(x,x,y)) = x * (L(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8968,a(flip),b,11668,a),flip(a)].">
      <j1 rule="hyper" parents="65 8968 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      a(x,x,y) * (T(z,a(x,x,y)) * L(x,u,w)) = (z * a(x,x,y)) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(11670(a,1),5235(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11670 5235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      a(x,x,y) * K(x,y) = (y / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(2176,a,11613,a)].">
      <j1 rule="hyper" parents="2176 11613"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      K(x,y) * a(x,x,y) = (y / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(7209,a,11673,a)].">
      <j1 rule="hyper" parents="7209 11673"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      K(x \ 1,y) * a(y \ (x \ y),y \ (x \ y),y) = (y / (y * (y \ (x \ y)))) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(2690(a,1),11674(a,1,1))].">
      <j1 rule="para" parents="2690 11674"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      a(x,y,z) = (z * y) \ (x \ ((x * y) * T(z,y)))
    ]]></literal>
    <justification jstring="[para(11627(a,1),71(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11627 71"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11677">
    <literal><![CDATA[
      x * (y * (z * a(x,z,y))) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(10565(a,1),11627(a,1,2))].">
      <j1 rule="para" parents="10565 11627"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      (x \ y) * ((x \ y) * a(x,x \ y,x \ y)) = x \ (y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10565,a(flip),b,11640,a)].">
      <j1 rule="hyper" parents="65 10565 11640"/>
    </justification>
  </clause>

  <clause id="11679">
    <literal><![CDATA[
      K(x \ y,z) * a(x,x \ y,z) = (z * (x \ y)) \ (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(132,a,11640,a(flip),b,6155,a),flip(a)].">
      <j1 rule="hyper" parents="132 11640 6155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ y,x) * (x * ((x \ y) \ y)) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(324(a,1),11648(a,1,2))].">
      <j1 rule="para" parents="324 11648"/>
    </justification>
  </clause>

  <clause id="11681">
    <literal><![CDATA[
      a(x,x \ y,z) * ((x \ y) * (z \ 1)) = x \ (y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(7484(a,1),11648(a,1,1))].">
      <j1 rule="para" parents="7484 11648"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      ((a(x,x \ y,K(z,u) * w) * ((x \ y) * w)) / w) * K(z,u) = (x \ (y * (K(z,u) * w))) / w
    ]]></literal>
    <justification jstring="[para(11648(a,1),9838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11648 9838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11683">
    <literal><![CDATA[
      a(x,y,z * (u \ (z \ u))) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10664,a(flip),b,11658,a)].">
      <j1 rule="hyper" parents="65 10664 11658"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      R(x,y,z * L(z,z,u)) = R(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8973,a(flip),b,11665,a)].">
      <j1 rule="hyper" parents="65 8973 11665"/>
    </justification>
  </clause>

  <clause id="11685">
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) = R(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(9915,a,11666,a)].">
      <j1 rule="hyper" parents="9915 11666"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      (x * y) \ ((y * L(y,z,u)) \ (((y * L(y,z,u)) * y) * T(x,y))) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,8810,a(flip),b,11676,a),flip(a)].">
      <j1 rule="hyper" parents="65 8810 11676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = z * (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(140,a,11677,a)].">
      <j1 rule="hyper" parents="140 11677"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      L(x * a(y,x,x),x,y) = T(x,x)
    ]]></literal>
    <justification jstring="[hyper(455,a,11677,a(flip))].">
      <j1 rule="hyper" parents="455 11677"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      L(x * a(y / z,x,z),z,y / z) = y \ (((y / z) * x) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(132,a,11677,a(flip),b,445,a),flip(a)].">
      <j1 rule="hyper" parents="132 11677 445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11690">
    <literal><![CDATA[
      (x * y) \ ((x * z) * T(y,z)) = L(z * a(x,z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,11677,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="132 11677 100"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      a(x,y,(z * (u * a(w,u,z))) * w) = a(x,y,(w * u) * T(z,u))
    ]]></literal>
    <justification jstring="[para(11677(a,1),10045(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11677 10045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11692">
    <literal><![CDATA[
      L(x * a(y,x,x),x,y) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,112,a(flip),b,11688,a),flip(a)].">
      <j1 rule="hyper" parents="325 112 11688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      L(a(x,y,y) * y,y,x) = y
    ]]></literal>
    <justification jstring="[para(7190(a,2),11692(a,1,1))].">
      <j1 rule="para" parents="7190 11692"/>
    </justification>
  </clause>

  <clause id="11694">
    <literal><![CDATA[
      x * ((a(y,x,x) * x) \ (z / L(a(y,x,x) * x,x,y))) = z / (a(y,x,x) * x)
    ]]></literal>
    <justification jstring="[para(11693(a,1),8375(a,1,1))].">
      <j1 rule="para" parents="11693 8375"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = z * (a(x,y,z) * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,7206,a,b,11687,a),flip(a)].">
      <j1 rule="hyper" parents="325 7206 11687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      a(x,y,z) = (x \ ((x * y) * T(z,y))) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(135,a,11687,a,b,10566,a),flip(a)].">
      <j1 rule="hyper" parents="135 11687 10566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11697">
    <literal><![CDATA[
      x * (a(y,y \ z,x) * (y \ z)) = y \ (z * T(x,y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11695(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      (x \ (a(y,z,u) * (x * w))) / (a(y,z,u) * w) = a(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7284(a,1),11696(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7284 11696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11699">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10367,a(flip),b,11610,a),flip(a)].">
      <j1 rule="hyper" parents="325 10367 11610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11700">
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(10153,a,11699,a)].">
      <j1 rule="hyper" parents="10153 11699"/>
    </justification>
  </clause>

  <clause id="11701">
    <literal><![CDATA[
      a(x,y,L(z,u \ z,u)) = a(x,y,(u \ z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11699(a,1,3,1))].">
      <j1 rule="para" parents="10 11699"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      ((1 / x) * y) \ (x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,692,a(flip),b,11616,a)].">
      <j1 rule="hyper" parents="65 692 11616"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      a(x,x \ 1,x \ (x \ y)) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,11653,a(flip),b,11661,a),flip(a)].">
      <j1 rule="hyper" parents="325 11653 11661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      a(x,x \ 1,x \ y) = a(x,x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11703(a,1,3,2))].">
      <j1 rule="para" parents="9 11703"/>
    </justification>
  </clause>

  <clause id="11705">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = z * (a(z,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1245,a,b,11664,a)].">
      <j1 rule="hyper" parents="36 1245 11664"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      (x * y) \ (L(x,z,y) * (y * z)) = L(a(y,z,x) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,11664,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="132 11664 100"/>
    </justification>
  </clause>

  <clause id="11707">
    <literal><![CDATA[
      (x * (y * z)) / z = x * (a(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8374,a(flip),b,11705,a)].">
      <j1 rule="hyper" parents="65 8374 11705"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,11705,a(flip),b,8374,a(flip))].">
      <j1 rule="hyper" parents="136 11705 8374"/>
    </justification>
  </clause>

  <clause id="11709">
    <literal><![CDATA[
      a(x,y,y) \ y = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1713,a(flip),b,11707,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 1713 11707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      a(x,y,z) = ((x * (y * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(11707(a,2),11621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11707 11621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      L(x,x,y) * a(y,x,x) = x
    ]]></literal>
    <justification jstring="[hyper(7208,a,11709,a)].">
      <j1 rule="hyper" parents="7208 11709"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      L(x,x,y) \ x = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,1779,a,b,11709,a)].">
      <j1 rule="hyper" parents="41 1779 11709"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      a(x,y,y) \ 1 = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,11709,a(flip),b,10574,a),flip(a)].">
      <j1 rule="hyper" parents="132 11709 10574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11714">
    <literal><![CDATA[
      L(L(x,x,y),a(y,x,x),z) = (z * a(y,x,x)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(11709(a,1),102(a,1,1))].">
      <j1 rule="para" parents="11709 102"/>
    </justification>
  </clause>

  <clause id="11715">
    <literal><![CDATA[
      x * L(y,a(z,x,x),L(x,x,z)) = L(x,x,z) * (a(z,x,x) * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,11711,a(flip),b,193,a)].">
      <j1 rule="hyper" parents="136 11711 193"/>
    </justification>
  </clause>

  <clause id="11716">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),L(y,y,x)) = y \ (L(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(11711(a,1),102(a,2,1))].">
      <j1 rule="para" parents="11711 102"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),a(y,x,x)) = x \ (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(11711(a,1),7216(a,2,1))].">
      <j1 rule="para" parents="11711 7216"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      L(x \ L(x,L(x,y,z),u),y,z) \ 1 = a(u,L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,4463,a(flip),b,11712,a)].">
      <j1 rule="hyper" parents="65 4463 11712"/>
    </justification>
  </clause>

  <clause id="11719">
    <literal><![CDATA[
      1 / ((x * y) \ x) = y * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(11712(a,1),6597(a,2,2))].">
      <j1 rule="para" parents="11712 6597"/>
    </justification>
  </clause>

  <clause id="11720">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[para(11712(a,1),6596(a,1,2))].">
      <j1 rule="para" parents="11712 6596"/>
    </justification>
  </clause>

  <clause id="11721">
    <literal><![CDATA[
      a((x * L(x,x,y)) * z,u,w) = a(a(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(11712(a,1),8913(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11712 8913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      R(x,y,y) \ x = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,5798,a,b,11713,a)].">
      <j1 rule="hyper" parents="65 5798 11713"/>
    </justification>
  </clause>

  <clause id="11723">
    <literal><![CDATA[
      R(x,a(y,z,z),a(y,z,z)) / (z \ L(z,z,y)) = x * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,11713,a(flip),b,573,a)].">
      <j1 rule="hyper" parents="201 11713 573"/>
    </justification>
  </clause>

  <clause id="11724">
    <literal><![CDATA[
      R(x,x \ y,y \ L(y,y,z)) \ L(y,y,z) = (x \ y) * (a(z,y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(11713(a,2),738(a,2,2))].">
      <j1 rule="para" parents="11713 738"/>
    </justification>
  </clause>

  <clause id="11725">
    <literal><![CDATA[
      L(1 / a(x,y,y),z,u) \ 1 = 1 / L(y \ L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11713(a,1),6588(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11713 6588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      x * ((y * x) \ y) = R(y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,1314,a(flip),b,11722,a)].">
      <j1 rule="hyper" parents="325 1314 11722"/>
    </justification>
  </clause>

  <clause id="11727">
    <literal><![CDATA[
      (R(x,y,y) \ x) \ z = (y \ L(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,11722,a)].">
      <j1 rule="hyper" parents="63 11722"/>
    </justification>
  </clause>

  <clause id="11728">
    <literal><![CDATA[
      T(x,x * y) * a(y,T(x,x * y),T(x,x * y)) = 1 / ((L(x,y,x) * y) \ y)
    ]]></literal>
    <justification jstring="[para(603(a,1),11719(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="603 11719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      L(K(x,y) * ((z * y) \ z),y,x) = (y * x) \ (x * (R(z,y,y) \ z))
    ]]></literal>
    <justification jstring="[para(11726(a,1),5238(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11726 5238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11730">
    <literal><![CDATA[
      R(x,y,(z * (a(z,u,L(w \ 1,v5,v6)) \ u)) * L(w,v5,v6)) = R(x,y,z * (u * L(w \ 1,v5,v6)))
    ]]></literal>
    <justification jstring="[para(11708(a,1),6615(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11708 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11731">
    <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(11708(a,1),7268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11708 7268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      ((x * (T(y,x) * z)) / z) \ (y * x) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,232,a(flip),b,11710,a)].">
      <j1 rule="hyper" parents="325 232 11710"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      (x / (y \ 1)) \ (x * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(566(a,1),11710(a,2,1)),flip(a)].">
      <j1 rule="para" parents="566 11710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      ((R(x,y,y) * (L(y,y,x) * z)) / z) \ (x * y) = a(R(x,y,y),L(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(1949(a,1),11710(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1949 11710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11735">
    <literal><![CDATA[
      (a(x,y,z) \ (u * (a(x,y,z) * w))) \ (u * w) = a(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(7304(a,1),11710(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7304 11710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      ((x \ y) \ y) * a(x \ y,T(x,x \ y),(x \ y) \ y) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(114(a,2),11720(a,1,2,2))].">
      <j1 rule="para" parents="114 11720"/>
    </justification>
  </clause>

  <clause id="11737">
    <literal><![CDATA[
      K(x,y) * (z \ ((z * y) * x)) = x * (y * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,10565,a(flip),b,11636,a),flip(a)].">
      <j1 rule="hyper" parents="325 10565 11636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      L(K(x,y) * a(z,x,y),y * x,z) = (z * (y * x)) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[para(11637(a,1),308(a,1,1))].">
      <j1 rule="para" parents="11637 308"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      a(x,y,z) = ((x * (T(y,x) * z)) / z) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,9991,a(flip),b,11732,a)].">
      <j1 rule="hyper" parents="325 9991 11732"/>
    </justification>
  </clause>

  <clause id="11741">
    <literal><![CDATA[
      ((x * (a(y,z,T(u,x)) \ T(u,x))) / (a(y,z,T(u,x)) \ 1)) \ (u * x) = a(x,u,a(y,z,T(u,x)) \ 1)
    ]]></literal>
    <justification jstring="[para(10574(a,1),11739(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10574 11739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      ((x \ y) * x) \ ((y * (x \ y)) * x) = x * ((x \ y) * a(y,x \ y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,6168,a(flip),b,11737,a)].">
      <j1 rule="hyper" parents="65 6168 11737"/>
    </justification>
  </clause>

  <clause id="11743">
    <literal><![CDATA[
      (x * (x \ y)) * (a(x,x,x \ y) * z) = a(x,x,x \ y) * (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11591(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      (x / y) * (a(x / y,z,u) \ y) = a(y \ x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(1870(a,1),11663(a,2,1))].">
      <j1 rule="para" parents="1870 11663"/>
    </justification>
  </clause>

  <clause id="11745">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * T(a(x,y,z),w)) = L(w * a(u,w,a(x,y,z)),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7257,a,11690,a)].">
      <j1 rule="hyper" parents="7257 11690"/>
    </justification>
  </clause>

  <clause id="11746">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w),w,u)) = L(x,y,(u * w) \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(11690(a,1),8369(a,1,3))].">
      <j1 rule="para" parents="11690 8369"/>
    </justification>
  </clause>

  <clause id="11747">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,w),w,u)) = a(x,y,(u * w) \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(11690(a,1),10090(a,1,3))].">
      <j1 rule="para" parents="11690 10090"/>
    </justification>
  </clause>

  <clause id="11748">
    <literal><![CDATA[
      a(x \ y,x,z) \ y = ((y / x) * (x * z)) / z
    ]]></literal>
    <justification jstring="[hyper(65,a,11707,a,b,11744,a),flip(a)].">
      <j1 rule="hyper" parents="65 11707 11744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11749">
    <literal><![CDATA[
      a(x,((y * z) \ z) * u,w) = a(x,(y \ a(y,y,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9998,a(flip),b,11614,a)].">
      <j1 rule="hyper" parents="325 9998 11614"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = ((z * K(x * y,z)) * x) \ (((x * (y * z)) / (x * y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(1602(a,1),11706(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1602 11706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      a(x,y,(z * u) \ (L(z,T(w,v5),u) * (u * T(w,v5)))) = a(x,y,L(a(u,T(w,v5),z) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(11706(a,2),10233(a,1,3))].">
      <j1 rule="para" parents="11706 10233"/>
    </justification>
  </clause>

  <clause id="11752">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,(u * y) \ (y * (z * u)),w)
    ]]></literal>
    <justification jstring="[para(11706(a,1),10926(a,1,2))].">
      <j1 rule="para" parents="11706 10926"/>
    </justification>
  </clause>

  <clause id="11753">
    <literal><![CDATA[
      a(x,(y \ a(y,y,z)) * u,w) = a(x,(z \ (y \ z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11230,a(flip),b,11749,a),flip(a)].">
      <j1 rule="hyper" parents="65 11230 11749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11754">
    <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(11585(a,1),5775(a,1,2))].">
      <j1 rule="para" parents="11585 5775"/>
    </justification>
  </clause>

  <clause id="11755">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(773,a,11629,a)].">
      <j1 rule="hyper" parents="773 11629"/>
    </justification>
  </clause>

  <clause id="11756">
    <literal><![CDATA[
      L(x,a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7192,a(flip),b,11755,a)].">
      <j1 rule="hyper" parents="65 7192 11755"/>
    </justification>
  </clause>

  <clause id="11758">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,a(x,u,w)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,10596,a(flip),b,11756,a),flip(a)].">
      <j1 rule="hyper" parents="65 10596 11756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11759">
    <literal><![CDATA[
      R(x,x,y) * L(z,x,a(x,x,y)) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(11756(a,1),11607(a,1,2))].">
      <j1 rule="para" parents="11756 11607"/>
    </justification>
  </clause>

  <clause id="11760">
    <literal><![CDATA[
      L(a(x,y,z),u,L(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(11020,a,11630,a)].">
      <j1 rule="hyper" parents="11020 11630"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,L(x,v6,v7)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(11760(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11760 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) \ 1 = L(1 / a(y,x,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,8480,a(flip),b,11725,a)].">
      <j1 rule="hyper" parents="325 8480 11725"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      (x * T(x,x * y)) * a(y,x,L(T(x,y),y,x)) = y \ (x * (T(y,x) * T(x,y)))
    ]]></literal>
    <justification jstring="[para(599(a,1),11641(a,1,1,2))].">
      <j1 rule="para" parents="599 11641"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      (x \ y) * (1 / (y \ x)) = x \ (y * (x \ y))
    ]]></literal>
    <justification jstring="[para(11720(a,1),11678(a,1,2))].">
      <j1 rule="para" parents="11720 11678"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      (x \ y) \ (y \ x) = y \ (x * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(6653,a,11764,a)].">
      <j1 rule="hyper" parents="6653 11764"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      (x \ (y * (x \ y))) / (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(135,a,11765,a(flip),b,6654,a)].">
      <j1 rule="hyper" parents="135 11765 6654"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      L(x * (((y \ L(y,z,u)) \ 1) / (y \ L(y,z,u))),w,v5) = L(x,w,v5) * (L(y,z,u) \ (y * (L(y,z,u) \ y)))
    ]]></literal>
    <justification jstring="[para(11765(a,1),8521(a,2,2))].">
      <j1 rule="para" parents="11765 8521"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      ((x \ y) \ (y * ((x \ y) \ y))) * K(x \ y,x) = (1 / (y \ (x \ y))) * x
    ]]></literal>
    <justification jstring="[para(11766(a,1),2873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11766 2873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) \ (u \ (w * z))) = a(x,y,a(u,u \ w,z))
    ]]></literal>
    <justification jstring="[para(11679(a,1),10027(a,1,3))].">
      <j1 rule="para" parents="11679 10027"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      a(x,y,(z * (u * a(w,u,z))) * w) = a(x,y,(w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10043,a(flip),b,11691,a),flip(a)].">
      <j1 rule="hyper" parents="325 10043 11691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11772">
    <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="[hyper(325,a,10609,a(flip),b,11715,a),flip(a)].">
      <j1 rule="hyper" parents="325 10609 11715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11773">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),L(y,y,x)) = L(y,y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1246,a(flip),b,11716,a),flip(a)].">
      <j1 rule="hyper" parents="325 1246 11716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      L(L(x,x,y) \ z,a(y,x,x),L(x,x,y)) = x \ (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11213,a(flip),b,11717,a)].">
      <j1 rule="hyper" parents="65 11213 11717"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      L(x,a(y,z,z),a(y,z,z)) / (z \ L(z,z,y)) = x * a(y,z,z)
    ]]></literal>
    <justification jstring="[para(9014(a,1),11723(a,1,1))].">
      <j1 rule="para" parents="9014 11723"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      a(x,y,a(z / u,(z / u) \ z,w)) = a(x,y,(w * u) \ ((z / u) \ (z * w)))
    ]]></literal>
    <justification jstring="[para(85(a,1),11769(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="85 11769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11777">
    <literal><![CDATA[
      L(L(x,x,y) \ z,a(y,x,x),L(x,x,y)) = (x \ z) * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,10585,a(flip),b,11774,a),flip(a)].">
      <j1 rule="hyper" parents="325 10585 11774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ L(z,a(y,x,x),a(y,x,x)) = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(8484,a,11775,a)].">
      <j1 rule="hyper" parents="8484 11775"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      L(a(x,x,y),x,R(x,x,y) \ z) \ z = (z / (x * a(x,x,y))) * x
    ]]></literal>
    <justification jstring="[hyper(7237,a,11609,a)].">
      <j1 rule="hyper" parents="7237 11609"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(x,w,v5)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(11622(a,1),11631(a,2,2,1))].">
      <j1 rule="para" parents="11622 11631"/>
    </justification>
  </clause>

  <clause id="11781">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,w,v5)) = L(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[para(11780(a,1),2346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11780 2346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2326,a,b,11781,a),flip(a)].">
      <j1 rule="hyper" parents="325 2326 11781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      a(a(x,y,z),u,a(x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,11782,a)].">
      <j1 rule="hyper" parents="55 11782"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      a(a(x,y,z),x,u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7475,a,11651,a),flip(a)].">
      <j1 rule="hyper" parents="7475 11651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * x) * u) = (x * u) * a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(137,a,11785,a(flip),b,11633,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 11785 11633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      L(x * a(y \ z,x,y),y,z / y) = z \ (((z / y) * x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(1870(a,1),11689(a,1,1,2))].">
      <j1 rule="para" parents="1870 11689"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      ((x \ (a(y,z,u) * (x * w))) * (v5 * v5)) / (a(y,z,u) * (w * (v5 * v5))) = a(x,w * (v5 * v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(882(a,1),11698(a,1,1))].">
      <j1 rule="para" parents="882 11698"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * y) = K(z,y) * a(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11588,a(flip),b,11738,a),flip(a)].">
      <j1 rule="hyper" parents="65 11588 11738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      (x * (y * (x \ z))) \ ((x * (x \ z)) * y) = (y * (x \ z)) \ (x \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,11679,a(flip),b,11789,a),flip(a)].">
      <j1 rule="hyper" parents="325 11679 11789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ (u * (z * w))) = R(x,y,K(w,u) * a(z,w,u))
    ]]></literal>
    <justification jstring="[para(11789(a,1),8705(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11789 8705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w),w,u)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,9933,a(flip),b,11746,a),flip(a)].">
      <j1 rule="hyper" parents="325 9933 11746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11794">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w),w,u \ 1)) = L(x,y,L(z,u \ 1,w))
    ]]></literal>
    <justification jstring="[para(1847(a,1),11793(a,1,3,1,2))].">
      <j1 rule="para" parents="1847 11793"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w),w,u)) = L(x,y,L(z,u \ 1,w))
    ]]></literal>
    <justification jstring="[para(1499(a,1),11794(a,1,3))].">
      <j1 rule="para" parents="1499 11794"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      L(x,y,L(z,u \ 1,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,11793,a(flip),b,11795,a),flip(a)].">
      <j1 rule="hyper" parents="65 11793 11795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,w),w,u)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10289,a(flip),b,11747,a),flip(a)].">
      <j1 rule="hyper" parents="325 10289 11747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,L(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11015,a(flip),b,11752,a),flip(a)].">
      <j1 rule="hyper" parents="325 11015 11752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11799">
    <literal><![CDATA[
      L(x,L(a(y,z,u \ 1) \ z,y,u),w) = L(x,L(z,u \ 1,y),w)
    ]]></literal>
    <justification jstring="[para(1499(a,1),11798(a,1,2))].">
      <j1 rule="para" parents="1499 11798"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,L(z,u \ 1,y),w)
    ]]></literal>
    <justification jstring="[para(7484(a,1),11799(a,1,2,1,1))].">
      <j1 rule="para" parents="7484 11799"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      L(x,L(y,z \ 1,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11798,a(flip),b,11800,a),flip(a)].">
      <j1 rule="hyper" parents="65 11798 11800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11802">
    <literal><![CDATA[
      L(a(x,x,y),x,R(x,x,y) \ z) \ z = (z / R(x,x,y)) * x
    ]]></literal>
    <justification jstring="[para(11595(a,1),11779(a,2,1,2))].">
      <j1 rule="para" parents="11595 11779"/>
    </justification>
  </clause>

  <clause id="11803">
    <literal><![CDATA[
      L(a(x,x,y),x,R(x,x,y) \ z) \ z = x * (R(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,3053,a(flip),b,11802,a),flip(a)].">
      <j1 rule="hyper" parents="325 3053 11802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * x) * u) = x * (u * a(x,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(325,a,11582,a(flip),b,11786,a),flip(a)].">
      <j1 rule="hyper" parents="325 11582 11786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      L(x * a(y \ z,x,y),y,y \ z) = z \ (((z / y) * x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(2351,a,11787,a)].">
      <j1 rule="hyper" parents="2351 11787"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,176,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="325 176 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      a(x,x,L(y,z,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(10743,a,11806,a)].">
      <j1 rule="hyper" parents="10743 11806"/>
    </justification>
  </clause>

  <clause id="11809">
    <literal><![CDATA[
      (x \ y) * T(a(x,z,u) \ 1,y) = x \ ((a(x,z,u) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(11806(a,1),728(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11806 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      a(x,x,L(L(y,z,x),u,w)) = a(x,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(10508,a,11807,a)].">
      <j1 rule="hyper" parents="10508 11807"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      a(x,x,y * a(x,y,z)) = a(x,x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11797,a(flip),b,11807,a),flip(a)].">
      <j1 rule="hyper" parents="65 11797 11807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      a(x,x,y) \ L(y,z,x) = L(L(y,z,x),x,x)
    ]]></literal>
    <justification jstring="[para(11807(a,1),1782(a,1,1))].">
      <j1 rule="para" parents="11807 1782"/>
    </justification>
  </clause>

  <clause id="11813">
    <literal><![CDATA[
      x \ ((a(x,y,z) \ 1) * u) = (x \ u) * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(8495(a,1),11809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8495 11809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      a(x \ y,x,x) * (x * ((x \ y) \ y)) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(9992(a,1),11680(a,1,1))].">
      <j1 rule="para" parents="9992 11680"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      x * (((x \ y) \ y) * a(x \ y,x,x)) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10566,a(flip),b,11815,a)].">
      <j1 rule="hyper" parents="65 10566 11815"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      R(T(x,(y \ x) * y),y \ x,y) = y * ((y \ x) * a(x,y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(836,a,11742,a)].">
      <j1 rule="hyper" parents="836 11742"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      x * ((x \ y) * a(y,x \ y,x)) = R(y,x \ y,x)
    ]]></literal>
    <justification jstring="[para(4870(a,1),11818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4870 11818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      a(x,y \ x,y) * x = R(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10570,a(flip),b,11819,a)].">
      <j1 rule="hyper" parents="65 10570 11819"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ (u * (z * w))) = R(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8689,a(flip),b,11792,a),flip(a)].">
      <j1 rule="hyper" parents="325 8689 11792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      R(x,x \ y,y * L(y,y,z)) \ L(y,y,z) = (x \ y) * (a(z,y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1039(a,1),11724(a,1,1))].">
      <j1 rule="para" parents="1039 11724"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      (x \ y) \ (y * ((x \ y) \ ((x \ y) * x))) = (1 / (y \ (x \ y))) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,8422,a(flip),b,11768,a)].">
      <j1 rule="hyper" parents="65 8422 11768"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      (1 / (x \ (y \ x))) * y = (y \ x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11824(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 11824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      (x * (y * (x \ z))) \ (z * y) = (y * (x \ z)) \ (x \ (z * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),11791(a,1,2,1))].">
      <j1 rule="para" parents="10 11791"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      R(x,y,((z \ 1) * (u \ w)) \ (u \ (w * (z \ 1)))) = R(x,y,(u * ((z \ 1) * (u \ w))) \ (w * z))
    ]]></literal>
    <justification jstring="[para(11827(a,1),1037(a,1,3))].">
      <j1 rule="para" parents="11827 1037"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      R(x,x \ y,a(y,y,z)) \ L(y,y,z) = (x \ y) * (a(z,y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(11684(a,1),11823(a,1,1))].">
      <j1 rule="para" parents="11684 11823"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      ((x \ y) * (a(x,z,u) \ 1)) * a(x,z,u) = x \ L(y,a(x,z,u),a(x,z,u))
    ]]></literal>
    <justification jstring="[para(11813(a,1),11660(a,1,1))].">
      <j1 rule="para" parents="11813 11660"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      (x * a(y,y,z)) * L(y,u,w) = a(y,y,z) * (x * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7179(a,1),11672(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7179 11672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      ((R(x,y,y) * (L(y,y,x) * z)) / z) \ (x * y) = a(L(x,y,y),L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,8679,a(flip),b,11734,a),flip(a)].">
      <j1 rule="hyper" parents="325 8679 11734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      ((x \ y) \ y) * a(x \ y,T(x,x \ y),x) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(10038(a,1),11736(a,1,2))].">
      <j1 rule="para" parents="10038 11736"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      ((x \ y) \ y) * a(x \ y,x,x) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5306(a,1),11834(a,1,2))].">
      <j1 rule="para" parents="5306 11834"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      x * (1 / (y \ (x \ y))) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(11835(a,1),11816(a,1,2))].">
      <j1 rule="para" parents="11835 11816"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      a(x,y,a(z / u,(z / u) \ z,w)) = a(x,y,(w * u) \ ((u \ z) \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10194,a(flip),b,11776,a),flip(a)].">
      <j1 rule="hyper" parents="325 10194 11776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      a(x,y,z) * ((x \ u) * (a(x,y,z) \ 1)) = x \ L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(7226,a,11831,a)].">
      <j1 rule="hyper" parents="7226 11831"/>
    </justification>
  </clause>

  <clause id="11841">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u \ w) \ (w * z))) = a(x,y,a(w / u,u,z))
    ]]></literal>
    <justification jstring="[para(85(a,1),11839(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="85 11839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u \ w) \ (w * z))) = a(x,y,a(u \ w,u,z))
    ]]></literal>
    <justification jstring="[para(1870(a,1),11841(a,2,3))].">
      <j1 rule="para" parents="1870 11841"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      L(x \ y,a(x,z,u),a(x,z,u)) = x \ L(y,a(x,z,u),a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8524,a(flip),b,11840,a)].">
      <j1 rule="hyper" parents="65 8524 11840"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((z * u) * L(w * (w * w),u,z))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(1340(a,2),11575(a,1,3,2,2))].">
      <j1 rule="para" parents="1340 11575"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = (z * y) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(89(a,1),11587(a,1,2)),flip(a)].">
      <j1 rule="para" parents="89 11587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,9,a(flip),b,11845,a),flip(a)].">
      <j1 rule="hyper" parents="325 9 11845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(132,a,9,a(flip),b,11845,a),flip(a)].">
      <j1 rule="hyper" parents="132 9 11845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = (x \ x) * (L(x,y,z) / x)
    ]]></literal>
    <justification jstring="[para(11846(a,1),8589(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11846 8589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      x / ((L(y,z,x) \ y) \ 1) = x * (L(y,z,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(137,a,11847,a(flip),b,1721,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 11847 1721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),v5,z) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(11847(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11847 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      x / (y \ L(y,z,x)) = x * (L(y,z,x) \ y)
    ]]></literal>
    <justification jstring="[para(6998(a,1),11850(a,1,2))].">
      <j1 rule="para" parents="6998 11850"/>
    </justification>
  </clause>

  <clause id="11853">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ z = z * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8484,a,11852,a)].">
      <j1 rule="hyper" parents="8484 11852"/>
    </justification>
  </clause>

  <clause id="11854">
    <literal><![CDATA[
      (x \ L(x,y,a(z,u,y))) \ y = y * (L(x,a(z,u,y),y) \ x)
    ]]></literal>
    <justification jstring="[para(10605(a,1),11853(a,1,1,2))].">
      <j1 rule="para" parents="10605 11853"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = 1 * (L(x,y,z) / x)
    ]]></literal>
    <justification jstring="[para(69(a,1),11849(a,2,1))].">
      <j1 rule="para" parents="69 11849"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = 1 * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1752(a,1),11855(a,2,2))].">
      <j1 rule="para" parents="1752 11855"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7,a(flip),b,11857,a),flip(a)].">
      <j1 rule="hyper" parents="325 7 11857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11859">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1752(a,1),11858(a,1,1))].">
      <j1 rule="para" parents="1752 11858"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,u,z)) = L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,11859,a(flip),b,4458,a)].">
      <j1 rule="hyper" parents="137 11859 4458"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,u,z)) \ 1) = L(L(x,y,z),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(11859(a,1),4467(a,1,2,1))].">
      <j1 rule="para" parents="11859 4467"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(L(x,u,z),y,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,11860,a(flip),b,7828,a)].">
      <j1 rule="hyper" parents="137 11860 7828"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      L(x,y,z) * L(x \ 1,u,z) = x \ L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[para(11860(a,1),1318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11860 1318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w) * v5) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(11860(a,1),2914(a,1,3,1))].">
      <j1 rule="para" parents="11860 2914"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      L(x,y,z * L(L(u,w,v5),w,v5)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11860(a,1),8386(a,1,3,2))].">
      <j1 rule="para" parents="11860 8386"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w) \ v5) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(11860(a,1),10389(a,1,3,1))].">
      <j1 rule="para" parents="11860 10389"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      L(x,y,z * (L(L(z,u,w),u,w) \ v5)) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),11864(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 11864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      L(x \ y,x,x * x) = L(L(x,z,u),z,u) \ ((L(L(x,z,u),z,u) / x) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1662,a(flip),b,11865,a),flip(a)].">
      <j1 rule="hyper" parents="65 1662 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      L(x,y,(z \ L(L(z,u,w),u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(11863(a,1),7724(a,1,3,1))].">
      <j1 rule="para" parents="11863 7724"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      a((x \ L(L(x,y,z),y,z)) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(11863(a,1),7725(a,1,1,1))].">
      <j1 rule="para" parents="11863 7725"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      x \ ((L(y,z,u) * L(y \ 1,z,u)) \ w) = (y \ L(L(y,z,u),z,u)) \ (x \ w)
    ]]></literal>
    <justification jstring="[para(11863(a,1),9178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11863 9178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(2585,a,11870,a)].">
      <j1 rule="hyper" parents="2585 11870"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      a(L((x * y) \ z,y,x),u,w) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(308(a,1),11872(a,1,1,1))].">
      <j1 rule="para" parents="308 11872"/>
    </justification>
  </clause>

  <clause id="11874">
    <literal><![CDATA[
      a(x \ (y \ (x * (z * y))),u,w) = a(L(R(z,x,y),y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(9026,a,11873,a),flip(a)].">
      <j1 rule="hyper" parents="9026 11873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      a((x * y) \ (((z / ((y \ 1) * x)) * (y \ 1)) * x),u,w) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11286,a,b,11873,a)].">
      <j1 rule="hyper" parents="65 11286 11873"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      a(L(L(a(x,y,z) \ y,x,z),x,z),u,w) = a(x \ (z \ (L(z,y,x) * (x * y))),u,w)
    ]]></literal>
    <justification jstring="[para(11706(a,1),11873(a,1,1,1))].">
      <j1 rule="para" parents="11706 11873"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      (x \ L(x,y,a(z,u,y))) \ y = y * (L(x,y,a(z,u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(10605(a,1),11854(a,2,2,1))].">
      <j1 rule="para" parents="10605 11854"/>
    </justification>
  </clause>

  <clause id="11878">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,u,z) \ x) = L(L(x,y,z),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(2015(a,1),11861(a,1,2))].">
      <j1 rule="para" parents="2015 11861"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ 1,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(11878(a,1),1321(a,1,1))].">
      <j1 rule="para" parents="11878 1321"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = x * (L(L(x,y,z),y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(11878(a,1),7022(a,2,2))].">
      <j1 rule="para" parents="11878 7022"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      x / (y * (L(L(y,z,u),z,u) \ 1)) = x * (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(11878(a,1),7755(a,1,2,2))].">
      <j1 rule="para" parents="11878 7755"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      L(L(L(x \ L(x,y,y),z,u),z,u) \ 1,z,u) = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,4466,a(flip),b,11879,a),flip(a)].">
      <j1 rule="hyper" parents="325 4466 11879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      L(L(a(L(x,y,z),u,u),y,z) \ 1,y,z) = L(a(x,u,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(11560(a,2),11879(a,1,1,1,1))].">
      <j1 rule="para" parents="11560 11879"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      a(x \ (y \ (x * (z * y))),u,w) = a(L(L(z,x,y),y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,8685,a(flip),b,11874,a),flip(a)].">
      <j1 rule="hyper" parents="325 8685 11874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      L(a(L(L(x,y,z),y,z),u,u) \ 1,y,z) = L(a(x,u,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(11560(a,2),11883(a,1,1,1))].">
      <j1 rule="para" parents="11560 11883"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) = L(a(x,y,y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(11872(a,1),11885(a,1,1,1))].">
      <j1 rule="para" parents="11872 11885"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) = a(L(x,z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[para(11560(a,2),11886(a,2,1))].">
      <j1 rule="para" parents="11560 11886"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      L(1 / a(x,y,y),z,u) \ 1 = a(L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,6590,a,b,11887,a(flip))].">
      <j1 rule="hyper" parents="41 6590 11887"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) \ 1 = a(L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11762,a,b,11889,a)].">
      <j1 rule="hyper" parents="65 11762 11889"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      x / (y * (L(L(y,z,u),z,u) \ 1)) = x * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(11863(a,1),11881(a,2,2))].">
      <j1 rule="para" parents="11863 11881"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ 1) = L(L(x,y,z),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,11891,a),flip(a)].">
      <j1 rule="hyper" parents="335 11891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = L(L(x,y,z),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,11880,a,b,11892,a)].">
      <j1 rule="hyper" parents="65 11880 11892"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(L(x,y,z),y,z) \ x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(132,a,11892,a(flip),b,11880,a)].">
      <j1 rule="hyper" parents="132 11892 11880"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      x / (L(L(y,z,u),z,u) \ y) = x * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(11892(a,1),11891(a,1,2))].">
      <j1 rule="para" parents="11892 11891"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ u = (L(L(x,y,z),y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(11893(a,1),7726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11893 7726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ u = (L(L(x,y,z),y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(11863(a,1),11896(a,1,1))].">
      <j1 rule="para" parents="11863 11896"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ ((L(L(x,y,z),y,z) / x) * u) = x \ u
    ]]></literal>
    <justification jstring="[hyper(461,a,11868,a),flip(a)].">
      <j1 rule="hyper" parents="461 11868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ ((x \ L(L(x,y,z),y,z)) * u) = x \ u
    ]]></literal>
    <justification jstring="[para(1766(a,1),11898(a,1,2,1))].">
      <j1 rule="para" parents="1766 11898"/>
    </justification>
  </clause>

  <clause id="11901">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) * u = L(L(x,y,z),y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(148,a,11900,a),flip(a)].">
      <j1 rule="hyper" parents="148 11900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,77,a(flip),b,11901,a)].">
      <j1 rule="hyper" parents="132 77 11901"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) * u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11897,a(flip),b,11902,a)].">
      <j1 rule="hyper" parents="65 11897 11902"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ u)) \ ((z \ u) * u)) = a(x,y,z * ((z / u) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10198,a(flip),b,11620,a),flip(a)].">
      <j1 rule="hyper" parents="325 10198 11620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      R(a(x,x,y),x * y,z) = ((x * y) * z) \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[para(7186(a,1),11649(a,1,1))].">
      <j1 rule="para" parents="7186 11649"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      x * ((a(y,x,x) * x) \ (z / x)) = z / (a(y,x,x) * x)
    ]]></literal>
    <justification jstring="[para(11693(a,1),11694(a,1,2,2,2))].">
      <j1 rule="para" parents="11693 11694"/>
    </justification>
  </clause>

  <clause id="11908">
    <literal><![CDATA[
      T(x,x * y) * a(y,T(x,x * y),T(x,x * y)) = 1 / R((x * y) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(9331(a,2),11728(a,2,2))].">
      <j1 rule="para" parents="9331 11728"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      (x * T(x,x * y)) * a(y,x,T(x,x * y)) = y \ (x * (T(y,x) * T(x,y)))
    ]]></literal>
    <justification jstring="[para(599(a,1),11763(a,1,2,3))].">
      <j1 rule="para" parents="599 11763"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      x \ (y * (T(x,y) * T(y,x))) = (y * T(y,y * x)) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(10037(a,1),11909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10037 11909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      x \ (y * (T(x,y) * T(y,x))) = y * (T(y,y * x) * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,10565,a(flip),b,11910,a),flip(a)].">
      <j1 rule="hyper" parents="325 10565 11910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      x * (T(x,x * y) * a(y,x,x)) = y \ (x * (y * x))
    ]]></literal>
    <justification jstring="[para(2487(a,1),11911(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2487 11911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ (z * (u * (w * (w * w))))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(100(a,1),11844(a,1,3,2))].">
      <j1 rule="para" parents="100 11844"/>
    </justification>
  </clause>

  <clause id="11915">
    <literal><![CDATA[
      a(x,y,(((z * u) * w) \ (z * (u * w))) * (w * w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(882(a,1),11914(a,1,3))].">
      <j1 rule="para" parents="882 11914"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ (z * (u * w))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(7482,a,11915,a)].">
      <j1 rule="hyper" parents="7482 11915"/>
    </justification>
  </clause>

  <clause id="11918">
    <literal><![CDATA[
      a(x,y,((z * u) * T(T(w,u),v5)) \ (z * (T(w,v5) * u))) = a(x,y,a(T(T(w,u),v5),u,z))
    ]]></literal>
    <justification jstring="[para(241(a,1),11916(a,1,3,2,2))].">
      <j1 rule="para" parents="241 11916"/>
    </justification>
  </clause>

  <clause id="11919">
    <literal><![CDATA[
      a(x,y,(T(z * u,w * w) * v5) \ (((w * w) \ z) * ((u * (w * w)) * v5))) = a(x,y,a(v5,u * (w * w),(w * w) \ z))
    ]]></literal>
    <justification jstring="[para(598(a,1),11916(a,1,3,1,1))].">
      <j1 rule="para" parents="598 11916"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ (u \ w) = u \ ((x \ L(L(x,y,z),y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(11863(a,1),11871(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11863 11871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11921">
    <literal><![CDATA[
      x \ ((y \ L(L(y,z,u),z,u)) \ w) = (L(L(y,z,u),z,u) \ y) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11897,a(flip),b,11920,a),flip(a)].">
      <j1 rule="hyper" parents="65 11897 11920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      x \ (y * (L(L(y,z,u),z,u) \ w)) = (L(L(y,z,u),z,u) \ y) * (x \ w)
    ]]></literal>
    <justification jstring="[para(11902(a,1),11921(a,1,2))].">
      <j1 rule="para" parents="11902 11921"/>
    </justification>
  </clause>

  <clause id="11923">
    <literal><![CDATA[
      x \ (y * (L(L(y,z,u),z,u) \ w)) = y * (L(L(y,z,u),z,u) \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,11903,a(flip),b,11922,a),flip(a)].">
      <j1 rule="hyper" parents="325 11903 11922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11924">
    <literal><![CDATA[
      x \ (y * (L(L(y,z,u),z,u) \ x)) = L(L(y,z,u),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,177,a(flip),b,11922,a),flip(a)].">
      <j1 rule="hyper" parents="325 177 11922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      x * (L(L(y,z,u),z,u) \ y) = y * (L(L(y,z,u),z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(137,a,177,a(flip),b,11922,a)].">
      <j1 rule="hyper" parents="137 177 11922"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      x \ (y * (L(L(x,z,u),z,u) \ x)) = L(L(x,z,u),z,u) \ y
    ]]></literal>
    <justification jstring="[para(11924(a,1),76(a,1,2,2))].">
      <j1 rule="para" parents="11924 76"/>
    </justification>
  </clause>

  <clause id="11927">
    <literal><![CDATA[
      (L(x,y,z) * (x \ (L(x,y,z) * (L(L(x,y,z),y,z) \ x)))) \ 1 = L(L(x,y,z) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(11926(a,2),6594(a,1,1,2))].">
      <j1 rule="para" parents="11926 6594"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      a((x * y) \ ((y * (z / ((y \ 1) * x))) * x),u,w) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9000,a(flip),b,11875,a)].">
      <j1 rule="hyper" parents="65 9000 11875"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      a(L(x / ((y \ 1) * z),y,z),u,w) = a(y \ (z \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8568,a(flip),b,11928,a)].">
      <j1 rule="hyper" parents="65 8568 11928"/>
    </justification>
  </clause>

  <clause id="11930">
    <literal><![CDATA[
      a(L(((x \ 1) * y) \ z,x,y),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1872,a(flip),b,11929,a)].">
      <j1 rule="hyper" parents="65 1872 11929"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      a(L((x * y) \ z,x,y),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9025,a(flip),b,11930,a)].">
      <j1 rule="hyper" parents="65 9025 11930"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ u)) \ ((z \ u) * u)) = a(x,y,z * ((u \ z) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10176,a(flip),b,11904,a),flip(a)].">
      <j1 rule="hyper" parents="325 10176 11904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      1 / R((x * y) \ y,y,x) = T(x,x * y) * a(y,x,x)
    ]]></literal>
    <justification jstring="[para(10068(a,1),11908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10068 11908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      (x * (y * x)) \ (x * (x * R(T(y,x),z,u))) = L(T(y,x) \ R(T(y,x),z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,805,a(flip),b,11556,a)].">
      <j1 rule="hyper" parents="65 805 11556"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      (x * (y * x)) \ R(x * (y * x),z,u) = L(T(y,x) \ R(T(y,x),z,u),x,x)
    ]]></literal>
    <justification jstring="[para(11112(a,1),11935(a,1,2))].">
      <j1 rule="para" parents="11112 11935"/>
    </justification>
  </clause>

  <clause id="11937">
    <literal><![CDATA[
      (x * (y * x)) \ R(x * (y * x),z,u) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(2228(a,1),11936(a,2,1))].">
      <j1 rule="para" parents="2228 11936"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      ((x * y) * y) \ R((x * y) * y,z,u) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,3363,a,b,11937,a)].">
      <j1 rule="hyper" parents="65 3363 11937"/>
    </justification>
  </clause>

  <clause id="11940">
    <literal><![CDATA[
      x * T(x \ R(1 / (1 / x),x \ 1,y),z) = T(a(1 / x,1 / x,y),z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(4320(a,1),11615(a,1,2,1,2))].">
      <j1 rule="para" parents="4320 11615"/>
    </justification>
  </clause>

  <clause id="11941">
    <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(325,a,7473,a(flip),b,11731,a),flip(a)].">
      <j1 rule="hyper" parents="325 7473 11731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      a(x \ (y \ (L(y,z,x) * (x * z))),u,w) = a(a(x,z,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11872,a(flip),b,11876,a),flip(a)].">
      <j1 rule="hyper" parents="65 11872 11876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      T(a(1 / x,1 / x,y),z) / (1 / x) = x * T((x \ 1) * R(x,x \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(1539(a,1),11940(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1539 11940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      T(a(1 / x,1 / x,y),z) / (1 / x) = x * T(a(x,x,y * x),z)
    ]]></literal>
    <justification jstring="[para(11596(a,1),11944(a,2,2,1))].">
      <j1 rule="para" parents="11596 11944"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      T(a(1 / x,1 / x,y),z) / (1 / x) = x * a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(7186(a,1),11945(a,2,2))].">
      <j1 rule="para" parents="7186 11945"/>
    </justification>
  </clause>

  <clause id="11947">
    <literal><![CDATA[
      T(a(1 / x,1 / x,y),z) / (1 / x) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,11595,a(flip),b,11946,a),flip(a)].">
      <j1 rule="hyper" parents="325 11595 11946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11949">
    <literal><![CDATA[
      T(a(1 / x,x \ 1,y),z) / (1 / x) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(4385(a,1),11947(a,1,1,1))].">
      <j1 rule="para" parents="4385 11947"/>
    </justification>
  </clause>

  <clause id="11950">
    <literal><![CDATA[
      T(a(x,x \ 1,y),z) / (1 / x) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(1842(a,1),11949(a,1,1,1))].">
      <j1 rule="para" parents="1842 11949"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      a(x,x \ 1,y) / (1 / x) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(112(a,1),11950(a,1,1))].">
      <j1 rule="para" parents="112 11950"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      R(x,y,z) \ (a(R(x,y,z),R(x,y,z) \ 1,u) / (1 / R(x,y,z))) = L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,11951,a,b,9228,a)].">
      <j1 rule="hyper" parents="132 11951 9228"/>
    </justification>
  </clause>

  <clause id="11953">
    <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),11754(a,1,2,2))].">
      <j1 rule="para" parents="100 11754"/>
    </justification>
  </clause>

  <clause id="11954">
    <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(456,a,11953,a),flip(a)].">
      <j1 rule="hyper" parents="456 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,11846,a(flip),b,11954,a),flip(a)].">
      <j1 rule="hyper" parents="65 11846 11954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      x * (y * a(x,x,y)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,11955,a(flip),b,650,a),flip(a)].">
      <j1 rule="hyper" parents="132 11955 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      L(a(x,x,y) * y,x,x) = y
    ]]></literal>
    <justification jstring="[para(7190(a,2),11955(a,1,1))].">
      <j1 rule="para" parents="7190 11955"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      x * (a(x,x,y) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,11957,a(flip),b,650,a),flip(a)].">
      <j1 rule="hyper" parents="132 11957 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * u) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(11957(a,1),11866(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="11957 11866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      x \ ((1 / x) \ y) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(140,a,11956,a)].">
      <j1 rule="hyper" parents="140 11956"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      x \ ((1 / x) \ y) = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(132,a,11956,a(flip),b,7206,a)].">
      <j1 rule="hyper" parents="132 11956 7206"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      x \ (y \ ((1 / y) \ x)) = a(y,y,x)
    ]]></literal>
    <justification jstring="[para(11956(a,1),71(a,1,2,2))].">
      <j1 rule="para" parents="11956 71"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,L(a(x,x,y),y,x),x * y) = (x * y) * (L(a(x,x,y),y,x) * z)
    ]]></literal>
    <justification jstring="[para(11956(a,1),459(a,1,1))].">
      <j1 rule="para" parents="11956 459"/>
    </justification>
  </clause>

  <clause id="11964">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),u,z)) = a(x,y,(u * z) \ ((1 / z) \ u))
    ]]></literal>
    <justification jstring="[para(11958(a,1),10399(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="11958 10399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (a(R(z,u,w),R(z,u,w),v5) * v5)) * v6) = a(x,y,((1 / R(z,u,w)) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(11958(a,1),11369(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11958 11369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11966">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) / y = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,11960,a,b,7190,a)].">
      <j1 rule="hyper" parents="135 11960 7190"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      (x * y) \ (x * (z \ ((1 / z) \ y))) = L(a(z,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(11960(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11960 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      x * L(y * a(x,x,y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(11960(a,1),1398(a,1,2,1))].">
      <j1 rule="para" parents="11960 1398"/>
    </justification>
  </clause>

  <clause id="11969">
    <literal><![CDATA[
      L(x * a(y,y,x),y,L(y,z,u)) = (L(y,z,u) \ y) \ ((1 / L(y,z,u)) * ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[para(11960(a,1),4369(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11960 4369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ 1 = L(y \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(11960(a,2),6600(a,1,1))].">
      <j1 rule="para" parents="11960 6600"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ 1) \ u) = u * a(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7180(a,1),11960(a,1,2,1))].">
      <j1 rule="para" parents="7180 11960"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      ((x \ ((1 / x) \ y)) * z) / (y * z) = R(a(x,x,y),y,z)
    ]]></literal>
    <justification jstring="[para(11960(a,2),7271(a,1,1,1))].">
      <j1 rule="para" parents="11960 7271"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      (x * y) \ ((z \ ((1 / z) \ x)) * y) = R(a(z,z,x),x,y)
    ]]></literal>
    <justification jstring="[para(11960(a,2),7548(a,1,2,1))].">
      <j1 rule="para" parents="11960 7548"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      (x * a(L(y,z,u),L(y,z,u),x)) * L(y,z,u) = (y \ ((1 / L(y,z,u)) \ x)) * y
    ]]></literal>
    <justification jstring="[para(11960(a,1),8334(a,1,1))].">
      <j1 rule="para" parents="11960 8334"/>
    </justification>
  </clause>

  <clause id="11975">
    <literal><![CDATA[
      L(x,y,z * a(u,u,z)) = L(x,y,u \ (u \ z))
    ]]></literal>
    <justification jstring="[para(11960(a,1),8591(a,1,3))].">
      <j1 rule="para" parents="11960 8591"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      L(x,(y \ ((1 / y) \ z)) * u,w) = L(x,u * (a(y,y,z) * z),w)
    ]]></literal>
    <justification jstring="[para(11960(a,2),10940(a,1,2,1))].">
      <j1 rule="para" parents="11960 10940"/>
    </justification>
  </clause>

  <clause id="11977">
    <literal><![CDATA[
      x \ ((y \ ((1 / y) \ z)) * u) = x \ ((z * a(y,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(11961(a,2),7305(a,1,2,1))].">
      <j1 rule="para" parents="11961 7305"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      a(x,y \ ((y \ 1) \ z),u) = a(x,a(y,y,z) * z,u)
    ]]></literal>
    <justification jstring="[para(11961(a,1),10103(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11961 10103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      a(x,y,(z \ ((1 / z) \ u)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(11961(a,2),10439(a,1,3,1))].">
      <j1 rule="para" parents="11961 10439"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ 1) \ u)) \ w) = a(x,y,(a(z,z,u) * u) \ w)
    ]]></literal>
    <justification jstring="[para(11961(a,1),10258(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11961 10258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11981">
    <literal><![CDATA[
      a(L(x,x,(1 / x) \ y) * ((1 / x) \ y),z,u) = a(a(x,x,y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(11961(a,1),10974(a,2,1))].">
      <j1 rule="para" parents="11961 10974"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      L(x,y \ ((y \ 1) \ z),u) = L(x,a(y,y,z) * z,u)
    ]]></literal>
    <justification jstring="[para(11961(a,1),10929(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11961 10929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      a(L(x,y * (a(z,z,y) \ 1),u),w,v5) = a(L(x,z \ ((1 / z) \ y),u),w,v5)
    ]]></literal>
    <justification jstring="[para(11961(a,2),11156(a,2,1,2))].">
      <j1 rule="para" parents="11961 11156"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      K(x \ (y \ ((1 / y) \ x)),x) * (z * (y \ ((1 / y) \ x))) = (a(y,y,x) * x) * T(z,y \ ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[para(11962(a,1),2817(a,2,1,1))].">
      <j1 rule="para" parents="11962 2817"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      (x * a(1 / y,z,u)) \ (y \ (((1 / y) \ x) * a(1 / y,z,u))) = a(y,y,x * a(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(11625(a,1),11962(a,1,2,2))].">
      <j1 rule="para" parents="11625 11962"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      (x \ (((1 / x) \ y) * a(z,u,1 / x))) / (y * a(z,u,1 / x)) = a(x,x,y * a(z,u,1 / x))
    ]]></literal>
    <justification jstring="[para(10580(a,1),11966(a,1,1,2))].">
      <j1 rule="para" parents="10580 11966"/>
    </justification>
  </clause>

  <clause id="11987">
    <literal><![CDATA[
      L(1 / x,y,y) \ 1 = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(41,a,6590,a,b,11970,a)].">
      <j1 rule="hyper" parents="41 6590 11970"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      L(x,y,z \ (z \ u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7010,a(flip),b,11975,a),flip(a)].">
      <j1 rule="hyper" parents="65 7010 11975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),11988(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 11988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      L(x,y,L(z * u,u,u)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(2353,a,11989,a)].">
      <j1 rule="hyper" parents="2353 11989"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,R(T(z,v5),u,w),R(T(z,v5),u,w))) = L(x,y,R(T(z,v5),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(243(a,1),11990(a,1,3,1))].">
      <j1 rule="para" parents="243 11990"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      L(x,y,z) * a(u,u,L(x,y,z)) = L(x * a(u,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,11956,a,b,11968,a)].">
      <j1 rule="hyper" parents="36 11956 11968"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * u) = a(x,y,(1 / u) \ z)
    ]]></literal>
    <justification jstring="[hyper(10138,a,11979,a),flip(a)].">
      <j1 rule="hyper" parents="10138 11979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11994">
    <literal><![CDATA[
      a(x,y,(z \ (z \ u)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10651,a(flip),b,11979,a)].">
      <j1 rule="hyper" parents="65 10651 11979"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10366,a(flip),b,11993,a),flip(a)].">
      <j1 rule="hyper" parents="325 10366 11993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(10346,a,11995,a)].">
      <j1 rule="hyper" parents="10346 11995"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(10153,a,11996,a)].">
      <j1 rule="hyper" parents="10153 11996"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      a(x,x,x \ y) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11807,a(flip),b,11996,a),flip(a)].">
      <j1 rule="hyper" parents="65 11807 11996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,10047,a(flip),b,11998,a),flip(a)].">
      <j1 rule="hyper" parents="325 10047 11998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      a(x,x,y * x) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,11593,a(flip),b,11998,a),flip(a)].">
      <j1 rule="hyper" parents="65 11593 11998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12001">
    <literal><![CDATA[
      x \ R(x,x,x \ (x \ y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11590,a,b,11999,a)].">
      <j1 rule="hyper" parents="65 11590 11999"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      a(x,x,x * y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(10136,a,12000,a)].">
      <j1 rule="hyper" parents="10136 12000"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      x * (((x \ y) / y) * x) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(137,a,12000,a(flip),b,11590,a)].">
      <j1 rule="hyper" parents="137 12000 11590"/>
    </justification>
  </clause>

  <clause id="12004">
    <literal><![CDATA[
      a(x,x,x * y) = ((1 / x) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,11702,a,b,12002,a),flip(a)].">
      <j1 rule="hyper" parents="325 11702 12002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12005">
    <literal><![CDATA[
      a(x,x,x * y) * z = (((x \ y) / y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,12002,a,b,11,a)].">
      <j1 rule="hyper" parents="136 12002 11"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      L(x,a(y,y,y * z),u) = L(x,(z \ (y \ z)) * y,u)
    ]]></literal>
    <justification jstring="[para(12002(a,2),10817(a,1,2))].">
      <j1 rule="para" parents="12002 10817"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      R(1 / x,x,x \ (x \ y)) * x = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,1080,a,b,12001,a)].">
      <j1 rule="hyper" parents="65 1080 12001"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      a(x,y,z \ (z \ u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11997(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 11997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      R(x,x,x \ y) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(1089,a,12003,a)].">
      <j1 rule="hyper" parents="1089 12003"/>
    </justification>
  </clause>

  <clause id="12010">
    <literal><![CDATA[
      R(x,x,y * x) * y = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(136,a,12009,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="136 12009 108"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      a(x,x,x * y) \ (x \ y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(7285,a,12004,a)].">
      <j1 rule="hyper" parents="7285 12004"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      a(x,y,z \ (z * L(z \ u,w,v5))) = a(x,y,L(L(z * u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(1322(a,1),12008(a,1,3,2))].">
      <j1 rule="para" parents="1322 12008"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      a(x,y,L(z,L(z,u,w),L(z,u,w))) = a(x,y,L(L(z,u,w),u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(11878(a,1),12008(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11878 12008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      a(x,y,(R(z,z,(u \ (w / v5)) * z) * (u \ (v5 \ w))) * v6) = a(x,y,((z * z) * (z \ (u \ (w / v5)))) * v6)
    ]]></literal>
    <justification jstring="[para(12010(a,1),11227(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12010 11227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12015">
    <literal><![CDATA[
      (x \ a(x,x \ 1,x \ y)) * x = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(11656(a,1),12007(a,1,1))].">
      <j1 rule="para" parents="11656 12007"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,z \ u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(12015(a,1),10047(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12015 10047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12017">
    <literal><![CDATA[
      a(x \ y,z,a(x,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,10560,a(flip),b,12016,a),flip(a)].">
      <j1 rule="hyper" parents="65 10560 12016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12018">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(11704(a,1),12016(a,1,3))].">
      <j1 rule="para" parents="11704 12016"/>
    </justification>
  </clause>

  <clause id="12019">
    <literal><![CDATA[
      L(1 \ x,y \ z,a(y,y,z)) = L(x,a(y,y,z),y \ z)
    ]]></literal>
    <justification jstring="[para(12017(a,1),11941(a,1,1,1))].">
      <j1 rule="para" parents="12017 11941"/>
    </justification>
  </clause>

  <clause id="12020">
    <literal><![CDATA[
      a(x,y,z * (u \ (u \ w))) = a(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,11994,a)].">
      <j1 rule="hyper" parents="10136 11994"/>
    </justification>
  </clause>

  <clause id="12021">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),11994(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="9 11994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12022">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) * w) = a(x,y,(u \ T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(22(a,2),11994(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="22 11994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      a(x,y,(z \ (z \ a(z,u,w))) * v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(2403(a,1),11994(a,2,3,1))].">
      <j1 rule="para" parents="2403 11994"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,u,u))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11390,a(flip),b,12021,a)].">
      <j1 rule="hyper" parents="65 11390 12021"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      a(x,y,L(z,z * u,z * u)) = a(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10426,a,b,12024,a)].">
      <j1 rule="hyper" parents="65 10426 12024"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      L(x,a(y,y,z),y \ z) = L(x,y \ z,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(67(a,1),12019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="67 12019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10132,a(flip),b,12022,a),flip(a)].">
      <j1 rule="hyper" parents="325 10132 12022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),u,z)) = a(x,y,(u * z) \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10194,a(flip),b,11964,a),flip(a)].">
      <j1 rule="hyper" parents="325 10194 11964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12030">
    <literal><![CDATA[
      a(x,y,((z * u) \ R((z * u) \ 1,u,z)) * w) = a(x,y,a(z * u,u,z) * w)
    ]]></literal>
    <justification jstring="[para(2406(a,1),12023(a,1,3,1,2))].">
      <j1 rule="para" parents="2406 12023"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),u,z)) = a(x,y,(u * z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10463,a(flip),b,12029,a),flip(a)].">
      <j1 rule="hyper" parents="325 10463 12029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12032">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u \ z)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(11577(a,1),12031(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11577 12031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10694,a,b,12032,a)].">
      <j1 rule="hyper" parents="65 10694 12032"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ z)) * u,w) = L(x,u * (a(y,y,z) * z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10983,a(flip),b,11976,a)].">
      <j1 rule="hyper" parents="65 10983 11976"/>
    </justification>
  </clause>

  <clause id="12036">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * u) \ w) = a(x,y,(z \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11539,a(flip),b,11980,a),flip(a)].">
      <j1 rule="hyper" parents="65 11539 11980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      a(x,y,(z \ (z \ u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11959,a(flip),b,12036,a),flip(a)].">
      <j1 rule="hyper" parents="65 11959 12036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      L(x,y * ((((z \ u) / u) * z) * (u * z)),w) = L(x,(z \ ((z \ 1) \ (u * z))) * y,w)
    ]]></literal>
    <justification jstring="[para(12000(a,1),12035(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12000 12035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12039">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),z,z)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,7495,a(flip),b,12012,a),flip(a)].">
      <j1 rule="hyper" parents="65 7495 12012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,z),w,v5),z,z)) = a(x,y,L(T(z,u) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(2644(a,2),12039(a,2,3,1))].">
      <j1 rule="para" parents="2644 12039"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      a(x,y,L(z,L(z,u,w),L(z,u,w))) = a(x,y,L(L(z,u,w),u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,7484,a(flip),b,12013,a),flip(a)].">
      <j1 rule="hyper" parents="325 7484 12013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w)) = a(x,y,L(z,L(z,u,w),z))
    ]]></literal>
    <justification jstring="[para(7063(a,1),12042(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7063 12042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10297,a(flip),b,12043,a),flip(a)].">
      <j1 rule="hyper" parents="325 10297 12043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12047">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,u,z)) = a(x,y,u \ (z \ w))
    ]]></literal>
    <justification jstring="[para(308(a,1),12044(a,1,3,1))].">
      <j1 rule="para" parents="308 12044"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ L(L(L(x,y,z),y,z),u,u) = a(u,u,x) \ 1
    ]]></literal>
    <justification jstring="[para(12044(a,1),7004(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12044 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      a(x,y,z * a(u,z,z)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(11692(a,1),12044(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11692 12044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,u)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(10396,a,12047,a)].">
      <j1 rule="hyper" parents="10396 12047"/>
    </justification>
  </clause>

  <clause id="12051">
    <literal><![CDATA[
      a(x,y,L(z \ u,w \ z,w)) = a(x,y,(w \ z) \ (w \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),12047(a,1,3,1,1))].">
      <j1 rule="para" parents="10 12047"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      a(x,y,L(L(z * K(z * u,w),u,w),w,T(u,z))) = a(x,y,w \ (T(u,z) \ ((T(u,z) * z) * w)))
    ]]></literal>
    <justification jstring="[para(10840(a,1),12050(a,1,3,1))].">
      <j1 rule="para" parents="10840 12050"/>
    </justification>
  </clause>

  <clause id="12053">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),u,u),y,z) = a(u,u,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(4459,a,12048,a)].">
      <j1 rule="hyper" parents="4459 12048"/>
    </justification>
  </clause>

  <clause id="12054">
    <literal><![CDATA[
      L(L(x \ L(x,y,y),z,u),z,u) = a(y,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4458(a,1),12053(a,1,1))].">
      <j1 rule="para" parents="4458 12053"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      L((a(x,x,y) \ 1) \ 1,z,u) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12054(a,1),11882(a,1,1,1))].">
      <j1 rule="para" parents="12054 11882"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7181(a,1),12055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7181 12055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12058">
    <literal><![CDATA[
      a(x,x,L(y,z,a(x,u,w))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,11782,a(flip),b,12056,a),flip(a)].">
      <j1 rule="hyper" parents="325 11782 12056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,L(u,y,z)) = L(R(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(12056(a,2),11606(a,1,2))].">
      <j1 rule="para" parents="12056 11606"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (L(R(x,x,w),y,z) * u) = R(a(x,x,L(w,y,z)),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12060(a,1),7548(a,1,2,1))].">
      <j1 rule="para" parents="12060 7548"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),u,u)) = a(x,y,L(T(u,z) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(113(a,1),12041(a,1,3,1,1))].">
      <j1 rule="para" parents="113 12041"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),u,u)) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10232,a(flip),b,12062,a),flip(a)].">
      <j1 rule="hyper" parents="325 10232 12062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      a(L(x,x,x \ y) * ((1 / x) \ y),z,u) = a(a(x,x,y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(5126(a,1),11981(a,1,1,1))].">
      <j1 rule="para" parents="5126 11981"/>
    </justification>
  </clause>

  <clause id="12066">
    <literal><![CDATA[
      a(L(x,x,x * y) * ((1 / x) \ y),z,u) = a(a(x,x,y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2368(a,1),12065(a,1,1,1))].">
      <j1 rule="para" parents="2368 12065"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      a((x \ y) * L(x,x,x * y),z,u) = a(a(x,x,y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3529,a,12066,a)].">
      <j1 rule="hyper" parents="3529 12066"/>
    </justification>
  </clause>

  <clause id="12068">
    <literal><![CDATA[
      a((x \ y) / (x \ 1),z,u) = a(a(x,x,y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2369(a,1),12067(a,1,1))].">
      <j1 rule="para" parents="2369 12067"/>
    </justification>
  </clause>

  <clause id="12069">
    <literal><![CDATA[
      a((x \ 1) \ (x \ y),z,u) = a(a(x,x,y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2574,a,12068,a)].">
      <j1 rule="hyper" parents="2574 12068"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      a(a(x,x,y) * y,z,u) = a(x \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5172,a(flip),b,12069,a),flip(a)].">
      <j1 rule="hyper" parents="65 5172 12069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      a(x \ (x \ y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7009,a(flip),b,12070,a),flip(a)].">
      <j1 rule="hyper" parents="65 7009 12070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      a(L(x \ (x \ y),z,u),w,v5) = a(L(L(y,z,u),x,x),w,v5)
    ]]></literal>
    <justification jstring="[para(1320(a,2),12071(a,1,1))].">
      <j1 rule="para" parents="1320 12071"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      a(L(x,a(y,y,z) \ z,u),w,v5) = a(L(x,y \ ((1 / y) \ z),u),w,v5)
    ]]></literal>
    <justification jstring="[para(10574(a,1),11983(a,1,1,2))].">
      <j1 rule="para" parents="10574 11983"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      a(L(x,y \ ((1 / y) \ z),u),w,v5) = a(L(x,L(z,y,y),u),w,v5)
    ]]></literal>
    <justification jstring="[para(1782(a,1),12073(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1782 12073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      a(L(x,y \ ((y \ 1) \ z),u),w,v5) = a(L(x,L(z,y,y),u),w,v5)
    ]]></literal>
    <justification jstring="[para(10929(a,1),12074(a,1,1))].">
      <j1 rule="para" parents="10929 12074"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      a(L(x,y \ (y \ z),u),w,v5) = a(L(x,L(z,y,y),u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11499,a(flip),b,12075,a)].">
      <j1 rule="hyper" parents="65 11499 12075"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      a(L(x \ (x \ y),L(y,x,x),x),z,u) = a((x \ y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1887,a,12076,a),flip(a)].">
      <j1 rule="hyper" parents="1887 12076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      a(L(L(x,L(x,y,y),y),y,y),z,u) = a((y \ x) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12072,a(flip),b,12077,a)].">
      <j1 rule="hyper" parents="65 12072 12077"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * L(u * w,w,u))) = a(x,y,a(u * w,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11394,a(flip),b,12030,a)].">
      <j1 rule="hyper" parents="65 11394 12030"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      a(x,y,L(a(z,u,z * u) \ 1,z * u,z * u) * w) = a(x,y,a(z * u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10290,a,b,12079,a)].">
      <j1 rule="hyper" parents="65 10290 12079"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      a(x,y,((z * u) * T(T(w,u),v5)) \ ((w * u) * z)) = a(x,y,a(T(T(w,u),v5),u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10421,a(flip),b,11918,a)].">
      <j1 rule="hyper" parents="65 10421 11918"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      a(x,y,a(T(T(z,u),w),u,v5)) = a(x,y,(T(z,u) * (v5 * u)) \ ((z * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10256,a(flip),b,12081,a),flip(a)].">
      <j1 rule="hyper" parents="65 10256 12081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      a(x,y,a(T(T(z,u),w),u,v5)) = a(x,y,(z * (v5 * u)) \ ((u * z) * v5))
    ]]></literal>
    <justification jstring="[para(2731(a,1),12083(a,2,3))].">
      <j1 rule="para" parents="2731 12083"/>
    </justification>
  </clause>

  <clause id="12086">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ ((w * z) * u)) = a(x,y,a(T(z,w),w,u))
    ]]></literal>
    <justification jstring="[para(112(a,1),12085(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="112 12085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ ((w * z) * u)) = a(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[para(1868(a,1),12086(a,2,3))].">
      <j1 rule="para" parents="1868 12086"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,a(x,x,y),x * y) = (x * y) * (L(a(x,x,y),y,x) * z)
    ]]></literal>
    <justification jstring="[para(11577(a,1),11963(a,1,2,2))].">
      <j1 rule="para" parents="11577 11963"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      a(x,y,(a(z,u,z * u) \ 1) * w) = a(x,y,a(z * u,u,z) * w)
    ]]></literal>
    <justification jstring="[para(10602(a,1),12080(a,1,3,1))].">
      <j1 rule="para" parents="10602 12080"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      a(x,y,a(z * u,u,z) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10752,a(flip),b,12091,a),flip(a)].">
      <j1 rule="hyper" parents="65 10752 12091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      a(x,y,a(z \ u,z \ u,z) * w) = a(x,y,a(u,z \ u,z) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),12092(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12095">
    <literal><![CDATA[
      a(x,y,((z / u) * (u / z)) * w) = a(x,y,a(u,z \ u,z) * w)
    ]]></literal>
    <justification jstring="[para(11597(a,1),12094(a,1,3,1))].">
      <j1 rule="para" parents="11597 12094"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      a(x,y,((z / u) * (z \ u)) * w) = a(x,y,a(u,z \ u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10307,a(flip),b,12095,a)].">
      <j1 rule="hyper" parents="65 10307 12095"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      a(x,y,((z \ u) * (u \ z)) * w) = a(x,y,a(z,u \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(10143,a,12096,a)].">
      <j1 rule="hyper" parents="10143 12096"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * (w \ u))) = a(x,y,a(w,u \ w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(10170,a,12097,a)].">
      <j1 rule="hyper" parents="10170 12097"/>
    </justification>
  </clause>

  <clause id="12099">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ u)) \ ((z \ u) * u)) = a(x,y,a(z,u \ z,u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11932,a,b,12098,a)].">
      <j1 rule="hyper" parents="65 11932 12098"/>
    </justification>
  </clause>

  <clause id="12100">
    <literal><![CDATA[
      a(x,y,a(z,u \ z,u) * z) = a(x,y,(1 / (z \ u)) * u)
    ]]></literal>
    <justification jstring="[para(647(a,1),12099(a,1,3)),flip(a)].">
      <j1 rule="para" parents="647 12099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      a(x,y,a(z,u \ z,u) * z) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10113,a(flip),b,12100,a),flip(a)].">
      <j1 rule="hyper" parents="325 10113 12100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      a(x,y,R(z,u \ z,u)) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[para(11820(a,1),12101(a,1,3))].">
      <j1 rule="para" parents="11820 12101"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      a(x,y,L(z,u \ z,u)) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10407,a(flip),b,12102,a)].">
      <j1 rule="hyper" parents="65 10407 12102"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      a(x,y,(z \ u) \ z) = a(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11701,a(flip),b,12103,a)].">
      <j1 rule="hyper" parents="65 11701 12103"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      L((x \ (y \ ((y * x) * z))) / z,z,x) = K(z,L(z,x,y) \ z) * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(8544(a,1),11646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8544 11646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12106">
    <literal><![CDATA[
      L((x \ (y \ ((y * x) * z))) / z,z,x) = 1 * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(7816(a,1),12105(a,2,1))].">
      <j1 rule="para" parents="7816 12105"/>
    </justification>
  </clause>

  <clause id="12107">
    <literal><![CDATA[
      a(x,y,z) = L((y \ (x \ ((x * y) * z))) / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,7,a(flip),b,12106,a)].">
      <j1 rule="hyper" parents="325 7 12106"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      (x * y) \ ((y * L(y,z,u)) \ (L((y * y) * y,z,u) * T(x,y))) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(1773(a,2),11686(a,1,2,2,1))].">
      <j1 rule="para" parents="1773 11686"/>
    </justification>
  </clause>

  <clause id="12110">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(z,u,w),y) = (a(z,u,w) * y) \ ((y * x) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(7186(a,1),11745(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7186 11745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12111">
    <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="[hyper(325,a,7268,a(flip),b,12110,a),flip(a)].">
      <j1 rule="hyper" parents="325 7268 12110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12113">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * y,a(z,u,w),x) = L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(7190(a,2),12111(a,1,1))].">
      <j1 rule="para" parents="7190 12111"/>
    </justification>
  </clause>

  <clause id="12114">
    <literal><![CDATA[
      L(1 * x,a(y,y,z),y * z) = L(x,y * z,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(11576(a,1),12113(a,1,1,1))].">
      <j1 rule="para" parents="11576 12113"/>
    </justification>
  </clause>

  <clause id="12115">
    <literal><![CDATA[
      L(x,a(y,y,z),y * z) = L(x,y * z,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),12114(a,1,1))].">
      <j1 rule="para" parents="7 12114"/>
    </justification>
  </clause>

  <clause id="12116">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,x * y,a(x,x,y)) = (x * y) * (L(a(x,x,y),y,x) * z)
    ]]></literal>
    <justification jstring="[para(12115(a,1),12089(a,1,2))].">
      <j1 rule="para" parents="12115 12089"/>
    </justification>
  </clause>

  <clause id="12117">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,x * y,a(x,x,y)) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(11577(a,1),12116(a,2,2,1))].">
      <j1 rule="para" parents="11577 12116"/>
    </justification>
  </clause>

  <clause id="12119">
    <literal><![CDATA[
      (x * y) \ ((y * L(y,z,u)) \ ((y * y) * (L(y,z,u) * T(x,y)))) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(1328(a,1),12109(a,1,2,2))].">
      <j1 rule="para" parents="1328 12109"/>
    </justification>
  </clause>

  <clause id="12120">
    <literal><![CDATA[
      (x * y) \ ((y * L(y,z,u)) \ ((y * y) * (x * L(y,z,u)))) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(7971(a,1),12119(a,1,2,2,2))].">
      <j1 rule="para" parents="7971 12119"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      (x * y) \ (((1 / y) * L(y,z,u)) \ (x * L(y,z,u))) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(692(a,1),12120(a,1,2))].">
      <j1 rule="para" parents="692 12120"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      (x * y) \ ((y \ L(y,z,u)) \ (x * L(y,z,u))) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(1757(a,1),12121(a,1,2,1))].">
      <j1 rule="para" parents="1757 12121"/>
    </justification>
  </clause>

  <clause id="12123">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) \ (((y \ 1) \ L(y \ 1,z,u)) \ ((x * L(y,z,u)) * (y \ 1))) = a(y \ 1,(y \ 1) \ L(y \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9035(a,2),12122(a,1,2,2))].">
      <j1 rule="para" parents="9035 12122"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      ((x \ K(y,z)) * u) \ ((w / x) \ ((w / (x * x)) * (K(y,z) * u))) = a(w / x,x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9595(a,1),11645(a,1,2,2))].">
      <j1 rule="para" parents="9595 11645"/>
    </justification>
  </clause>

  <clause id="12125">
    <literal><![CDATA[
      K(x \ 1,y) * ((y / (x \ y)) * ((x \ y) / y)) = (y / (y * (y \ (x \ y)))) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(11597(a,1),11675(a,1,2))].">
      <j1 rule="para" parents="11597 11675"/>
    </justification>
  </clause>

  <clause id="12126">
    <literal><![CDATA[
      K(x \ 1,y) * (x * ((x \ y) / y)) = (y / (y * (y \ (x \ y)))) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(82(a,1),12125(a,1,2,1))].">
      <j1 rule="para" parents="82 12125"/>
    </justification>
  </clause>

  <clause id="12128">
    <literal><![CDATA[
      K(x \ 1,y) * a(x,x \ 1,y) = (y / (y * (y \ (x \ y)))) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(11655(a,1),12126(a,1,2))].">
      <j1 rule="para" parents="11655 12126"/>
    </justification>
  </clause>

  <clause id="12129">
    <literal><![CDATA[
      (x / (x * (x \ (y \ x)))) * (x \ (y \ x)) = (y * (x * (y \ 1))) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,9816,a(flip),b,12128,a),flip(a)].">
      <j1 rule="hyper" parents="65 9816 12128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      (x / (y \ x)) * (x \ (y \ x)) = (y * (x * (y \ 1))) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),12129(a,1,1,2))].">
      <j1 rule="para" parents="10 12129"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      (x * (y * (x \ 1))) \ y = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,12130,a),flip(a)].">
      <j1 rule="hyper" parents="334 12130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      K(x \ 1,y) * a(x,x \ 1,y) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,9816,a,b,12131,a)].">
      <j1 rule="hyper" parents="65 9816 12131"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      L(x,y * (z \ (y \ z)),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(12131(a,1),11435(a,1,2))].">
      <j1 rule="para" parents="12131 11435"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      L(x,(y \ (z \ y)) * z,u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(10884,a,12135,a)].">
      <j1 rule="hyper" parents="10884 12135"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      L(x,a(y,y,y * z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12006,a,b,12136,a)].">
      <j1 rule="hyper" parents="65 12006 12136"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      (x * (y \ 1)) \ (y \ (1 * x)) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11679,a(flip),b,12134,a)].">
      <j1 rule="hyper" parents="65 11679 12134"/>
    </justification>
  </clause>

  <clause id="12139">
    <literal><![CDATA[
      a(x,x \ 1,y) \ K(y,x \ 1) = (x * (y \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(12134(a,1),2616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12134 2616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      (x * (y \ 1)) \ (y \ x) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(7(a,1),12138(a,1,2,2))].">
      <j1 rule="para" parents="7 12138"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      (x * (y \ 1)) * (y * (x \ (y \ x))) = y \ x
    ]]></literal>
    <justification jstring="[hyper(148,a,12140,a)].">
      <j1 rule="hyper" parents="148 12140"/>
    </justification>
  </clause>

  <clause id="12142">
    <literal><![CDATA[
      ((x \ y) \ (y * (x \ 1))) * a(x \ y,(x \ y) \ (y * (x \ 1)),(x \ y) \ (y * (x \ 1))) = 1 / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(12140(a,1),11720(a,2,2))].">
      <j1 rule="para" parents="12140 11720"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * a(y * (x \ 1),x * (y \ (x \ y)),x * (y \ (x \ y))) = 1 / ((x \ y) \ (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(12141(a,1),11719(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12141 11719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      x \ L(T(x,y \ 1),y \ 1,y) = (y * (x \ (y \ x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,10611,a(flip),b,12139,a)].">
      <j1 rule="hyper" parents="65 10611 12139"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ 1 = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(511(a,1),12144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="511 12144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      ((a(x,x \ y,z) * ((x \ y) * z)) / z) * K(u,w) = (x \ (y * (K(u,w) * z))) / z
    ]]></literal>
    <justification jstring="[para(10027(a,1),11682(a,1,1,1,1))].">
      <j1 rule="para" parents="10027 11682"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      (x \ (y * (K(z,u) * w))) / w = ((x \ (y * w)) / w) * K(z,u)
    ]]></literal>
    <justification jstring="[para(11648(a,1),12146(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11648 12146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      ((x \ ((y * z) * u)) / u) * K(z,w) = (x \ ((y * T(z,w)) * u)) / u
    ]]></literal>
    <justification jstring="[para(9586(a,1),12148(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9586 12148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12150">
    <literal><![CDATA[
      a(x,y,(z * u) \ (L(z,w,u) * (u * T(w,v5)))) = a(x,y,L(a(u,T(w,v5),z) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(10806(a,1),11751(a,1,3,2,1))].">
      <j1 rule="para" parents="10806 11751"/>
    </justification>
  </clause>

  <clause id="12151">
    <literal><![CDATA[
      a(x,y,L(a(z,T(u,w),v5) \ u,z,v5)) = a(x,y,(v5 * z) \ ((u * z) * L(v5,u,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11186,a(flip),b,12150,a),flip(a)].">
      <j1 rule="hyper" parents="65 11186 12150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12154">
    <literal><![CDATA[
      a(x,y,L(a(z,T(u,w),v5) \ u,z,v5)) = a(x,y,(v5 * z) \ (z * (T(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5232(a,1),12151(a,2,3,2))].">
      <j1 rule="para" parents="5232 12151"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      a(x,y,L(a(z,T(u,w),v5) \ u,z,v5)) = a(x,y,(v5 * z) \ ((u * v5) * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10421,a(flip),b,12154,a),flip(a)].">
      <j1 rule="hyper" parents="325 10421 12154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12157">
    <literal><![CDATA[
      a(x,y,L(a(z,T(u,w),v5) \ u,z,v5)) = a(x,y,L(u,v5,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10400,a(flip),b,12155,a),flip(a)].">
      <j1 rule="hyper" parents="325 10400 12155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ u,z,w)) = a(x,y,L(u,w,z))
    ]]></literal>
    <justification jstring="[para(112(a,1),12157(a,1,3,1,1,2))].">
      <j1 rule="para" parents="112 12157"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      a(x,y,L(a(z,u,(w \ v5) * v6) \ u,z,v6 * ((w \ 1) \ v5))) = a(x,y,L(u,v6 * ((w \ 1) \ v5),z))
    ]]></literal>
    <justification jstring="[para(10636(a,1),12158(a,1,3,1,1))].">
      <j1 rule="para" parents="10636 12158"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,R(T(z,v5),u,w),L(T(z,v5),u,w))) = L(x,y,R(T(z,v5),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(9931(a,1),11991(a,1,3))].">
      <j1 rule="para" parents="9931 11991"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      ((x \ K(y,z)) * u) \ ((w / (x \ 1)) \ (w * (K(y,z) * u))) = a(w / x,x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(11240(a,1),12124(a,1,2))].">
      <j1 rule="para" parents="11240 12124"/>
    </justification>
  </clause>

  <clause id="12162">
    <literal><![CDATA[
      ((x \ K(y,z)) * u) \ ((w / (x \ K(y,z))) \ (w * u)) = a(w / x,x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(11032(a,1),12161(a,1,2))].">
      <j1 rule="para" parents="11032 12161"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,R(T(z,v5),u,w),L(z,u,w))) = L(x,y,R(T(z,v5),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(1550(a,1),12160(a,1,3))].">
      <j1 rule="para" parents="1550 12160"/>
    </justification>
  </clause>

  <clause id="12165">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,L(T(z,v5),u,w),L(z,u,w))) = L(x,y,R(T(z,v5),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(11049(a,1),12163(a,1,3))].">
      <j1 rule="para" parents="11049 12163"/>
    </justification>
  </clause>

  <clause id="12166">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,L(z,u,w),L(z,u,w))) = L(x,y,R(T(z,v5),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(10810(a,1),12165(a,1,3))].">
      <j1 rule="para" parents="10810 12165"/>
    </justification>
  </clause>

  <clause id="12168">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,y,z),u),u * a(x,y,z),x) = L(a(x,y,z),a(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(1430,a,11628,a)].">
      <j1 rule="hyper" parents="1430 11628"/>
    </justification>
  </clause>

  <clause id="12169">
    <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(65,a,11584,a(flip),b,12168,a),flip(a)].">
      <j1 rule="hyper" parents="65 11584 12168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      R(x,y,(z * (a(z,u,L(w,v5,v6)) \ u)) * L(w,v5,v6)) = R(x,y,z * (u * L(w \ 1,v5,v6)))
    ]]></literal>
    <justification jstring="[para(10453(a,1),11730(a,1,3,1,2,1))].">
      <j1 rule="para" parents="10453 11730"/>
    </justification>
  </clause>

  <clause id="12172">
    <literal><![CDATA[
      R(x,y,z * (u * L(w \ 1,v5,v6))) = R(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(11708(a,1),12171(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11708 12171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      R(x,y,z * (u * L(1 / w,v5,v6))) = R(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8765,a,b,12172,a)].">
      <j1 rule="hyper" parents="65 8765 12172"/>
    </justification>
  </clause>

  <clause id="12174">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (y \ (((1 / y) \ x) * a(1 / y,z,u))) = a(y,y,x * a(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(1842(a,1),11985(a,1,1,2))].">
      <j1 rule="para" parents="1842 11985"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (y \ (((1 / y) \ x) * a(y,z,u))) = a(y,y,x * a(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(1842(a,1),12174(a,1,2,2,2))].">
      <j1 rule="para" parents="1842 12174"/>
    </justification>
  </clause>

  <clause id="12176">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((y \ ((1 / y) \ x)) * a(y,z,u)) = a(y,y,x * a(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(11625(a,1),12175(a,1,2))].">
      <j1 rule="para" parents="11625 12175"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      (x \ (((1 / x) \ y) * a(z,u,x))) / (y * a(z,u,1 / x)) = a(x,x,y * a(z,u,1 / x))
    ]]></literal>
    <justification jstring="[para(7490(a,1),11986(a,1,1,2,2))].">
      <j1 rule="para" parents="7490 11986"/>
    </justification>
  </clause>

  <clause id="12178">
    <literal><![CDATA[
      ((x \ ((1 / x) \ y)) * a(z,u,x)) / (y * a(z,u,1 / x)) = a(x,x,y * a(z,u,1 / x))
    ]]></literal>
    <justification jstring="[para(10580(a,1),12177(a,1,1))].">
      <j1 rule="para" parents="10580 12177"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      ((x \ ((1 / x) \ y)) * a(z,u,x)) / (y * a(z,u,x)) = a(x,x,y * a(z,u,1 / x))
    ]]></literal>
    <justification jstring="[para(7490(a,1),12178(a,1,2,2))].">
      <j1 rule="para" parents="7490 12178"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      R(a(x,x,y),y,a(z,u,x)) = a(x,x,y * a(z,u,1 / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11972,a(flip),b,12179,a)].">
      <j1 rule="hyper" parents="65 11972 12179"/>
    </justification>
  </clause>

  <clause id="12181">
    <literal><![CDATA[
      a(x,y,L(L(z * K(z * u,w),u,w),w,u)) = a(x,y,w \ (T(u,z) \ ((T(u,z) * z) * w)))
    ]]></literal>
    <justification jstring="[para(1545(a,1),12052(a,1,3))].">
      <j1 rule="para" parents="1545 12052"/>
    </justification>
  </clause>

  <clause id="12182">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) \ ((T(u,w) * w) * z))) = a(x,y,L(L(w,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(10398,a,12181,a),flip(a)].">
      <j1 rule="hyper" parents="10398 12181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12184">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * w) * z))) = a(x,y,L(L(w,u,z),z,u))
    ]]></literal>
    <justification jstring="[para(2262(a,1),12182(a,1,3,2))].">
      <j1 rule="para" parents="2262 12182"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (a(R(z,u,w),R(z,u,w),v5) * v5)) * v6) = a(x,y,((R(z,u,w) \ 1) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10131,a(flip),b,11965,a),flip(a)].">
      <j1 rule="hyper" parents="325 10131 11965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      a(x,y,L(a(z,u,(w \ v5) * v6) \ u,z,(w \ v5) * v6)) = a(x,y,L(u,v6 * ((w \ 1) \ v5),z))
    ]]></literal>
    <justification jstring="[para(5032(a,1),12159(a,1,3))].">
      <j1 rule="para" parents="5032 12159"/>
    </justification>
  </clause>

  <clause id="12188">
    <literal><![CDATA[
      a(x,y,L(z,u * ((w \ 1) \ v5),v6)) = a(x,y,L(z,(w \ v5) * u,v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,12158,a(flip),b,12187,a),flip(a)].">
      <j1 rule="hyper" parents="65 12158 12187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (a(R(z,u,w),R(z,u,w),v5) * v5)) * v6) = a(x,y,v6 * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10639,a(flip),b,12186,a),flip(a)].">
      <j1 rule="hyper" parents="325 10639 12186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (a(R(z,u,w),L(z,u,w),v5) * v5)) * v6) = a(x,y,v6 * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(10526(a,1),12189(a,1,3,1,2,1))].">
      <j1 rule="para" parents="10526 12189"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (a(L(z,u,w),L(z,u,w),v5) * v5)) * v6) = a(x,y,v6 * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(8679(a,1),12190(a,1,3,1,2,1))].">
      <j1 rule="para" parents="8679 12190"/>
    </justification>
  </clause>

  <clause id="12192">
    <literal><![CDATA[
      a(x,y,((1 / L(z,u,w)) \ v5) * v6) = a(x,y,v6 * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(11958(a,1),12191(a,1,3,1))].">
      <j1 rule="para" parents="11958 12191"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      a(x,y,((L(z,u,w) \ 1) \ v5) * v6) = a(x,y,v6 * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(10276,a,12192,a)].">
      <j1 rule="hyper" parents="10276 12192"/>
    </justification>
  </clause>

  <clause id="12194">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) \ v6)) = a(x,y,z * (L(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,10639,a(flip),b,12193,a),flip(a)].">
      <j1 rule="hyper" parents="65 10639 12193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      a(x,y,L(z,R(u,w,v5) \ v6,R(u,w,v5) \ v6) * (L(u,w,v5) \ v6)) = a(x,y,(R(u,w,v5) \ v6) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11995,a(flip),b,12194,a),flip(a)].">
      <j1 rule="hyper" parents="65 11995 12194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12196">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w,v5) \ v6,R(u,w,v5) \ v6) * (L(u,w,v5) \ v6)) = a(x,y,(R(u,w,v5) \ v6) \ z)
    ]]></literal>
    <justification jstring="[para(11427(a,1),12195(a,1,3,1))].">
      <j1 rule="para" parents="11427 12195"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      ((x * (a(y,z,u) \ T(u,x))) / (a(y,z,T(u,x)) \ 1)) \ (u * x) = a(x,u,a(y,z,T(u,x)) \ 1)
    ]]></literal>
    <justification jstring="[para(10037(a,1),11741(a,1,1,1,2,1))].">
      <j1 rule="para" parents="10037 11741"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      ((x * T(a(y,z,u) \ u,x)) / (a(y,z,T(u,x)) \ 1)) \ (u * x) = a(x,u,a(y,z,T(u,x)) \ 1)
    ]]></literal>
    <justification jstring="[para(8626(a,2),12197(a,1,1,1,2))].">
      <j1 rule="para" parents="8626 12197"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      (((a(x,y,z) \ z) * u) / (a(x,y,T(z,u)) \ 1)) \ (z * u) = a(u,z,a(x,y,T(z,u)) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),12198(a,1,1,1))].">
      <j1 rule="para" parents="113 12198"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      (((a(x,y,z) \ z) * u) / (a(x,y,z) \ 1)) \ (z * u) = a(u,z,a(x,y,T(z,u)) \ 1)
    ]]></literal>
    <justification jstring="[para(10037(a,1),12200(a,1,1,2,1))].">
      <j1 rule="para" parents="10037 12200"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ ((a(x,y,z) \ z) * u)) \ (z * u) = a(u,z,a(x,y,T(z,u)) \ 1)
    ]]></literal>
    <justification jstring="[para(8490(a,1),12201(a,1,1))].">
      <j1 rule="para" parents="8490 12201"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      (a(x,y,z) \ ((a(x,y,z) * z) * u)) \ (z * u) = a(u,z,a(x,y,T(z,u)) \ 1)
    ]]></literal>
    <justification jstring="[para(10575(a,1),12202(a,1,1))].">
      <j1 rule="para" parents="10575 12202"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      (a(x,y,z) \ ((a(x,y,z) * z) * u)) \ (z * u) = a(u,z,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(10037(a,1),12204(a,2,3,1))].">
      <j1 rule="para" parents="10037 12204"/>
    </justification>
  </clause>

  <clause id="12206">
    <literal><![CDATA[
      (a(x,y,z) \ ((a(x,y,z) * z) * u)) \ (z * u) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7484,a(flip),b,12205,a),flip(a)].">
      <j1 rule="hyper" parents="325 7484 12205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      (x \ (a(y,z,u) * (x * w))) / ((a(y,z,u) * (w * (v5 * v5))) / (v5 * v5)) = a(x,w * (v5 * v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(698,a,11788,a)].">
      <j1 rule="hyper" parents="698 11788"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      (x \ (a(y,z,u) * (x * w))) / (a(y,z,u) * ((w * (v5 * v5)) / (v5 * v5))) = a(x,w * (v5 * v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(704(a,1),12208(a,1,2))].">
      <j1 rule="para" parents="704 12208"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      a(x,y * (z * z),a(u,w,v5)) = (x \ (a(u,w,v5) * (x * y))) / (a(u,w,v5) * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),12209(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 12209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      a(x,y * (z * z),a(u,w,v5)) = a(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,11698,a(flip),b,12210,a),flip(a)].">
      <j1 rule="hyper" parents="325 11698 12210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      a(x,(y * y) \ z,a(u,w,v5)) = a(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10161,a,12211,a),flip(a)].">
      <j1 rule="hyper" parents="10161 12211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      a(x,(y * y) * z,a(u,w,v5)) = a(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10160,a,12211,a)].">
      <j1 rule="hyper" parents="10160 12211"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,a(u,w,v5)) = a(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10266,a(flip),b,12211,a)].">
      <j1 rule="hyper" parents="65 10266 12211"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      a(x,y \ 1,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(221(a,1),12211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="221 12211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      a(x,(y * y) \ z,a(u,w,v5)) = a(x,z \ (y * y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(434(a,1),12215(a,1,2)),flip(a)].">
      <j1 rule="para" parents="434 12215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      a(x,y \ (z * z),a(u,w,v5)) = a(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,12212,a(flip),b,12216,a),flip(a)].">
      <j1 rule="hyper" parents="65 12212 12216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12219">
    <literal><![CDATA[
      a(x,y * (L(y,z,u) \ y),a(w,v5,v6)) = a(x,L(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(1256(a,1),12217(a,1,2))].">
      <j1 rule="para" parents="1256 12217"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      ((1 / (x * y)) * y) \ (K(y,x) * R(K(x,y) * ((1 / (x * y)) * y),z,u)) = L(x \ R(x,z,u),y,x * y)
    ]]></literal>
    <justification jstring="[para(2618(a,1),11552(a,1,2,2,1))].">
      <j1 rule="para" parents="2618 11552"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      K(x \ (y \ ((1 / y) \ x)),x) * (z * (y \ ((1 / y) \ x))) = (a(y,y,x) * x) * T(z,x)
    ]]></literal>
    <justification jstring="[para(7360(a,1),11984(a,2,2))].">
      <j1 rule="para" parents="7360 11984"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      K(a(x,x,y),y) * (z * (x \ ((1 / x) \ y))) = (a(x,x,y) * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(11962(a,1),12221(a,1,1,1))].">
      <j1 rule="para" parents="11962 12221"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      (a(x,x,y) * y) * T(z,y) = z * (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(7187,a,12223,a),flip(a)].">
      <j1 rule="hyper" parents="7187 12223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      R(T(a(x,x,y),z * y),y,z) = (z * y) \ (z * (x \ ((1 / x) \ y)))
    ]]></literal>
    <justification jstring="[para(12224(a,1),6541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12224 6541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      R(T(a(x,x,y),z * y),y,z) = L(a(x,x,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,11967,a(flip),b,12226,a),flip(a)].">
      <j1 rule="hyper" parents="325 11967 12226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      R(a(x,x,y),y,z) = L(a(x,x,y),y,z)
    ]]></literal>
    <justification jstring="[para(7186(a,1),12227(a,1,1))].">
      <j1 rule="para" parents="7186 12227"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      (x * y) \ ((z \ ((1 / z) \ x)) * y) = L(a(z,z,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11973,a,b,12228,a)].">
      <j1 rule="hyper" parents="65 11973 12228"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      L(a(x,x,y),y,a(z,u,x)) = a(x,x,y * a(z,u,1 / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,12180,a(flip),b,12228,a),flip(a)].">
      <j1 rule="hyper" parents="65 12180 12228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      (x * y) \ ((z \ ((1 / z) \ x)) * y) = a(z,z,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12056,a,b,12229,a),flip(a)].">
      <j1 rule="hyper" parents="325 12056 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      a(x,x,L(y,y,a(x,z,u))) = a(x,x,y * a(1 / x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12176,a(flip),b,12232,a),flip(a)].">
      <j1 rule="hyper" parents="65 12176 12232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      L(a(x,x,y),y,a(z,u,x)) = a(x,x,y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(7490(a,1),12230(a,2,3,2))].">
      <j1 rule="para" parents="7490 12230"/>
    </justification>
  </clause>

  <clause id="12235">
    <literal><![CDATA[
      a(x,x,y * a(1 / x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12058,a(flip),b,12233,a),flip(a)].">
      <j1 rule="hyper" parents="65 12058 12233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      a(x,x,y * a(x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(1842(a,1),12235(a,1,3,2))].">
      <j1 rule="para" parents="1842 12235"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      a(x,x,a(x,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(10136,a,12237,a)].">
      <j1 rule="hyper" parents="10136 12237"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      a(x,x,L(y,x,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11811,a(flip),b,12237,a)].">
      <j1 rule="hyper" parents="65 11811 12237"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      a(x,x,(y * z) * R(x,z,y)) = a(x,x,(y * z) * x)
    ]]></literal>
    <justification jstring="[para(2345(a,1),12237(a,1,3))].">
      <j1 rule="para" parents="2345 12237"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      L(a(x,x,y),x,z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12056,a(flip),b,12239,a)].">
      <j1 rule="hyper" parents="65 12056 12239"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      L(x * a(y,y,x),y,z) = L(x,y,z) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(12239(a,1),11992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12239 11992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      (x * y) * a(y,y,z) = x * R(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12242,a(flip),b,11600,a)].">
      <j1 rule="hyper" parents="137 12242 11600"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      x * (R(x,x,y) \ z) = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[para(12242(a,1),11803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12242 11803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      a(x,x,y) * (z * x) = z * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(7226,a,12244,a)].">
      <j1 rule="hyper" parents="7226 12244"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,z,u))) = L(a(z,z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(12244(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12244 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12248">
    <literal><![CDATA[
      a(x,x,y) * (x * z) = R(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,157,a(flip),b,12245,a(flip))].">
      <j1 rule="hyper" parents="137 157 12245"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      a((x * R(x,x,y)) * z,u,w) = a(a(x,x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(12246(a,1),2243(a,1,1,1))].">
      <j1 rule="para" parents="12246 2243"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      a(L(x * y,y,x),z,u) = a(x * R(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12246(a,1),8917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12246 8917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      x * (y * a(x,x,z)) = R(x,x,z) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,11583,a(flip),b,12248,a)].">
      <j1 rule="hyper" parents="65 11583 12248"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      x * (a(x,x,y) * z) = R(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(7219,a,12252,a)].">
      <j1 rule="hyper" parents="7219 12252"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      a(x,x,y) \ (x \ z) = R(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(549,a,12253,a),flip(a)].">
      <j1 rule="hyper" parents="549 12253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,11759,a,b,12253,a(flip))].">
      <j1 rule="hyper" parents="36 11759 12253"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * x) \ z = x \ ((a(x,x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(1503,a,12255,a),flip(a)].">
      <j1 rule="hyper" parents="1503 12255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,10715,a,b,12255,a)].">
      <j1 rule="hyper" parents="65 10715 12255"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      (a(x,y,y) * y) \ z = y \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(526,a,12257,a),flip(a)].">
      <j1 rule="hyper" parents="526 12257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      L(x,a(y,z,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,10605,a,b,12257,a)].">
      <j1 rule="hyper" parents="65 10605 12257"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      (a(x,y,y) * y) * z = y * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,12257,a(flip),b,10581,a)].">
      <j1 rule="hyper" parents="137 12257 10581"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      R(x,x,x * y) \ y = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,12011,a(flip),b,12254,a),flip(a)].">
      <j1 rule="hyper" parents="65 12011 12254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      R(x,x,y * x) \ y = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(8690(a,1),12261(a,1,1))].">
      <j1 rule="para" parents="8690 12261"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      R(x * (y * x),x * (y * x),L(y,x,x) * z) \ z = (1 / (x * (y * x))) * z
    ]]></literal>
    <justification jstring="[para(8763(a,1),12262(a,1,1))].">
      <j1 rule="para" parents="8763 12262"/>
    </justification>
  </clause>

  <clause id="12264">
    <literal><![CDATA[
      a(x,x,y * x) \ y = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(12262(a,1),12245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12262 12245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      ((a(x,y,y) * y) * (z / (a(x,y,y) * y))) \ (z / (a(x,y,y) * y)) = z \ (y \ (a(x,y,y) \ z))
    ]]></literal>
    <justification jstring="[para(12258(a,1),2912(a,2,2))].">
      <j1 rule="para" parents="12258 2912"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      x * (x \ (a(y,x,x) \ (z / x))) = z / (a(y,x,x) * x)
    ]]></literal>
    <justification jstring="[para(12258(a,1),11907(a,1,2))].">
      <j1 rule="para" parents="12258 11907"/>
    </justification>
  </clause>

  <clause id="12267">
    <literal><![CDATA[
      a(L(x * y,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,5173,a(flip),b,12251,a),flip(a)].">
      <j1 rule="hyper" parents="325 5173 12251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      a(L(x,y \ x,y),z,u) = a((y \ x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12267(a,1,1,1))].">
      <j1 rule="para" parents="10 12267"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      a(x,x,(y * z) * L(x,z,y)) = a(x,x,(y * z) * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11354,a(flip),b,12240,a)].">
      <j1 rule="hyper" parents="65 11354 12240"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      a(x,x,(y * z) * x) = a(x,x,y * (z * x))
    ]]></literal>
    <justification jstring="[para(100(a,1),12269(a,1,3)),flip(a)].">
      <j1 rule="para" parents="100 12269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      x \ ((a(x,x,y) \ 1) \ z) = (a(x,x,y) \ x) \ z
    ]]></literal>
    <justification jstring="[para(11589(a,1),12256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11589 12256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      x / (a(y,z,z) * z) = a(y,z,z) \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(260,a,12266,a),flip(a)].">
      <j1 rule="hyper" parents="260 12266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,z,u))) = a(z,z,L(u,y * z,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,12056,a,b,12247,a),flip(a)].">
      <j1 rule="hyper" parents="325 12056 12247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (z * (y * R(T(x,z * y),T(x,z * y),u))) = a(T(x,z * y),T(x,z * y),L(u,y * T(x,z * y),z))
    ]]></literal>
    <justification jstring="[para(584(a,1),12274(a,1,1))].">
      <j1 rule="para" parents="584 12274"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      (x * (y * (z / u))) \ (x * (y * R(z / u,u \ z,w))) = a(z / u,z / u,L(w,y * (z / u),x))
    ]]></literal>
    <justification jstring="[para(9894(a,1),12274(a,1,2,2,2))].">
      <j1 rule="para" parents="9894 12274"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      R(x * (y * x),x * (y * x),y * L(y,x,x)) \ y = (1 / (x * (y * x))) * y
    ]]></literal>
    <justification jstring="[para(249(a,1),12263(a,1,1,3))].">
      <j1 rule="para" parents="249 12263"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      L(x * (y * x),x * (y * x),y * L(y,x,x)) \ y = (1 / (x * (y * x))) * y
    ]]></literal>
    <justification jstring="[para(11475(a,1),12277(a,1,1))].">
      <j1 rule="para" parents="11475 12277"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      L(x * (y * x),x * (y * x),a(x,x,y)) \ y = (1 / (x * (y * x))) * y
    ]]></literal>
    <justification jstring="[para(1639(a,1),12279(a,1,1))].">
      <j1 rule="para" parents="1639 12279"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      ((a(x,y,y) * y) * (a(x,y,y) \ (z / y))) \ (z / (a(x,y,y) * y)) = z \ (y \ (a(x,y,y) \ z))
    ]]></literal>
    <justification jstring="[para(12272(a,1),12265(a,1,1,2))].">
      <j1 rule="para" parents="12272 12265"/>
    </justification>
  </clause>

  <clause id="12282">
    <literal><![CDATA[
      (x * ((a(y,x,x) \ (z / x)) * a(y,x,x))) \ (z / (a(y,x,x) * x)) = z \ (x \ (a(y,x,x) \ z))
    ]]></literal>
    <justification jstring="[para(12260(a,1),12281(a,1,1))].">
      <j1 rule="para" parents="12260 12281"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      (x * (y / x)) \ (y / (a(z,x,x) * x)) = y \ (x \ (a(z,x,x) \ y))
    ]]></literal>
    <justification jstring="[para(7191(a,1),12282(a,1,1,2))].">
      <j1 rule="para" parents="7191 12282"/>
    </justification>
  </clause>

  <clause id="12285">
    <literal><![CDATA[
      (x * (y / x)) \ (a(z,x,x) \ (y / x)) = y \ (x \ (a(z,x,x) \ y))
    ]]></literal>
    <justification jstring="[para(12272(a,1),12283(a,1,2))].">
      <j1 rule="para" parents="12272 12283"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      a(x / y,x / y,L(z,y * (x / y),x)) = (1 / (y * (x / y))) * (y * R(x / y,y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,2439,a(flip),b,12276,a),flip(a)].">
      <j1 rule="hyper" parents="65 2439 12276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      a(x,y,(R(z,z,(u \ (w / v5)) * z) * (u \ (v5 \ w))) * v6) = a(x,y,(z * z) * ((z \ (u \ (w / v5))) * v6))
    ]]></literal>
    <justification jstring="[para(33(a,1),12014(a,2,3))].">
      <j1 rule="para" parents="33 12014"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x * u) = ((1 / (x * u)) * u) \ R((1 / (x * u)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(2662(a,1),12220(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2662 12220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x * u) = ((x * u) * u) \ R((x * u) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,4430,a(flip),b,12288,a),flip(a)].">
      <j1 rule="hyper" parents="325 4430 12288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x * u) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,11938,a(flip),b,12289,a),flip(a)].">
      <j1 rule="hyper" parents="325 11938 12289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u * x) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(2349,a,12291,a)].">
      <j1 rule="hyper" parents="2349 12291"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      (1 / (x * y)) * (x * R(y,z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11553,a(flip),b,12292,a)].">
      <j1 rule="hyper" parents="65 11553 12292"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      L((x / y) \ R(x / y,y \ x,z),y,y) = a(x / y,x / y,L(z,y * (x / y),x))
    ]]></literal>
    <justification jstring="[hyper(65,a,12286,a,b,12293,a),flip(a)].">
      <j1 rule="hyper" parents="65 12286 12293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      L(x \ (y * R(y \ x,x \ y,z)),x,x) = a(y / x,y / x,L(z,x * (y / x),y))
    ]]></literal>
    <justification jstring="[para(4241(a,1),12294(a,1,1))].">
      <j1 rule="para" parents="4241 12294"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      a(x / y,x / y,L(z,y * (x / y),x)) = L(a(y \ x,y \ x,z),y,y)
    ]]></literal>
    <justification jstring="[para(11592(a,1),12295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11592 12295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      a(x / y,x / y,L(z,y * (x / y),x)) = a(y \ x,y \ x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12056,a,b,12296,a),flip(a)].">
      <j1 rule="hyper" parents="325 12056 12296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      a(x,y,(R(z,z,(u \ (w / v5)) * z) * (u \ (v5 \ w))) * v6) = a(x,y,(z \ (u \ (w / v5))) * v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10075,a(flip),b,12287,a),flip(a)].">
      <j1 rule="hyper" parents="325 10075 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      a(x,y,(R(z,z,(u \ (w \ v5)) * z) * (u \ (w \ v5))) * v6) = a(x,y,(z \ (u \ (v5 / w))) * v6)
    ]]></literal>
    <justification jstring="[para(9681(a,1),12298(a,1,3,1,1))].">
      <j1 rule="para" parents="9681 12298"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      a(x,y,((z * z) * (z \ (u \ (w \ v5)))) * v6) = a(x,y,(z \ (u \ (v5 / w))) * v6)
    ]]></literal>
    <justification jstring="[para(12010(a,1),12300(a,1,3,1))].">
      <j1 rule="para" parents="12010 12300"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      a(x,y,(z * z) * ((z \ (u \ (w \ v5))) * v6)) = a(x,y,(z \ (u \ (v5 / w))) * v6)
    ]]></literal>
    <justification jstring="[para(33(a,1),12301(a,1,3))].">
      <j1 rule="para" parents="33 12301"/>
    </justification>
  </clause>

  <clause id="12303">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (w / v5))) * v6) = a(x,y,(z \ (u \ (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[hyper(10081,a,12302,a),flip(a)].">
      <j1 rule="hyper" parents="10081 12302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      L(x * (((y \ L(y,z,u)) \ 1) / (y \ L(y,z,u))),w,v5) = L(x,w,v5) * (y * (L(y,z,u) \ (L(y,z,u) \ y)))
    ]]></literal>
    <justification jstring="[para(1256(a,1),11767(a,2,2))].">
      <j1 rule="para" parents="1256 11767"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      L(x * (((y \ L(y,z,u)) \ 1) / (y \ L(y,z,u))),w,v5) = L(x,w,v5) * (y * (L(L(y,z,u),z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(11878(a,1),12305(a,2,2,2))].">
      <j1 rule="para" parents="11878 12305"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      L(x * (((y \ L(y,z,u)) \ 1) / (y \ L(y,z,u))),w,v5) = L(x,w,v5) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(11892(a,1),12306(a,2,2))].">
      <j1 rule="para" parents="11892 12306"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      L(x * ((L(y,z,u) \ y) / (y \ L(y,z,u))),w,v5) = L(x,w,v5) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(2015(a,1),12307(a,1,1,2,1))].">
      <j1 rule="para" parents="2015 12307"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      L(x * ((y \ L(y,z,u)) \ (L(y,z,u) \ y)),w,v5) = L(x,w,v5) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(8474(a,1),12308(a,1,1,2))].">
      <j1 rule="para" parents="8474 12308"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      L(x * (L(y,z,u) \ (y * (L(y,z,u) \ y))),w,v5) = L(x,w,v5) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(11765(a,1),12309(a,1,1,2))].">
      <j1 rule="para" parents="11765 12309"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      L(x * (y * (L(y,z,u) \ (L(y,z,u) \ y))),w,v5) = L(x,w,v5) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(1256(a,1),12310(a,1,1,2))].">
      <j1 rule="para" parents="1256 12310"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      L(x * (y * (L(L(y,z,u),z,u) \ 1)),w,v5) = L(x,w,v5) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(11878(a,1),12311(a,1,1,2,2))].">
      <j1 rule="para" parents="11878 12311"/>
    </justification>
  </clause>

  <clause id="12313">
    <literal><![CDATA[
      L(x * (L(L(y,z,u),z,u) \ y),w,v5) = L(x,w,v5) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(11892(a,1),12312(a,1,1,2))].">
      <j1 rule="para" parents="11892 12312"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      L(x * (L(L(y,z,u),z,u) \ y),w,v5) = y * (L(L(y,z,u),z,u) \ L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,11925,a(flip),b,12313,a),flip(a)].">
      <j1 rule="hyper" parents="325 11925 12313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x * (L(L(x,y,z),y,z) \ x),y,z))) \ 1 = L(L(x,y,z) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(12313(a,2),11927(a,1,1,2,2))].">
      <j1 rule="para" parents="12313 11927"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ L(L(L(x,y,z),y,z),u,w)) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),12314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      L(x * (L(L(x,y,z),y,z) \ x),y,z) = x * (L(x \ L(x,y,z),y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(4463(a,1),12314(a,2,2))].">
      <j1 rule="para" parents="4463 12314"/>
    </justification>
  </clause>

  <clause id="12318">
    <literal><![CDATA[
      L(x * (L(L(x,y,z),y,z) \ u),w,v5) = x * (L(L(x,y,z),y,z) \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(11925(a,1),12314(a,1,1))].">
      <j1 rule="para" parents="11925 12314"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      x * L(L(x,y,z) \ L(L(x,y,z),u,w),y,z) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(4458(a,1),12316(a,1,2))].">
      <j1 rule="para" parents="4458 12316"/>
    </justification>
  </clause>

  <clause id="12320">
    <literal><![CDATA[
      x * L(L(x \ L(x,y,z),u,w),u,w) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4458(a,1),12319(a,1,2,1))].">
      <j1 rule="para" parents="4458 12319"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),u,w) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,12320,a),flip(a)].">
      <j1 rule="hyper" parents="140 12320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      L(((x * y) * z) \ (x * (y * z)),z,x * y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(478(a,1),12321(a,1,1))].">
      <j1 rule="para" parents="478 12321"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      L(x \ (x / ((y \ L(y,z,u)) \ 1)),y \ L(y,z,u),x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1721(a,1),12321(a,1,1))].">
      <j1 rule="para" parents="1721 12321"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,w) = L(x \ L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(12321(a,1),11879(a,1,1,1))].">
      <j1 rule="para" parents="12321 11879"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(2015(a,1),12324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2015 12324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      L(x * (y * x),z,u) \ (x * (y * x)) = L(L(y,z,u) \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(8807,a,12325,a)].">
      <j1 rule="hyper" parents="8807 12325"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,z) = L(L(x,u,w) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4464,a,12325,a)].">
      <j1 rule="hyper" parents="4464 12325"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,4468,a,b,12325,a)].">
      <j1 rule="hyper" parents="65 4468 12325"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      L(L(x,L(x,y,z),u) \ x,y,z) = a(u,L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11718,a(flip),b,12325,a),flip(a)].">
      <j1 rule="hyper" parents="65 11718 12325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ 1 = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(41,a,8581,a,b,12325,a)].">
      <j1 rule="hyper" parents="41 8581 12325"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      L(R(x \ L(x,y,z),L(L(x,y,z) \ x,u,w),v5),u,w) \ (1 * v5) = (L(x \ L(x,y,z),u,w) \ 1) * v5
    ]]></literal>
    <justification jstring="[para(12325(a,1),739(a,1,1,1,2))].">
      <j1 rule="para" parents="12325 739"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w) \ (T(x,y) \ z),x \ z,x) = (z \ (T(x,y) * L(T(x,y) \ z,u,w))) \ 1
    ]]></literal>
    <justification jstring="[para(4990(a,1),12325(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 12325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      T(L(x,y,z) * L(L(x,y,z) \ x,u,w),L(x,y,z)) = L(x,u,w) * (L(L(x,u,w),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(12328(a,1),8433(a,1,1,2))].">
      <j1 rule="para" parents="12328 8433"/>
    </justification>
  </clause>

  <clause id="12334">
    <literal><![CDATA[
      L(x \ (x / (L(y,z,u) \ y)),y \ L(y,z,u),x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2015(a,1),12323(a,1,1,2,2))].">
      <j1 rule="para" parents="2015 12323"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      L(x \ ((L(y,z,u) \ y) \ x),y \ L(y,z,u),x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(7819(a,1),12334(a,1,1,2))].">
      <j1 rule="para" parents="7819 12334"/>
    </justification>
  </clause>

  <clause id="12336">
    <literal><![CDATA[
      L(x * (L(L(x,y,z),y,z) \ x),y,z) = x * ((x \ L(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(11859(a,1),12317(a,2,2,1))].">
      <j1 rule="para" parents="11859 12317"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      L(x * (L(L(x,y,z),y,z) \ x),y,z) = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2015(a,1),12336(a,2,2))].">
      <j1 rule="para" parents="2015 12336"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      L(x,y,L(z * (L(L(z,u,w),u,w) \ v5),v6,v7)) = L(x,y,L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(12318(a,2),11867(a,1,3))].">
      <j1 rule="para" parents="12318 11867"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      (L(x,y,z) * (x \ (x * (L(x,y,z) \ x)))) \ 1 = L(L(x,y,z) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(12337(a,1),12315(a,1,1,2,2))].">
      <j1 rule="para" parents="12337 12315"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) = x \ 1
    ]]></literal>
    <justification jstring="[para(77(a,1),12340(a,1,1)),flip(a)].">
      <j1 rule="para" parents="77 12340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      L(x * y,y,x) \ 1 = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(526,a,12341,a),flip(a)].">
      <j1 rule="hyper" parents="526 12341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12344">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) \ 1,u,w) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,2015,a(flip),b,12341,a),flip(a)].">
      <j1 rule="hyper" parents="325 2015 12341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,85,a(flip),b,12341,a),flip(a)].">
      <j1 rule="hyper" parents="325 85 12341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      L(R(L(x,y,z) \ 1,u,w),y,z) = R(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(12341(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12341 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      L(L(L(x,y,z) \ 1,u,w),y,z) = L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(12341(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12341 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      L(((x * y) \ z) \ 1,y,x) = (y \ (x \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(308(a,1),12341(a,1,1,1))].">
      <j1 rule="para" parents="308 12341"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),y,z) \ u) = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(12341(a,1),1523(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12341 1523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      (x / (L(y,z,u) \ 1)) * L(L(y,z,u) \ 1,z,u) = (y \ 1) * ((L(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(12341(a,1),8336(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12341 8336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) * ((L(x,y,z) \ 1) \ u) = (u * (x \ 1)) / (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(12341(a,1),8338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12341 8338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      (1 / L(x,y,z)) * (L(1 / L(x,y,z),y,z) \ u) = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(12341(a,1),9368(a,2,2,1))].">
      <j1 rule="para" parents="12341 9368"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ R(L(x,y,z) \ 1,u,w),y,z) = (x \ 1) \ L(R(L(x,y,z) \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(12341(a,1),11548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12341 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) = L(1 / z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(43,a,448,a,b,12345,a)].">
      <j1 rule="hyper" parents="43 448 12345"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ x),y,z) = x
    ]]></literal>
    <justification jstring="[para(4168(a,1),12345(a,1,1))].">
      <j1 rule="para" parents="4168 12345"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      L(1 / L(x,y,z),y,z) = 1 / x
    ]]></literal>
    <justification jstring="[para(6589(a,1),12345(a,1,1))].">
      <j1 rule="para" parents="6589 12345"/>
    </justification>
  </clause>

  <clause id="12359">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),x,z * y) \ a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2335,a,12357,a),flip(a)].">
      <j1 rule="hyper" parents="2335 12357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      L(L(x * (L(x,y,z) \ x),u,w),y,z) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(12357(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12357 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12361">
    <literal><![CDATA[
      (x \ (x * (L(x,y,z) \ x))) * L(L(x * (L(x,y,z) \ x),u,z),y,z) = L(x * (L(x,y,z) \ x),u,z)
    ]]></literal>
    <justification jstring="[para(12357(a,1),11862(a,1,1,1))].">
      <j1 rule="para" parents="12357 11862"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      L((x \ y) * T(x,x \ y),T(x,x \ y),x \ y) \ 1 = x \ ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(325,a,4858,a(flip),b,12342,a),flip(a)].">
      <j1 rule="hyper" parents="325 4858 12342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12363">
    <literal><![CDATA[
      L(x,y \ x,y) \ 1 = (y \ x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),12342(a,1,1,1))].">
      <j1 rule="para" parents="10 12342"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      L(x,y,L(z * u,u,z)) = L(x,y,u \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(12342(a,1),1499(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12342 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12365">
    <literal><![CDATA[
      a(x,y,L(L(z * u,u,z),w,v5)) = a(x,y,L(u \ (z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[para(12342(a,1),10453(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12342 10453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      ((x \ y) \ (x \ 1)) \ y = y * L(y,x \ y,x)
    ]]></literal>
    <justification jstring="[para(12363(a,1),8911(a,1,1))].">
      <j1 rule="para" parents="12363 8911"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      L((x \ y) \ 1,z \ x,z) = ((z \ x) \ (z \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),12349(a,1,1,1,1))].">
      <j1 rule="para" parents="10 12349"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      (x \ (y \ (z * (y * x)))) \ 1 = L(T(z,y * x) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),12349(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 12349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12369">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) \ 1 = L(y \ 1,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(170(a,1),12349(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="170 12349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / T(y,y \ (x \ ((x * y) * z))) = L(1 / z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(2895,a,12356,a)].">
      <j1 rule="hyper" parents="2895 12356"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      L(1 / T(x,y),y,z) \ 1 = y \ (x * (y * a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(11687(a,1),12356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11687 12356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      a(x,y,z) = L((L(1 / z,y,x) \ 1) / z,z,y)
    ]]></literal>
    <justification jstring="[para(12356(a,1),12107(a,2,1,1))].">
      <j1 rule="para" parents="12356 12107"/>
    </justification>
  </clause>

  <clause id="12373">
    <literal><![CDATA[
      L(x,y,L(z * u,u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1627,a(flip),b,12364,a),flip(a)].">
      <j1 rule="hyper" parents="325 1627 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      ((x \ y) \ (x \ 1)) \ y = x * ((x \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,414,a(flip),b,12366,a),flip(a)].">
      <j1 rule="hyper" parents="325 414 12366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      x * a(y,y \ 1,x) = (y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(41,a,6599,a,b,12369,a)].">
      <j1 rule="hyper" parents="41 6599 12369"/>
    </justification>
  </clause>

  <clause id="12376">
    <literal><![CDATA[
      a(x * L(y \ 1,z \ 1,z),u,w) = a(x * ((z \ 1) \ (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(12369(a,1),1890(a,1,1,2))].">
      <j1 rule="para" parents="12369 1890"/>
    </justification>
  </clause>

  <clause id="12377">
    <literal><![CDATA[
      L(x,L(y \ 1,z \ 1,z) \ 1,u) = L(x,(z \ 1) \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(12369(a,1),4394(a,1,2,1))].">
      <j1 rule="para" parents="12369 4394"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u \ 1,u) \ w) = a(x,y,((u \ 1) \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(12369(a,1),10368(a,1,3,1))].">
      <j1 rule="para" parents="12369 10368"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      a(x,y,z \ L(u \ 1,w \ 1,w)) = a(x,y,z \ ((w \ 1) \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(12369(a,1),10466(a,1,3,2))].">
      <j1 rule="para" parents="12369 10466"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      a(x,x \ 1,y) * y = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(7226,a,12375,a)].">
      <j1 rule="hyper" parents="7226 12375"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * a(y,z,u) = (x \ 1) \ (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[para(8979(a,1),12380(a,1,1))].">
      <j1 rule="para" parents="8979 12380"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      a(x,y,z) = L(z \ (L(1 / z,y,x) \ 1),z,y)
    ]]></literal>
    <justification jstring="[para(9372(a,1),12372(a,2,1))].">
      <j1 rule="para" parents="9372 12372"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[para(4169(a,1),12382(a,2,1))].">
      <j1 rule="para" parents="4169 12382"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      L(x,a(x,y,z),u) \ x = a(u,a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,11758,a(flip),b,12383,a)].">
      <j1 rule="hyper" parents="325 11758 12383"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      L(L(a(x,y,z),x,u) \ a(x,y,z),x,a(x,y,z)) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,11756,a(flip),b,12383,a)].">
      <j1 rule="hyper" parents="325 11756 12383"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      L(L(x,a(y,z,z),u) \ x,x,a(z,z,y)) = a(u,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,10715,a(flip),b,12383,a)].">
      <j1 rule="hyper" parents="325 10715 12383"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      L(L(a(x,y,z),z,u) \ a(x,y,z),z,a(x,y,z)) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10605,a(flip),b,12383,a)].">
      <j1 rule="hyper" parents="325 10605 12383"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      L(L(x,a(y * z,y,z),u) \ x,x,a(y,y,z)) = a(u,a(y * z,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,10536,a(flip),b,12383,a)].">
      <j1 rule="hyper" parents="325 10536 12383"/>
    </justification>
  </clause>

  <clause id="12389">
    <literal><![CDATA[
      L(L(L(x \ 1,y,z),x,u) \ L(x \ 1,y,z),x \ 1,L(x,y,z)) = a(u,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7466,a(flip),b,12383,a)].">
      <j1 rule="hyper" parents="325 7466 12383"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      x * (y * (L(y,x,z) \ y)) = (x * y) * a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,12383,a,b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 12383 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,y) = L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(12383(a,2),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12383 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      L(x,y,z) \ L(x * L(x,y,z),x,y) = L(x,y,z) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(12383(a,2),1339(a,2,2))].">
      <j1 rule="para" parents="12383 1339"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,u)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(12383(a,2),10556(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12383 10556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12394">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ w,v5) \ x,x,R(y,z,u) \ w) = a(v5,R(y,z,u) \ w,x)
    ]]></literal>
    <justification jstring="[para(11427(a,1),12383(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11427 12383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      L(L(x,L(y,z,u),w) \ x,x,L(y,z \ 1,u)) = a(w,L(y,z \ 1,u),x)
    ]]></literal>
    <justification jstring="[para(11801(a,1),12383(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11801 12383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = L(x,z,y) * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(12383(a,2),11954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12383 11954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),w,u)) = a(x,y,L(w,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(12383(a,2),12044(a,1,3,1))].">
      <j1 rule="para" parents="12383 12044"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(12383(a,2),12330(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12383 12330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      x \ (y * L(y \ x,y,z)) = a(z,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(538,a,12398,a)].">
      <j1 rule="hyper" parents="538 12398"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      (x * y) \ (x * L(y,x,z)) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,102,a(flip),b,12398,a)].">
      <j1 rule="hyper" parents="65 102 12398"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      (x * y) * (a(z,x,y) \ 1) = x * L(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12398,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="137 12398 102"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),x,y) = L(a(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(12398(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12398 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(12398(a,1),12321(a,1,1))].">
      <j1 rule="para" parents="12398 12321"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      L(a(x,y,R(z,u,w)) \ 1,L(z,u,w),y) = R(z,u,w) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(11051,a,12403,a)].">
      <j1 rule="hyper" parents="11051 12403"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      (x * y) * (y \ L(y,x,z)) = x * (y * (a(z,x,y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(137,a,12403,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 12403 18"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      L(a(x,x \ L(x,y,z),u) \ 1,u,x) = u \ L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8810(a,1),12403(a,1,1,1))].">
      <j1 rule="para" parents="8810 12403"/>
    </justification>
  </clause>

  <clause id="12407">
    <literal><![CDATA[
      L(a(x,y,L(z,z,u)) \ 1,L(z,z,z * u),y) = L(z,z,z * u) \ L(L(z,z,z * u),y,x)
    ]]></literal>
    <justification jstring="[para(11269(a,1),12403(a,1,1,1))].">
      <j1 rule="para" parents="11269 12403"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      a(x,x,a(y,x,z) \ 1) \ (z \ L(z,x,y)) = L(L(a(y,x,z) \ 1,z,x),x,x)
    ]]></literal>
    <justification jstring="[para(12403(a,1),11812(a,1,2))].">
      <j1 rule="para" parents="12403 11812"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      (x * L(y,x,z)) / (x * y) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,12401,a(flip),b,8489,a)].">
      <j1 rule="hyper" parents="135 12401 8489"/>
    </justification>
  </clause>

  <clause id="12411">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ 1,a(x,y,z) \ 1,y * z) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(12401(a,1),225(a,2,1))].">
      <j1 rule="para" parents="12401 225"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      (x * y) \ (L(x,y,z) * y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,9069,a(flip),b,12410,a)].">
      <j1 rule="hyper" parents="65 9069 12410"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      x \ (y * (L(y,z,u) \ ((y \ L(y,z,u)) * x))) = a(y * L(y,z,u),y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(1796(a,1),12399(a,1,2,2))].">
      <j1 rule="para" parents="1796 12399"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      L(L(L(x,L(y,z,u),y) \ x,w,v5),x,L(y,z,u)) = L(a(L(y,z,u),y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(7452(a,2),12391(a,2,1))].">
      <j1 rule="para" parents="7452 12391"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      L(L(L(x,y,a(z,u,y)) \ x,w,v5),x,a(z,u,y)) = L(a(y,a(z,u,y),x),w,v5)
    ]]></literal>
    <justification jstring="[para(10605(a,1),12391(a,1,1,1,1))].">
      <j1 rule="para" parents="10605 12391"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),w,u)) = a(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7497,a(flip),b,12397,a),flip(a)].">
      <j1 rule="hyper" parents="325 7497 12397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),u,w) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(12325(a,1),12344(a,1,1))].">
      <j1 rule="para" parents="12325 12344"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      L(a(x,y,z),z,y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,12391,a(flip),b,12417,a)].">
      <j1 rule="hyper" parents="65 12391 12417"/>
    </justification>
  </clause>

  <clause id="12419">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),z,y) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(12418(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12418 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      L(a(x,y \ L(y,z,u),y),y,y \ L(y,z,u)) = ((x * (y \ L(y,z,u))) \ (x * L(y,z,u))) \ y
    ]]></literal>
    <justification jstring="[para(1758(a,2),12418(a,2,1))].">
      <j1 rule="para" parents="1758 12418"/>
    </justification>
  </clause>

  <clause id="12421">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),y,L(y,z,u)) = L(y,L(y,z,u),x) \ y
    ]]></literal>
    <justification jstring="[para(7454(a,1),12418(a,1,1))].">
      <j1 rule="para" parents="7454 12418"/>
    </justification>
  </clause>

  <clause id="12422">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w) \ 1,x,y) = L(a(z,y,x),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(12419(a,1),12341(a,1,1,1))].">
      <j1 rule="para" parents="12419 12341"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      T(L(1 / x,y,z) \ 1,y) = y \ (x * (y * a(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(10787,a,12371,a)].">
      <j1 rule="hyper" parents="10787 12371"/>
    </justification>
  </clause>

  <clause id="12424">
    <literal><![CDATA[
      (x * y) * (y \ L(y,x,z)) = x * (a(z,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(10574(a,1),12405(a,2,2))].">
      <j1 rule="para" parents="10574 12405"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      x * (a(y,x,x \ z) \ (x \ z)) = z * ((x \ z) \ L(x \ z,x,y))
    ]]></literal>
    <justification jstring="[hyper(528,a,12424,a),flip(a)].">
      <j1 rule="hyper" parents="528 12424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ x),y) = y \ (x * (y * a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(4168(a,1),12423(a,1,1))].">
      <j1 rule="para" parents="4168 12423"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      T((L(x,y,z) \ x) * x,y) = y \ (x * (y * a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(7826(a,1),12423(a,1,1))].">
      <j1 rule="para" parents="7826 12423"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      a(x,y,(z \ (u * (z * a(w,z,u)))) \ v5) = a(x,y,(L(1 / u,z,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(12423(a,1),10056(a,1,3,1))].">
      <j1 rule="para" parents="12423 10056"/>
    </justification>
  </clause>

  <clause id="12429">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * y = x * (y * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(149,a,12426,a)].">
      <j1 rule="hyper" parents="149 12426"/>
    </justification>
  </clause>

  <clause id="12430">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * (w * (L(w,z,v5) \ w)))) * v6) = a(x,y,(w * (z * a(v5,z,w))) * v6)
    ]]></literal>
    <justification jstring="[para(12429(a,1),10512(a,2,3,1))].">
      <j1 rule="para" parents="12429 10512"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ x),z * y) = y \ (z \ (x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(41,a,9804,a,b,12368,a)].">
      <j1 rule="hyper" parents="41 9804 12368"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      L(T(a(x,y,z),(y * z) * x) \ 1,x,y * z) = (x \ ((y * z) \ ((y * z) * R(x,y,z)))) \ 1
    ]]></literal>
    <justification jstring="[para(7258(a,1),12368(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7258 12368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      K(((x \ (y \ (z * (y * x)))) \ u) * K(y * x,z * (L(z,x,y) \ z)),w) = K((z * (L(z,x,y) \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(12431(a,1),9460(a,1,1,1,1))].">
      <j1 rule="para" parents="12431 9460"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      (x \ 1) \ (x \ a(y,z,u)) = x \ ((1 / x) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11961,a,b,12381,a),flip(a)].">
      <j1 rule="hyper" parents="65 11961 12381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12439">
    <literal><![CDATA[
      (x \ a(y,z,u)) / (x \ 1) = x \ ((1 / x) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7217,a,b,12438,a)].">
      <j1 rule="hyper" parents="65 7217 12438"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      L(x,L(x,y,z),u) \ x = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10594,a,12421,a),flip(a)].">
      <j1 rule="hyper" parents="10594 12421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ y = L(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(41,a,7205,a,b,12440,a)].">
      <j1 rule="hyper" parents="41 7205 12440"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = L(a(x,y,L(y,z,u)),z,u)
    ]]></literal>
    <justification jstring="[para(12440(a,1),12329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12440 12329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12444">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,y,z)) = a(x,L(u,y,z),L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(11562,a,12443,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11562 12443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      a(x,y,L(L(z * u,u,z),w,v5)) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10553,a(flip),b,12365,a),flip(a)].">
      <j1 rule="hyper" parents="325 10553 12365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),u,z)) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10508,a,12445,a)].">
      <j1 rule="hyper" parents="10508 12445"/>
    </justification>
  </clause>

  <clause id="12447">
    <literal><![CDATA[
      L(x,L(y \ 1,z,z) \ 1,u) = L(x,(z \ 1) \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11428,a(flip),b,12377,a)].">
      <j1 rule="hyper" parents="65 11428 12377"/>
    </justification>
  </clause>

  <clause id="12448">
    <literal><![CDATA[
      L(x,(y \ 1) \ (y \ z),a(u,w,v5)) = L(x,L(z \ 1,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10958,a,12447,a),flip(a)].">
      <j1 rule="hyper" parents="10958 12447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),x,y) = L(a(z,y,x),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(12330(a,1),12422(a,1,1))].">
      <j1 rule="para" parents="12330 12422"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = L(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12402,a(flip),b,12449,a)].">
      <j1 rule="hyper" parents="65 12402 12449"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),x * (y * z)) \ 1 = ((x * y) * z) \ ((x * (y * z)) * 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,711,a(flip),b,12450,a),flip(a)].">
      <j1 rule="hyper" parents="65 711 12450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,z,u)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,11970,a,b,12450,a(flip))].">
      <j1 rule="hyper" parents="41 11970 12450"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ a(x,y,z)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(41,a,6594,a,b,12450,a(flip))].">
      <j1 rule="hyper" parents="41 6594 12450"/>
    </justification>
  </clause>

  <clause id="12455">
    <literal><![CDATA[
      (x \ a(y,z,u)) / (x \ 1) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12439,a,b,12452,a)].">
      <j1 rule="hyper" parents="65 12439 12452"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      ((x \ 1) \ L(a(y,z,u),x,x)) * (x \ 1) = x \ T((1 / x) \ a(y,z,u),x \ 1)
    ]]></literal>
    <justification jstring="[para(12452(a,1),5109(a,1,1,2))].">
      <j1 rule="para" parents="12452 5109"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(x,y,z) \ L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(140,a,12453,a),flip(a)].">
      <j1 rule="hyper" parents="140 12453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      L(a(x,x,y),z,u) \ a(x,x,y) = a(x,x,y) \ a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,12056,a,b,12453,a),flip(a)].">
      <j1 rule="hyper" parents="132 12056 12453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12453(a,1),12357(a,1,1))].">
      <j1 rule="para" parents="12453 12357"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      L(a(x,y,z),x,z * y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2335,a,12459,a),flip(a)].">
      <j1 rule="hyper" parents="2335 12459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      L(a(x,y,z),x,y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1908,a,12459,a),flip(a)].">
      <j1 rule="hyper" parents="1908 12459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      x * (y * L(a(z,u,w),y,x)) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,12459,a(flip),b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 12459 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(12459(a,1),307(a,1,2,2))].">
      <j1 rule="para" parents="12459 307"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      L(a(x,y,y \ z),x,z) = x \ R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(2350,a,12460,a)].">
      <j1 rule="hyper" parents="2350 12460"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      L(a(x,y,z),x,z * y) = L(x \ R(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[para(12460(a,1),10568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12460 10568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12466">
    <literal><![CDATA[
      L(a(x,y,y \ L(z,u,w)),x,R(z,u,w)) = x \ R(x,y,y \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(11384(a,1),12464(a,1,1))].">
      <j1 rule="para" parents="11384 12464"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12460,a(flip),b,12465,a),flip(a)].">
      <j1 rule="hyper" parents="65 12460 12465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12468">
    <literal><![CDATA[
      L(x,y,z) * (x \ R(x,u,z)) = L(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12467,a(flip),b,11548,a)].">
      <j1 rule="hyper" parents="137 12467 11548"/>
    </justification>
  </clause>

  <clause id="12469">
    <literal><![CDATA[
      R(x,y,z) * (x \ R(x,u,z)) = R(R(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12467,a(flip),b,9229,a)].">
      <j1 rule="hyper" parents="137 12467 9229"/>
    </justification>
  </clause>

  <clause id="12470">
    <literal><![CDATA[
      L(x,y,z) * R(x \ 1,u,z) = x * L(R(x \ 1,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12468,a(flip),b,4133,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 12468 4133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12471">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / x) * L(T(x,x \ R(x,y,z)),u,z) = L(R(x,y,z),u,z) / x
    ]]></literal>
    <justification jstring="[para(12468(a,1),1941(a,2,1))].">
      <j1 rule="para" parents="12468 1941"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      (x \ y) * L(a(z,u,w),x \ y,x) = x \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,155,a(flip),b,12462,a),flip(a)].">
      <j1 rule="hyper" parents="132 155 12462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      x * (L(a(y,z,u),w,x) * w) = (x * w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(7227(a,2),12462(a,1,2))].">
      <j1 rule="para" parents="7227 12462"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      x * ((y \ 1) * L(a(z,u,w),y,x)) = (x * (y \ 1)) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(8977(a,1),12462(a,1,2,2))].">
      <j1 rule="para" parents="8977 12462"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,w,v5)) = (a(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(11782(a,1),12472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11782 12472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12476">
    <literal><![CDATA[
      L(x,y,z) * R(x \ 1,u,z) = x \ L(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1327,a(flip),b,12470,a),flip(a)].">
      <j1 rule="hyper" parents="325 1327 12470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      a(x,y,(z \ L(R(z,u,w),u,w)) * v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(12476(a,1),11379(a,1,3,1))].">
      <j1 rule="para" parents="12476 11379"/>
    </justification>
  </clause>

  <clause id="12478">
    <literal><![CDATA[
      x * (a(y,z,u) \ L(a(y,z,u),a(y,z,u),x)) = (x * (a(y,z,u) \ 1)) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(7241(a,1),12474(a,1,2))].">
      <j1 rule="para" parents="7241 12474"/>
    </justification>
  </clause>

  <clause id="12479">
    <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="[para(12056(a,2),12458(a,1,1))].">
      <j1 rule="para" parents="12056 12458"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      a(x,y,z) * ((x \ R(x,y,z)) \ a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12460(a,1),12359(a,1,2,1))].">
      <j1 rule="para" parents="12460 12359"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (R(x,y,z) \ x)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5805(a,1),12480(a,1,2))].">
      <j1 rule="para" parents="5805 12480"/>
    </justification>
  </clause>

  <clause id="12482">
    <literal><![CDATA[
      a(x * L(y \ 1,z \ 1,z),u,w) = a((z \ (z \ y)) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,5033,a(flip),b,12376,a),flip(a)].">
      <j1 rule="hyper" parents="325 5033 12376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12483">
    <literal><![CDATA[
      a(x * L(y,z \ 1,z),u,w) = a((z \ (z \ y)) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1909,a(flip),b,12482,a)].">
      <j1 rule="hyper" parents="65 1909 12482"/>
    </justification>
  </clause>

  <clause id="12484">
    <literal><![CDATA[
      a(x * (((y \ 1) * z) * y),u,w) = a((y \ (y \ z)) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,3516,a,b,12483,a)].">
      <j1 rule="hyper" parents="65 3516 12483"/>
    </justification>
  </clause>

  <clause id="12485">
    <literal><![CDATA[
      a((x \ (x \ y)) * z,u,w) = a(z * ((x * y) * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,4291,a(flip),b,12484,a),flip(a)].">
      <j1 rule="hyper" parents="65 4291 12484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12486">
    <literal><![CDATA[
      a((x \ (x \ y)) * z,u,w) = a(z * R(y,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2441,a(flip),b,12485,a),flip(a)].">
      <j1 rule="hyper" parents="325 2441 12485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12487">
    <literal><![CDATA[
      a((x \ (x \ y)) * z,u,w) = a(z * L(y,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11282,a(flip),b,12486,a),flip(a)].">
      <j1 rule="hyper" parents="325 11282 12486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      a(x * L(y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2585,a,12487,a),flip(a)].">
      <j1 rule="hyper" parents="2585 12487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      a(x * (y \ (y \ z)),u,w) = a(x * L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(2363,a,12487,a)].">
      <j1 rule="hyper" parents="2363 12487"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      a(L(x,y,y) * y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2363,a,12488,a)].">
      <j1 rule="hyper" parents="2363 12488"/>
    </justification>
  </clause>

  <clause id="12492">
    <literal><![CDATA[
      a(x * L(y * z,y * z,z),u,w) = a(x * L(y \ z,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11259,a,b,12489,a)].">
      <j1 rule="hyper" parents="65 11259 12489"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ (z \ u)) \ w) = a(x,y,L(u,z \ 1,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10688,a(flip),b,12378,a),flip(a)].">
      <j1 rule="hyper" parents="65 10688 12378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12497">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,u) \ w) = a(x,y,(u \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10452,a(flip),b,12496,a),flip(a)].">
      <j1 rule="hyper" parents="65 10452 12496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12498">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,u) \ w) = a(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,12037,a(flip),b,12497,a),flip(a)].">
      <j1 rule="hyper" parents="325 12037 12497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12499">
    <literal><![CDATA[
      a(x,y,z \ L(u \ 1,w \ 1,w)) = a(x,y,z \ (w \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10463,a(flip),b,12379,a),flip(a)].">
      <j1 rule="hyper" parents="325 10463 12379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12500">
    <literal><![CDATA[
      a(x,y,z \ L(u \ 1,w,w)) = a(x,y,z \ (w \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10698,a(flip),b,12499,a)].">
      <j1 rule="hyper" parents="65 10698 12499"/>
    </justification>
  </clause>

  <clause id="12501">
    <literal><![CDATA[
      a(x,y,z \ (u \ (u \ w))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10496,a(flip),b,12500,a),flip(a)].">
      <j1 rule="hyper" parents="65 10496 12500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12502">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,u,u)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(9(a,1),12501(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 12501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w,u \ 1,u))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10672,a,b,12502,a)].">
      <j1 rule="hyper" parents="65 10672 12502"/>
    </justification>
  </clause>

  <clause id="12504">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ 1,w) * w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(10157,a,12503,a)].">
      <j1 rule="hyper" parents="10157 12503"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,w) * w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(11203,a,12504,a)].">
      <j1 rule="hyper" parents="11203 12504"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      a(x,y,R(z / u,u,z \ (L(w,v5,v5) * v5)) \ (v5 \ w)) = a(x,y,u * (z \ (L(w,v5,v5) * v5)))
    ]]></literal>
    <justification jstring="[para(480(a,1),12505(a,1,3)),flip(a)].">
      <j1 rule="para" parents="480 12505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      L(a(x,y,z),x,u) \ a(x,y,z) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10569,a,12385,a),flip(a)].">
      <j1 rule="hyper" parents="10569 12385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12509">
    <literal><![CDATA[
      a(x,y,z) * a(u,x,a(x,y,z)) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,12507,a(flip),b,12457,a(flip))].">
      <j1 rule="hyper" parents="137 12507 12457"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      L(a(x,y,z),x,u) \ a(x,y,z) = a(x \ u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11070(a,1),12507(a,1,1))].">
      <j1 rule="para" parents="11070 12507"/>
    </justification>
  </clause>

  <clause id="12511">
    <literal><![CDATA[
      a(x,y,z) * a(y * z,x,a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,12461,a(flip),b,12509,a),flip(a)].">
      <j1 rule="hyper" parents="325 12461 12509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      a(x,y,z) * (R(x,y,z) \ x) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,12481,a,b,12511,a)].">
      <j1 rule="hyper" parents="36 12481 12511"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      (R(x,y,z) \ x) * a(x,y,z) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10766,a,12512,a)].">
      <j1 rule="hyper" parents="10766 12512"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(y * z,x,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12512,a(flip),b,5805,a)].">
      <j1 rule="hyper" parents="137 12512 5805"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      L(a(x * y,z,a(z,x,y)),z \ R(z,x,y),z) * R(z,x,y) = z * a(z,x,y)
    ]]></literal>
    <justification jstring="[para(12514(a,1),7231(a,2,2))].">
      <j1 rule="para" parents="12514 7231"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      a(x \ y,x,a(x,z,u)) = a(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12507,a(flip),b,12510,a),flip(a)].">
      <j1 rule="hyper" parents="65 12507 12510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      a(x * y,y,a(y,z,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1877,a,12516,a),flip(a)].">
      <j1 rule="hyper" parents="1877 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      (x / y) \ (x * a(y,z,u)) = (y * a(y,z,u)) * a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,12516,a(flip),b,11632,a),flip(a)].">
      <j1 rule="hyper" parents="137 12516 11632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      (x / y) \ (x * a(y,z,u)) = x \ ((x * y) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,11624,a,b,12518,a),flip(a)].">
      <j1 rule="hyper" parents="325 11624 12518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12520">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ a(x,y,z) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10569,a,12387,a),flip(a)].">
      <j1 rule="hyper" parents="10569 12387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12522">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,u) \ (a(x,y,z) \ 1) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1518,a,b,12520,a)].">
      <j1 rule="hyper" parents="65 1518 12520"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),z,u) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12457,a(flip),b,12520,a)].">
      <j1 rule="hyper" parents="65 12457 12520"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      a(x,y,z) * a(u,z,a(x,y,z)) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,12520,a(flip),b,12457,a(flip))].">
      <j1 rule="hyper" parents="137 12520 12457"/>
    </justification>
  </clause>

  <clause id="12525">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),z,u) = a(u,z,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(12520(a,1),6998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12520 6998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12418(a,1),12523(a,1,2))].">
      <j1 rule="para" parents="12418 12523"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(y,z,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(12418(a,1),12525(a,1,2))].">
      <j1 rule="para" parents="12418 12525"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(a(x,y,z) \ 1,z,u) = a(u,z,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(12522(a,1),6998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12522 6998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),u) \ 1 = u \ L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11806,a(flip),b,12406,a)].">
      <j1 rule="hyper" parents="65 11806 12406"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) \ x = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(41,a,6998,a,b,12529,a)].">
      <j1 rule="hyper" parents="41 6998 12529"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      L(x,(y \ 1) \ (y \ z),a(u,w,v5)) = L(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,11065,a(flip),b,12448,a),flip(a)].">
      <j1 rule="hyper" parents="325 11065 12448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12533">
    <literal><![CDATA[
      L(x,y \ (y \ z),a(u,w,v5)) = L(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(11010,a,12532,a)].">
      <j1 rule="hyper" parents="11010 12532"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      L(x,L(y * a(z,u,w),a(z,u,w),a(z,u,w)),a(v5,v6,v7)) = L(x,a(z,u,w) \ y,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(7193(a,1),12533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7193 12533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12535">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (z \ L(z,y,x)) = a(y,z,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(12403(a,1),12528(a,1,2))].">
      <j1 rule="para" parents="12403 12528"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      (a(x,y,z) \ z) \ L(z,y,x) = a(y,z,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,8660,a(flip),b,12535,a)].">
      <j1 rule="hyper" parents="65 8660 12535"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ z) \ L(z,y,x)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(137,a,12536,a,b,12527,a)].">
      <j1 rule="hyper" parents="137 12536 12527"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      a(x,y,z) * ((z / a(x,y,z)) \ L(z,y,x)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(7194(a,2),12537(a,1,2,1))].">
      <j1 rule="para" parents="7194 12537"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (a(z,y,x) * a(z,y,x)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,9217,a,b,12538,a)].">
      <j1 rule="hyper" parents="65 9217 12538"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ x = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,11894,a,b,12539,a)].">
      <j1 rule="hyper" parents="40 11894 12539"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      x / (a(y,z,u) * a(y,z,u)) = x * (u \ L(L(u,z,y),z,y))
    ]]></literal>
    <justification jstring="[para(12540(a,1),11895(a,1,2))].">
      <j1 rule="para" parents="12540 11895"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(12540(a,1),11903(a,1,1))].">
      <j1 rule="para" parents="12540 11903"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) * a(x,y,z \ L(z,u,w)) = (z \ L(z,u,w)) \ (z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(12321(a,1),12540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12321 12540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(x,y,z) \ u) = u * (z \ L(L(z,y,x),y,x))
    ]]></literal>
    <justification jstring="[hyper(8980,a,12541,a)].">
      <j1 rule="hyper" parents="8980 12541"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u = u * (z \ L(L(z,y,x),y,x))
    ]]></literal>
    <justification jstring="[hyper(8666,a,12541,a)].">
      <j1 rule="hyper" parents="8666 12541"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ z) = z * (z \ L(L(z,y,x),y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,10576,a(flip),b,12541,a)].">
      <j1 rule="hyper" parents="65 10576 12541"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      a(x,y,z) * (u * (z \ L(L(z,y,x),y,x))) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(137,a,12541,a(flip),b,8662,a)].">
      <j1 rule="hyper" parents="137 12541 8662"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      (x * (y \ L(L(y,z,u),z,u))) \ w = x \ ((a(u,z,y) * a(u,z,y)) * w)
    ]]></literal>
    <justification jstring="[para(12545(a,1),554(a,1,1))].">
      <j1 rule="para" parents="12545 554"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ z) = L(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,10,a(flip),b,12546,a),flip(a)].">
      <j1 rule="hyper" parents="325 10 12546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * a(z,y,x) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(7208,a,12549,a)].">
      <j1 rule="hyper" parents="7208 12549"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ a(z,u,w) = a(z,u,w) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(12459(a,1),12550(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12459 12550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      T(x,(y * (z \ L(L(z,u,w),u,w))) \ (a(w,u,z) \ v5)) = T(x,((a(w,u,z) \ 1) * y) \ v5)
    ]]></literal>
    <justification jstring="[para(12547(a,1),7973(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12547 7973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(41,a,10584,a,b,12552,a)].">
      <j1 rule="hyper" parents="41 10584 12552"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      L(L(x,L(y,z,u),w) \ x,x,L(y,z,u)) = a(w,L(y,z \ 1,u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11796,a(flip),b,12395,a)].">
      <j1 rule="hyper" parents="65 11796 12395"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      a(x,L(y,z \ 1,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12383,a,b,12555,a),flip(a)].">
      <j1 rule="hyper" parents="65 12383 12555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      L(a(x,y,y * L(y,z,u)),x,R(y,z,u)) = x \ R(x,y,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(7498(a,1),12466(a,1,1))].">
      <j1 rule="para" parents="7498 12466"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      (x * (y \ L(L(y,z,u),z,u))) \ w = x \ (y * (L(L(y,z,u),z,u) \ w))
    ]]></literal>
    <justification jstring="[para(12542(a,1),12548(a,2,2))].">
      <j1 rule="para" parents="12542 12548"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      L(a(x,y,y * L(y,z,u)),x,L(y,z,u)) = x \ R(x,y,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9932,a,12557,a)].">
      <j1 rule="hyper" parents="9932 12557"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      (x * (y \ L(L(y,z,u),z,u))) \ w = y * (L(L(y,z,u),z,u) \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,11923,a(flip),b,12558,a),flip(a)].">
      <j1 rule="hyper" parents="325 11923 12558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      L(x,T(y,y \ x),y \ x) \ 1 = y \ ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(231(a,1),12362(a,1,1,1))].">
      <j1 rule="para" parents="231 12362"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      L(x,y,y \ x) \ 1 = y \ ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(5233(a,1),12561(a,1,1))].">
      <j1 rule="para" parents="5233 12561"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / T(y,L(1 / z,y,x) \ 1) = L(1 / z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(12356(a,1),12370(a,1,2,2))].">
      <j1 rule="para" parents="12356 12370"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / T(y,(1 / z) \ 1) = L(1 / z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(8847(a,1),12564(a,1,2))].">
      <j1 rule="para" parents="8847 12564"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / T(y,z) = L(1 / z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(85(a,1),12565(a,1,2,2))].">
      <j1 rule="para" parents="85 12565"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      (x \ (y * z)) / T(x \ y,z) = L(1 / z,x \ y,x) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),12566(a,1,1,2,1))].">
      <j1 rule="para" parents="10 12566"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)) \ 1,L(z,u,w),y) = R(z,u,w) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(10407(a,1),12404(a,1,1,1))].">
      <j1 rule="para" parents="10407 12404"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z),u,w) = L(x,y,z) \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12403,a(flip),b,12569,a),flip(a)].">
      <j1 rule="hyper" parents="65 12403 12569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z),u,w) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,4458,a(flip),b,12570,a),flip(a)].">
      <j1 rule="hyper" parents="325 4458 12570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ R(x,y,z) = L(x \ L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(12571(a,1),2015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12571 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ R(x,y,z) = L(L(x,u,w) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,12325,a(flip),b,12574,a),flip(a)].">
      <j1 rule="hyper" parents="325 12325 12574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x * u) = L(u * ((x * u) \ 1),y,z) \ (u * ((x * u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,5778,a(flip),b,12575,a),flip(a)].">
      <j1 rule="hyper" parents="65 5778 12575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      a(x,x,a(y,x,z)) \ (z \ L(z,x,y)) = L(L(a(y,x,z) \ 1,z,x),x,x)
    ]]></literal>
    <justification jstring="[para(7484(a,1),12409(a,1,1))].">
      <j1 rule="para" parents="7484 12409"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      a(x,x,a(y,x,z)) \ (z \ L(z,x,y)) = L(z \ L(z,x,y),x,x)
    ]]></literal>
    <justification jstring="[para(12403(a,1),12577(a,2,1))].">
      <j1 rule="para" parents="12403 12577"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ 1,y * z) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(7181(a,1),12411(a,1,1))].">
      <j1 rule="para" parents="7181 12411"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),y * z) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8977,a(flip),b,12579,a)].">
      <j1 rule="hyper" parents="65 8977 12579"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      L(L(L(x,y,L(y,z,u)) \ x,w,v5),x,L(y,z,u)) = L(a(L(y,z,u),y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(7460(a,1),12414(a,1,1,1,1))].">
      <j1 rule="para" parents="7460 12414"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      L(L(x,y,a(z,u,y)) \ x,w,v5) = L(a(y,a(z,u,y),x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11851,a(flip),b,12415,a)].">
      <j1 rule="hyper" parents="65 11851 12415"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) \ x = a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(43,a,11851,a(flip),b,12415,a(flip))].">
      <j1 rule="hyper" parents="43 11851 12415"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ u = L(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(41,a,7205,a,b,12584,a)].">
      <j1 rule="hyper" parents="41 7205 12584"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ 1 = u \ L(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(12584(a,1),6998(a,1,1))].">
      <j1 rule="para" parents="12584 6998"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      (x \ L(x,y,a(z,u,y))) \ y = y * a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(12584(a,1),11877(a,2,2))].">
      <j1 rule="para" parents="12584 11877"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      a(x,y,(z \ (u * (z * a(w,z,u)))) \ v5) = a(x,y,L(1 / u,z,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10368,a(flip),b,12428,a),flip(a)].">
      <j1 rule="hyper" parents="325 10368 12428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      a(x,y,(z \ (u * (z * a(w,z,u)))) \ v5) = a(x,y,L(u \ 1,z,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10109,a(flip),b,12589,a),flip(a)].">
      <j1 rule="hyper" parents="325 10109 12589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      a(x,y,(z \ (u * (z * a(w,z,u)))) \ v5) = a(x,y,L(u,z,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10688,a(flip),b,12590,a),flip(a)].">
      <j1 rule="hyper" parents="325 10688 12590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      L(a(x * y,z,a(z,x,y)),z,z * R(z,x,y)) * R(z,x,y) = z * a(z,x,y)
    ]]></literal>
    <justification jstring="[para(5407(a,1),12515(a,1,1))].">
      <j1 rule="para" parents="5407 12515"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      L(L(x,y,L(y,z,u)) \ x,w,v5) = L(a(L(y,z,u),y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11851,a(flip),b,12582,a)].">
      <j1 rule="hyper" parents="65 11851 12582"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      L(L(x,y,L(y,z,u)) \ x,w,v5) = L(a(y,L(y,z,u),x),w,v5)
    ]]></literal>
    <justification jstring="[para(7452(a,1),12593(a,2,1))].">
      <j1 rule="para" parents="7452 12593"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) \ x = a(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(52,a,12595,a)].">
      <j1 rule="hyper" parents="52 12595"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ u = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,7205,a,b,12596,a)].">
      <j1 rule="hyper" parents="41 7205 12596"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),y * z) \ 1 = ((x * y) * z) \ ((x * (y * z)) * 1)
    ]]></literal>
    <justification jstring="[para(12169(a,1),12451(a,1,1))].">
      <j1 rule="para" parents="12169 12451"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      ((x * L(y,x,z)) \ (x * y)) \ 1 = ((z * x) * y) \ ((z * (x * y)) * 1)
    ]]></literal>
    <justification jstring="[para(12580(a,1),12598(a,1,1))].">
      <j1 rule="para" parents="12580 12598"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      ((x * L(y,x,z)) \ (x * y)) \ 1 = ((z * x) * y) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,160,a(flip),b,12599,a),flip(a)].">
      <j1 rule="hyper" parents="325 160 12599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      x \ T((1 / x) \ a(y,z,u),x \ 1) = (((x \ 1) \ 1) * a(y,z,u)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4399(a,1),12456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4399 12456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      x \ T((1 / x) \ a(y,z,u),x \ 1) = ((x \ 1) \ 1) * (a(y,z,u) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(325,a,7677,a(flip),b,12601,a),flip(a)].">
      <j1 rule="hyper" parents="325 7677 12601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      x \ T((1 / x) \ a(y,z,u),x \ 1) = x * ((1 / x) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,7282,a(flip),b,12602,a),flip(a)].">
      <j1 rule="hyper" parents="325 7282 12602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      R((x \ x) / x,y,z) * L(T(x,x \ R(x,y,z)),u,z) = L(R(x,y,z),u,z) / x
    ]]></literal>
    <justification jstring="[para(1075(a,2),12471(a,1,1))].">
      <j1 rule="para" parents="1075 12471"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x * u) = L(u * (x * u),y,z) \ (u * (x * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,9260,a(flip),b,12576,a),flip(a)].">
      <j1 rule="hyper" parents="325 9260 12576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x * u) = L(L(x,y,z) \ x,u,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,12326,a(flip),b,12605,a),flip(a)].">
      <j1 rule="hyper" parents="325 12326 12605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,u),x,y) = L(a(z,y,x),u,x * u)
    ]]></literal>
    <justification jstring="[para(12606(a,1),12391(a,1,1))].">
      <j1 rule="para" parents="12606 12391"/>
    </justification>
  </clause>

  <clause id="12608">
    <literal><![CDATA[
      L(a(x,y,z),u,z * u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12391,a(flip),b,12607,a),flip(a)].">
      <j1 rule="hyper" parents="65 12391 12607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12609">
    <literal><![CDATA[
      ((x * y) * (y * a(z,u,x))) / ((y * y) * L(a(z,u,x),y,y)) = R(R(x,y,y),y * y,L(a(z,u,x),y,x * y))
    ]]></literal>
    <justification jstring="[para(12608(a,1),1065(a,1,2,2))].">
      <j1 rule="para" parents="12608 1065"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      R(1 / x,y,z) * L(T(x,x \ R(x,y,z)),u,z) = L(R(x,y,z),u,z) / x
    ]]></literal>
    <justification jstring="[para(69(a,1),12604(a,1,1,1,1))].">
      <j1 rule="para" parents="69 12604"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      R(1 / x,y,z) * L(x,u,z) = L(R(x,y,z),u,z) / x
    ]]></literal>
    <justification jstring="[para(1463(a,1),12610(a,1,2,1))].">
      <j1 rule="para" parents="1463 12610"/>
    </justification>
  </clause>

  <clause id="12613">
    <literal><![CDATA[
      R(1 / x,y,z) * L(x,u,z) = x \ L(R(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1753,a(flip),b,12612,a),flip(a)].">
      <j1 rule="hyper" parents="325 1753 12612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      R(x,y,z) * L(x \ 1,u,z) = x \ L(R(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11507,a(flip),b,12613,a)].">
      <j1 rule="hyper" parents="65 11507 12613"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      (x / (L(y,z,u) \ 1)) * (y \ 1) = (y \ 1) * ((L(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(12341(a,1),12351(a,1,2))].">
      <j1 rule="para" parents="12341 12351"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      (x * (y \ 1)) / (L(y,z,u) \ 1) = (y \ 1) * ((L(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(12341(a,1),12352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12341 12352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      (1 / L(x,y,z)) * ((1 / x) \ u) = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(12358(a,1),12353(a,1,2,1))].">
      <j1 rule="para" parents="12358 12353"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      a(x * L(x,y,z),x,x \ u) \ 1 = u \ L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8967(a,1),12413(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8967 12413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),x \ u) \ 1 = u \ L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8810(a,1),12621(a,1,1))].">
      <j1 rule="para" parents="8810 12621"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * a(y,z,u) = x * a(a(y,z,u),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(11603(a,1),12478(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11603 12478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ 1)) = u * a(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7226,a,12623,a)].">
      <j1 rule="hyper" parents="7226 12623"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      x * a(a(y,z,u),a(y,z,u),x) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8524,a(flip),b,12624,a),flip(a)].">
      <j1 rule="hyper" parents="65 8524 12624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ 1) \ u) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11971,a,b,12625,a)].">
      <j1 rule="hyper" parents="65 11971 12625"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),u) * (u * L(a(x,y,z),w,v5)) = L(u,a(x,y,z),a(x,y,z)) * L(a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(12625(a,1),11832(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12625 11832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (a(x,y,z) \ u) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,8663,a,b,12626,a)].">
      <j1 rule="hyper" parents="65 8663 12626"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,a(x,y,z),a(x,y,z)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(9(a,1),12626(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12630">
    <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="[para(7193(a,1),12628(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7193 12628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12631">
    <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="[para(8489(a,1),12629(a,1,1))].">
      <j1 rule="para" parents="8489 12629"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) / L(w \ 1,z,v5))) * v6) = a(x,y,(w * (z * a(v5,z,w))) * v6)
    ]]></literal>
    <justification jstring="[para(6598(a,1),12430(a,1,3,1,2))].">
      <j1 rule="para" parents="6598 12430"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      a(x,y,(z * (L(u \ 1,z,w) \ (v5 * v5))) * v6) = a(x,y,(u * (z * a(w,z,u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10307,a(flip),b,12632,a)].">
      <j1 rule="hyper" parents="65 10307 12632"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,u,w) * u) * v5) = a(x,y,(z * (u * a(w,u,z))) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10448,a(flip),b,12633,a)].">
      <j1 rule="hyper" parents="65 10448 12633"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      a(x,y,(z * (u * a(w,u,z))) * v5) = a(x,y,(L(z,u,w) * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11305,a(flip),b,12634,a),flip(a)].">
      <j1 rule="hyper" parents="65 11305 12634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * u) * w) = a(x,y,(w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11770,a(flip),b,12635,a),flip(a)].">
      <j1 rule="hyper" parents="65 11770 12635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,u,z))) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(10170,a,12636,a)].">
      <j1 rule="hyper" parents="10170 12636"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) * a(x,y,z \ L(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,69,a(flip),b,12543,a),flip(a)].">
      <j1 rule="hyper" parents="325 69 12543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * a(x,y,z \ L(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(7498(a,1),12638(a,1,1))].">
      <j1 rule="para" parents="7498 12638"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) \ 1 = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(140,a,12640,a)].">
      <j1 rule="hyper" parents="140 12640"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) \ 1 = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,7498,a(flip),b,12641,a),flip(a)].">
      <j1 rule="hyper" parents="325 7498 12641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      T(x,(y * (z \ L(L(z,u,w),u,w))) \ (a(w,u,z) \ v5)) = T(x,y \ ((a(w,u,z) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,7973,a(flip),b,12553,a),flip(a)].">
      <j1 rule="hyper" parents="325 7973 12553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      T(x,(y * (z \ L(L(z,u,w),u,w))) \ (a(w,u,z) \ v5)) = T(x,a(w,u,z) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,9833,a(flip),b,12643,a),flip(a)].">
      <j1 rule="hyper" parents="325 9833 12643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      T(x,y * (L(L(y,z,u),z,u) \ (w \ (a(u,z,y) \ v5)))) = T(x,a(u,z,y) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(12560(a,1),12644(a,1,2))].">
      <j1 rule="para" parents="12560 12644"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ v5)) = T(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,8848,a(flip),b,12645,a)].">
      <j1 rule="hyper" parents="65 8848 12645"/>
    </justification>
  </clause>

  <clause id="12648">
    <literal><![CDATA[
      T(x,a(y,z,u) * ((w / v5) \ w)) = T(x,a(y,z,u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,9770,a(flip),b,12646,a),flip(a)].">
      <j1 rule="hyper" parents="65 9770 12646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(85(a,1),12648(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="85 12648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      K(x,x \ ((a(y,z,u) \ x) * w)) = x \ T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(12649(a,1),8350(a,2,2))].">
      <j1 rule="para" parents="12649 8350"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      K(x,x \ ((a(y,z,u) \ x) * w)) = K(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,2104,a,b,12650,a),flip(a)].">
      <j1 rule="hyper" parents="325 2104 12650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(8387,a,12651,a)].">
      <j1 rule="hyper" parents="8387 12651"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      K(x,y \ (a(z,u,w) \ v5)) = K(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(8445,a,12652,a)].">
      <j1 rule="hyper" parents="8445 12652"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      L(L(L(x \ 1,y,z),x,u) \ L(x \ 1,y,z),x \ 1,L(x,y,z)) = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10453,a(flip),b,12389,a),flip(a)].">
      <j1 rule="hyper" parents="325 10453 12389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      L(L((x \ 1) \ L(x \ 1,x,y),z,u) \ 1,x \ 1,L(x,z,u)) = a(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4463(a,1),12654(a,1,1))].">
      <j1 rule="para" parents="4463 12654"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      L(L(x \ (1 * L(1 \ x,x,y)),z,u) \ 1,x \ 1,L(x,z,u)) = a(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(1410(a,1),12655(a,1,1,1,1))].">
      <j1 rule="para" parents="1410 12655"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      L(L(x \ (1 * L(x,x,y)),z,u) \ 1,x \ 1,L(x,z,u)) = a(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(67(a,1),12656(a,1,1,1,1,2,2,1))].">
      <j1 rule="para" parents="67 12656"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      L(L(x \ L(x,x,y),z,u) \ 1,x \ 1,L(x,z,u)) = a(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),12657(a,1,1,1,1,2))].">
      <j1 rule="para" parents="7 12657"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      L(a(L(x,y,z),u,u),u \ 1,L(u,y,z)) = a(x,u,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(11890(a,1),12658(a,1,1))].">
      <j1 rule="para" parents="11890 12658"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = a(x,u,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(10569,a,12659,a),flip(a)].">
      <j1 rule="hyper" parents="10569 12659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      x \ (R(y,z,z) * (y \ x)) = a(y,z,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11559,a,b,12660,a)].">
      <j1 rule="hyper" parents="65 11559 12660"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,y,z)) = a(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11872,a(flip),b,12660,a),flip(a)].">
      <j1 rule="hyper" parents="65 11872 12660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12664">
    <literal><![CDATA[
      a(x,x \ y,L(x \ y,x,y)) = a(x,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11563,a(flip),b,12660,a),flip(a)].">
      <j1 rule="hyper" parents="65 11563 12660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) = L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11560,a(flip),b,12660,a),flip(a)].">
      <j1 rule="hyper" parents="65 11560 12660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ y = L(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(12660(a,1),11709(a,1,1))].">
      <j1 rule="para" parents="12660 11709"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      a(x,y,z * a(u,z,L(z,w,v5))) = a(x,y,L(z,z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(12660(a,1),12049(a,1,3,2))].">
      <j1 rule="para" parents="12660 12049"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12444,a(flip),b,12663,a)].">
      <j1 rule="hyper" parents="65 12444 12663"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      R(x,y,y) \ (x * a(x,y,L(y,z,z))) = a(z,z,a(x,y,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12665(a,2),7020(a,1,2,2))].">
      <j1 rule="para" parents="12665 7020"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = a(x,y,y) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,12668,a(flip),b,1897,a),flip(a)].">
      <j1 rule="hyper" parents="136 12668 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      L(x,a(y,z,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(12668(a,1),12259(a,1,2))].">
      <j1 rule="para" parents="12668 12259"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      (x \ y) * a(z,x,x) = L(x,x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,11777,a(flip),b,12672,a)].">
      <j1 rule="hyper" parents="65 11777 12672"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      L(x,x,y) * (x \ z) = a(y,x,x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,11773,a(flip),b,12672,a)].">
      <j1 rule="hyper" parents="65 11773 12672"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      a(x,y,y) * (L(y,y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(12672(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12672 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      L(L(x,a(y,z,z),L(z,u,w)),L(z,u,w),L(z,u,w)) = a(L(z,u,w),L(z,u,w),x) \ x
    ]]></literal>
    <justification jstring="[para(12672(a,1),11812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12672 11812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      a(x,y,y) \ (L(y,y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(7273,a,12673,a)].">
      <j1 rule="hyper" parents="7273 12673"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      x * (L(x,x,y) \ z) = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,12673,a(flip),b,10580,a)].">
      <j1 rule="hyper" parents="137 12673 10580"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      a(((x \ y) * (a(z,x,x) \ 1)) \ u,w,v5) = a((L(x,x,z) \ y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(12673(a,1),5204(a,2,1,1))].">
      <j1 rule="para" parents="12673 5204"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      (a(x,y,y) \ z) * y = z * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,12674,a(flip),b,8338,a)].">
      <j1 rule="hyper" parents="136 12674 8338"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      a(x,y,y) * (K(z,L(y,y,x)) * u) = y * (T(L(y,y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(2652(a,1),12675(a,1,2))].">
      <j1 rule="para" parents="2652 12675"/>
    </justification>
  </clause>

  <clause id="12684">
    <literal><![CDATA[
      L(x * a(y,z,z),u,a(u,u,w)) = z * (L(z,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,12255,a,b,12679,a)].">
      <j1 rule="hyper" parents="325 12255 12679"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      (x * a(y,z,z)) \ (x * z) = L(z,z,y)
    ]]></literal>
    <justification jstring="[para(12679(a,1),8359(a,1,1))].">
      <j1 rule="para" parents="12679 8359"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      (a(x,y,L(y,z,u)) \ w) * y = w * L(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(12660(a,1),12682(a,1,1,1))].">
      <j1 rule="para" parents="12660 12682"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (z * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(7257,a,12685,a)].">
      <j1 rule="hyper" parents="7257 12685"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      L(L(x,x,y),a(y,x,x),z) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11714,a,b,12685,a)].">
      <j1 rule="hyper" parents="65 11714 12685"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      L(x,a(y,x,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(152,a,12688,a)].">
      <j1 rule="hyper" parents="152 12688"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      L(x,L(x,y,z),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12442,a(flip),b,12666,a)].">
      <j1 rule="hyper" parents="65 12442 12666"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      L(x,L(x,y,z),z) = L(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,6555,a(flip),b,12692,a),flip(a)].">
      <j1 rule="hyper" parents="325 6555 12692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) \ L(L(x,w,v5),L(x,z,u),y) = L(x \ L(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12692(a,1),4460(a,1,1))].">
      <j1 rule="para" parents="12692 4460"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      (x * (y * L(z,z,L(u,w,v5)))) / T(x * y,z) = L(L(z,y,x),L(z,w,v5),u)
    ]]></literal>
    <justification jstring="[para(12692(a,1),8634(a,1,1,2,2))].">
      <j1 rule="para" parents="12692 8634"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      a(x,y,L(L(z,z,L(u,w,v5)),w,v5)) = a(x,y,u \ (L(z,w,v5) \ u))
    ]]></literal>
    <justification jstring="[para(12692(a,1),10468(a,1,3,1))].">
      <j1 rule="para" parents="12692 10468"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      a(L(L(x,x,y),y,y),z,u) = a((y \ x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(12693(a,1),12078(a,1,1,1))].">
      <j1 rule="para" parents="12693 12078"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1900,a(flip),b,12671,a),flip(a)].">
      <j1 rule="hyper" parents="325 1900 12671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      R(x,y,y) / (L(y,z,u) \ 1) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,12698,a(flip),b,568,a)].">
      <j1 rule="hyper" parents="135 12698 568"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      R(x,a(y,z,u),L(y \ R(y,z,u),y,u * z)) = R(x,y \ R(y,z,u),y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2326(a,2),12698(a,1,2))].">
      <j1 rule="para" parents="2326 12698"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      L(x,y,L(z,L(u,w,v5),L(u,w,v5))) = L(x,y,R(z,u,u))
    ]]></literal>
    <justification jstring="[para(12698(a,1),9931(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12698 9931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      a(x,y,L(y,x,z)) * z = R(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(40,a,7207,a,b,12661,a)].">
      <j1 rule="hyper" parents="40 7207 12661"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      (x * (y \ 1)) / (L(y,z,u) \ 1) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(572(a,1),12699(a,1,1))].">
      <j1 rule="para" parents="572 12699"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      a((x \ y) \ x,z,u) = a((y \ x) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(5079,a,12697,a),flip(a)].">
      <j1 rule="hyper" parents="5079 12697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      a(L(x,y \ x,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12268,a,b,12704,a)].">
      <j1 rule="hyper" parents="65 12268 12704"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      a(x,x \ y,x \ y) = a(x,x \ y,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10285,a(flip),b,12664,a),flip(a)].">
      <j1 rule="hyper" parents="65 10285 12664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ z = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(43,a,11671,a,b,12684,a)].">
      <j1 rule="hyper" parents="43 11671 12684"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      x * a(y,y \ z,y \ z) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(43,a,11669,a,b,12684,a),flip(a)].">
      <j1 rule="hyper" parents="43 11669 12684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      (R(x,y,y) \ x) \ z = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11727,a,b,12708,a)].">
      <j1 rule="hyper" parents="65 11727 12708"/>
    </justification>
  </clause>

  <clause id="12711">
    <literal><![CDATA[
      L(x,a(y,z,z),a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,11778,a,b,12708,a)].">
      <j1 rule="hyper" parents="40 11778 12708"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ w = w * a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(11602(a,1),12708(a,1,1))].">
      <j1 rule="para" parents="11602 12708"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      L(x,a(y,y,z),a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(11058,a,12711,a)].">
      <j1 rule="hyper" parents="11058 12711"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ z = a(x,y,y) * z
    ]]></literal>
    <justification jstring="[hyper(10955,a,12711,a),flip(a)].">
      <j1 rule="hyper" parents="10955 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12716">
    <literal><![CDATA[
      x * (a(y,z,z) \ 1) = a(y,z,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,12631,a(flip),b,12711,a),flip(a)].">
      <j1 rule="hyper" parents="65 12631 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * z = a(x,y,y) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,12629,a(flip),b,12711,a),flip(a)].">
      <j1 rule="hyper" parents="65 12629 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12718">
    <literal><![CDATA[
      x * (a(y,y,z) \ 1) = a(y,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,12631,a(flip),b,12714,a),flip(a)].">
      <j1 rule="hyper" parents="65 12631 12714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12719">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ z = z * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12630,a(flip),b,12714,a)].">
      <j1 rule="hyper" parents="65 12630 12714"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      x \ (a(y,y,z) \ x) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,12631,a(flip),b,12714,a(flip))].">
      <j1 rule="hyper" parents="132 12631 12714"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      a(x,a(y,y,z),a(y,y,z)) = x \ x
    ]]></literal>
    <justification jstring="[para(12714(a,1),9016(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12714 9016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ z = z * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(12714(a,1),9018(a,1,2))].">
      <j1 rule="para" parents="12714 9018"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      a(x,a(y,y,z),a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(325,a,69,a(flip),b,12721,a),flip(a)].">
      <j1 rule="hyper" parents="325 69 12721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      a(x,a(y,y \ 1,z),a(y \ 1,y \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[para(1847(a,1),12723(a,1,2))].">
      <j1 rule="para" parents="1847 12723"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(x \ R(x,y,y),z,u)) = L(a(x,y,y) \ 1,z,u) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(5800,a,12710,a)].">
      <j1 rule="hyper" parents="5800 12710"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      R(x,x \ y,a(y,y,z)) \ L(y,y,z) = a(z,y,y) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11830,a,b,12716,a)].">
      <j1 rule="hyper" parents="65 11830 12716"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      x * (R(y,z,z) \ y) = a(y,z,z) \ x
    ]]></literal>
    <justification jstring="[para(5798(a,2),12716(a,1,2))].">
      <j1 rule="para" parents="5798 12716"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      L(x,y,y) * ((L(x,y,y) \ x) * z) = R(x,y,y) * (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(12717(a,1),11444(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12717 11444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      x * (y \ L(y,z,z)) = a(z,z,y) \ x
    ]]></literal>
    <justification jstring="[para(7004(a,1),12718(a,1,2))].">
      <j1 rule="para" parents="7004 12718"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) \ v5)) = a(x,y,z * (v5 * a(u,u,w)))
    ]]></literal>
    <justification jstring="[para(12718(a,1),10643(a,1,3,2))].">
      <j1 rule="para" parents="12718 10643"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      x * L(a(y,y,z) \ 1,u,w) = a(y,y,L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(10742(a,2),12718(a,1,2))].">
      <j1 rule="para" parents="10742 12718"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ w = w * a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10742(a,2),12719(a,1,1))].">
      <j1 rule="para" parents="10742 12719"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ z = x \ (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(12719(a,1),12271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12719 12271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      a(x,x,y) * (z * L(z \ (a(x,x,y) \ (z * 1)),u,w)) = z * (a(x,x,y) * L(v5 \ (a(x,x,y) \ v5),u,w))
    ]]></literal>
    <justification jstring="[para(12720(a,2),8817(a,2,2,2,1))].">
      <j1 rule="para" parents="12720 8817"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      (x \ L(x,y,y)) * z = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(7275,a,12722,a)].">
      <j1 rule="hyper" parents="7275 12722"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      L(K(x,y) * ((z * y) \ z),y,x) = (y * x) \ (a(z,y,y) \ x)
    ]]></literal>
    <justification jstring="[para(12728(a,1),11729(a,2,2))].">
      <j1 rule="para" parents="12728 11729"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * w = a(y,y,L(x,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(4458(a,1),12736(a,1,1))].">
      <j1 rule="para" parents="4458 12736"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ z = (x \ z) * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,11625,a(flip),b,12734,a),flip(a)].">
      <j1 rule="hyper" parents="325 11625 12734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      a(x,a(y,y \ 1,z),a(y,y \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[para(1847(a,1),12725(a,1,3))].">
      <j1 rule="para" parents="1847 12725"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      a(a(x,y,z),u,u) = a(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,12712,a(flip),b,12554,a(flip))].">
      <j1 rule="hyper" parents="130 12712 12554"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      a(x,x,a(y,z,u) \ 1) \ w = w * a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(7484(a,2),12712(a,1,1))].">
      <j1 rule="para" parents="7484 12712"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      x * a(a(y,z,u),x,x) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,12741,a,b,11602,a)].">
      <j1 rule="hyper" parents="137 12741 11602"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      x * a(y,y \ z,y * z) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[para(12707(a,1),12709(a,1,2))].">
      <j1 rule="para" parents="12707 12709"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      a(x,x \ y,x * y) \ z = z * (z / (((x \ y) * (y \ x)) \ z))
    ]]></literal>
    <justification jstring="[para(12744(a,1),8531(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12744 8531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      L(x,y,L(z,L(u,w,v5),L(u,w,v5))) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,9931,a(flip),b,12701,a),flip(a)].">
      <j1 rule="hyper" parents="325 9931 12701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,z) \ 1) \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12617,a(flip),b,12703,a)].">
      <j1 rule="hyper" parents="65 12617 12703"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      (x * L(y,z,z)) * a(z,z,L(y,y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(65,a,8598,a(flip),b,12733,a),flip(a)].">
      <j1 rule="hyper" parents="65 8598 12733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      a(x,x,L(y,y,y * z)) \ z = (z / y) * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9289,a(flip),b,12738,a),flip(a)].">
      <j1 rule="hyper" parents="65 9289 12738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * ((x \ L(x,y,y)) \ w) = (x \ L(x,y,y)) \ (a(y,y,L(x,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(132,a,12738,a(flip),b,1245,a),flip(a)].">
      <j1 rule="hyper" parents="132 12738 1245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,z,z)) = L(x,y,R(T(z,v5),u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,12166,a(flip),b,12747,a),flip(a)].">
      <j1 rule="hyper" parents="65 12166 12747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12753">
    <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(65,a,11989,a(flip),b,12747,a),flip(a)].">
      <j1 rule="hyper" parents="65 11989 12747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      (x / (L(y,z,u) \ 1)) * (y \ 1) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12615,a,b,12748,a)].">
      <j1 rule="hyper" parents="65 12615 12748"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * L(u,w,v5)) = L(x,y,L(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4188,a(flip),b,12753,a)].">
      <j1 rule="hyper" parents="65 4188 12753"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      a(x,y,z * a(u,z,L(z,w,v5))) = a(x,y,L(z,L(z,w,v5),u))
    ]]></literal>
    <justification jstring="[para(12692(a,2),12667(a,2,3))].">
      <j1 rule="para" parents="12692 12667"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      L((x * T(y,z)) \ x,y,z) = (y * z) \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(9607(a,1),12737(a,1,1))].">
      <j1 rule="para" parents="9607 12737"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      (x * y) \ (a(z,x,x) \ y) = L((x * y) \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(10898,a,12757,a),flip(a)].">
      <j1 rule="hyper" parents="10898 12757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      L((x * (y / x)) \ (y / x),x,z) = y \ (x \ (a(z,x,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12285,a(flip),b,12758,a),flip(a)].">
      <j1 rule="hyper" parents="65 12285 12758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12760">
    <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(65,a,12667,a(flip),b,12756,a),flip(a)].">
      <j1 rule="hyper" parents="65 12667 12756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      x \ (y \ (a(z,y,y) \ x)) = L(x \ (y \ x),y,z)
    ]]></literal>
    <justification jstring="[para(2912(a,1),12759(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2912 12759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      a(x,y,y) * (K(z,y) * u) = y * (T(L(y,y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(7923(a,1),12683(a,1,2,1))].">
      <j1 rule="para" parents="7923 12683"/>
    </justification>
  </clause>

  <clause id="12763">
    <literal><![CDATA[
      a(x,y,y) * (K(z,y) * u) = y * (L(T(y,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(25(a,2),12762(a,2,2,1))].">
      <j1 rule="para" parents="25 12762"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      a(x,x \ y,x * y) \ z = z * ((x \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(535,a,12746,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="535 12746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      a(x,x \ (y * (z * y)),L(z,y,y) * x) \ u = u * ((x \ (y * (z * y))) * ((y * (z * y)) \ x))
    ]]></literal>
    <justification jstring="[para(10343(a,1),12765(a,1,1))].">
      <j1 rule="para" parents="10343 12765"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w) * v5,z,z)) = L(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,4602,a(flip),b,12752,a),flip(a)].">
      <j1 rule="hyper" parents="325 4602 12752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * R(u,w,v5)) = L(x,y,R(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4187,a(flip),b,12768,a)].">
      <j1 rule="hyper" parents="65 4187 12768"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      R(x,y,y) * (a(x,y,y) \ z) = L(x,y,y) * (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(824(a,1),12729(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="824 12729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * z) = R(y,x,x) * (a(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10609,a(flip),b,12772,a)].">
      <j1 rule="hyper" parents="325 10609 12772"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      a((a(x,y,y) \ (y \ z)) \ u,w,v5) = a((L(y,y,x) \ z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(12716(a,1),12680(a,1,1,1))].">
      <j1 rule="para" parents="12716 12680"/>
    </justification>
  </clause>

  <clause id="12775">
    <literal><![CDATA[
      a((x \ (a(y,x,x) \ z)) \ u,w,v5) = a((L(x,x,y) \ z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(10590(a,1),12774(a,1,1,1))].">
      <j1 rule="para" parents="10590 12774"/>
    </justification>
  </clause>

  <clause id="12776">
    <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(65,a,8634,a(flip),b,12695,a),flip(a)].">
      <j1 rule="hyper" parents="65 8634 12695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,L(w * u,u,w))) = a(x,y,(w * (u * z)) \ (w * u))
    ]]></literal>
    <justification jstring="[para(12776(a,1),10756(a,1,3))].">
      <j1 rule="para" parents="12776 10756"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,u \ w)) = a(x,y,(w * (u * z)) \ (w * u))
    ]]></literal>
    <justification jstring="[para(12373(a,1),12777(a,1,3))].">
      <j1 rule="para" parents="12373 12777"/>
    </justification>
  </clause>

  <clause id="12779">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) \ L(L(x,w,v5),x,L(y,z,u)) = L(x \ L(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12776(a,1),12694(a,1,2))].">
      <j1 rule="para" parents="12776 12694"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(x \ R(x,y,y),z,u)) = (a(x,y,y) \ 1) * L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1273,a(flip),b,12726,a),flip(a)].">
      <j1 rule="hyper" parents="325 1273 12726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      L(x \ L(x,y,z),L(x,u,w),v5) = L(x \ L(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(4470,a,12779,a),flip(a)].">
      <j1 rule="hyper" parents="4470 12779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(x \ R(x,y,y),z,u)) = (a(x,y,y) \ 1) * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12665(a,2),12780(a,2,2))].">
      <j1 rule="para" parents="12665 12780"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(x \ R(x,y,y),z,u)) = a(x,y,y) \ a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12717,a(flip),b,12782,a),flip(a)].">
      <j1 rule="hyper" parents="325 12717 12782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12784">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(a(x,y,y),z,u)) = a(x,y,y) \ a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1896(a,1),12783(a,1,2,2,1))].">
      <j1 rule="para" parents="1896 12783"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      R(x,y,y) \ (x * a(x,y,L(y,z,u))) = a(x,y,y) \ a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12665(a,2),12784(a,1,2,2))].">
      <j1 rule="para" parents="12665 12784"/>
    </justification>
  </clause>

  <clause id="12786">
    <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(2326(a,2),12700(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2326 12700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12787">
    <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(325,a,9014,a(flip),b,12786,a),flip(a)].">
      <j1 rule="hyper" parents="325 9014 12786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      L(a(x,y,L(z,z,u)) \ 1,L(z,z,u),y) = L(z,z,z * u) \ L(L(z,z,z * u),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11057,a(flip),b,12407,a)].">
      <j1 rule="hyper" parents="65 11057 12407"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      L(x,x,x * y) \ L(L(x,x,x * y),z,u) = L(x,x,y) \ L(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12403,a(flip),b,12788,a),flip(a)].">
      <j1 rule="hyper" parents="65 12403 12788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      L(x,x,x * y) \ L(L(x,x,x * y),z,u) = L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,4458,a(flip),b,12789,a),flip(a)].">
      <j1 rule="hyper" parents="325 4458 12789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(4459,a,12790,a)].">
      <j1 rule="hyper" parents="4459 12790"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = (z * y) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9291,a(flip),b,12791,a),flip(a)].">
      <j1 rule="hyper" parents="65 9291 12791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = u \ ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9290,a(flip),b,12791,a),flip(a)].">
      <j1 rule="hyper" parents="65 9290 12791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      x \ ((x / y) * L(y,x,z)) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12398,a(flip),b,12793,a),flip(a)].">
      <j1 rule="hyper" parents="65 12398 12793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12795">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,102,a(flip),b,12793,a)].">
      <j1 rule="hyper" parents="65 102 12793"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * y = (y / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,12794,a(flip),b,8657,a)].">
      <j1 rule="hyper" parents="136 12794 8657"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      x \ (y * L(y \ x,x,z)) = a(z,x,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),12794(a,1,2,1))].">
      <j1 rule="para" parents="82 12794"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      a(x,y,L(z,y,x) \ 1) \ 1 = y \ ((y / (L(z,y,x) \ 1)) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(12341(a,1),12794(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12341 12794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) = (a(z,y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,8336,a,b,12796,a)].">
      <j1 rule="hyper" parents="325 8336 12796"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * y) * z = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,12796,a,b,1712,a)].">
      <j1 rule="hyper" parents="136 12796 1712"/>
    </justification>
  </clause>

  <clause id="12801">
    <literal><![CDATA[
      K(x,((y / z) * L(z,y,u)) \ w) = K(x,y \ ((a(u,y,z) \ 1) \ w))
    ]]></literal>
    <justification jstring="[para(12796(a,1),7946(a,1,2,1))].">
      <j1 rule="para" parents="12796 7946"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      x * ((a(y,z,x) \ 1) * z) = L(x,z,y) * z
    ]]></literal>
    <justification jstring="[para(12796(a,2),8380(a,1,2))].">
      <j1 rule="para" parents="12796 8380"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      (a(x,y,L(y,x,z) \ y) \ 1) * y = (y / (L(y,x,z) \ y)) * a(z,x,y)
    ]]></literal>
    <justification jstring="[para(12383(a,2),12796(a,2,2))].">
      <j1 rule="para" parents="12383 12796"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ u) = a(w,u,a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(12554(a,1),12799(a,2,1))].">
      <j1 rule="para" parents="12554 12799"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      ((x * y) \ (x * z)) \ (y \ z) = a(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(7017,a,12797,a)].">
      <j1 rule="hyper" parents="7017 12797"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      x \ (L(x,y,z) * L(L(x,y,z) \ x,x,u)) = a(u,x,x * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(7497(a,1),12797(a,2,1))].">
      <j1 rule="para" parents="7497 12797"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      ((T(x,y) * z) \ (z * u)) \ (T(T(x,z),y) \ u) = a(z,T(T(x,z),y),u \ T(T(x,z),y))
    ]]></literal>
    <justification jstring="[para(241(a,1),12805(a,1,1,1))].">
      <j1 rule="para" parents="241 12805"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      L(x \ y,x,z) \ (x \ y) = a(z,x,y \ x)
    ]]></literal>
    <justification jstring="[para(102(a,2),12805(a,1,1))].">
      <j1 rule="para" parents="102 12805"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w \ u),(z * u) \ (z * w),u \ w)) = a(x,y,((z * u) \ (z * w)) * (u \ w))
    ]]></literal>
    <justification jstring="[para(12805(a,1),10285(a,1,3,1))].">
      <j1 rule="para" parents="12805 10285"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      (x * y) \ (((x * y) / z) * L(z,x,y)) = ((x * y) * z) \ (y * (T(x,y) * z))
    ]]></literal>
    <justification jstring="[para(5232(a,1),12795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5232 12795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(a(x,y,z),u,w) = a(w,u,a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(7236,a,12804,a)].">
      <j1 rule="hyper" parents="7236 12804"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      K(x,L(y,z,u) \ ((z / y) \ w)) = K(x,z \ ((a(u,z,y) \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(8262,a,12801,a)].">
      <j1 rule="hyper" parents="8262 12801"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      K(x,L(y,z,u) \ ((z / y) \ w)) = K(x,a(u,z,y) * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,8652,a(flip),b,12812,a),flip(a)].">
      <j1 rule="hyper" parents="325 8652 12812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,a(w,z,y) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(8904,a,12813,a)].">
      <j1 rule="hyper" parents="8904 12813"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      K(x,a(y,z,u) * (z \ w)) = K(x,z \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8325,a(flip),b,12814,a),flip(a)].">
      <j1 rule="hyper" parents="65 8325 12814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      a(x,y,L(z,y,x) \ 1) \ 1 = y \ ((y / z) * L(z,y,x))
    ]]></literal>
    <justification jstring="[para(12754(a,1),12798(a,2,2))].">
      <j1 rule="para" parents="12754 12798"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      a(x,y,L(z,y,x) \ 1) \ 1 = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,12794,a(flip),b,12818,a),flip(a)].">
      <j1 rule="hyper" parents="325 12794 12818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ 1 = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(7484(a,1),12819(a,1,1))].">
      <j1 rule="para" parents="7484 12819"/>
    </justification>
  </clause>

  <clause id="12821">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(286,a,12820,a),flip(a)].">
      <j1 rule="hyper" parents="286 12820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      a(x,y,y * L(y,x,z)) = a(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12416,a(flip),b,12821,a)].">
      <j1 rule="hyper" parents="65 12416 12821"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      a(x,y,L(y,x,z) \ y) = a(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12397,a(flip),b,12821,a)].">
      <j1 rule="hyper" parents="65 12397 12821"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      a(x,y,(x * y) \ z) = a(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12047,a(flip),b,12821,a),flip(a)].">
      <j1 rule="hyper" parents="65 12047 12821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      a(x,y,z) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11639,a(flip),b,12821,a),flip(a)].">
      <j1 rule="hyper" parents="65 11639 12821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      a(x,y,z) \ (y * z) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(7285,a,12825,a)].">
      <j1 rule="hyper" parents="7285 12825"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      a(x,y,z) * (y * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[hyper(7225,a,12825,a)].">
      <j1 rule="hyper" parents="7225 12825"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      (L(x,y,z) / y) \ (y * (y \ (x / y))) = a(z,y,y \ (x / y))
    ]]></literal>
    <justification jstring="[para(1748(a,1),12825(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1748 12825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(12825(a,2),12600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12825 12600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      (x \ ((x * y) * z)) \ (y * z) = (y * z) \ (y * L(z,y,x))
    ]]></literal>
    <justification jstring="[para(12827(a,1),11643(a,2,2))].">
      <j1 rule="para" parents="12827 11643"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      a(x,y,L(z,y,x) \ 1) * (y * (z \ 1)) = y * (L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(12341(a,1),12828(a,1,2,2))].">
      <j1 rule="para" parents="12341 12828"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(779,a,12830,a)].">
      <j1 rule="hyper" parents="779 12830"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ 1) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(12830(a,1),11916(a,1,3))].">
      <j1 rule="para" parents="12830 11916"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,x * y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(12830(a,1),12322(a,1,1))].">
      <j1 rule="para" parents="12830 12322"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(10121,a,12834,a)].">
      <j1 rule="hyper" parents="10121 12834"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(v5,w,u * z))
    ]]></literal>
    <justification jstring="[hyper(10789,a,12836,a),flip(a)].">
      <j1 rule="hyper" parents="10789 12836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(y * x,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(2363,a,12836,a)].">
      <j1 rule="hyper" parents="2363 12836"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      a(x,y \ 1,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,12215,a,b,12836,a)].">
      <j1 rule="hyper" parents="325 12215 12836"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      a(x * y,y,a(z,u,y)) = a(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,12517,a(flip),b,12836,a),flip(a)].">
      <j1 rule="hyper" parents="325 12517 12836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,12836,a,b,7207,a),flip(a)].">
      <j1 rule="hyper" parents="137 12836 7207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,12836,a,b,9,a)].">
      <j1 rule="hyper" parents="137 12836 9"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      a(x,y,a(((z * z) * u) * w,v5,v6)) = a(x,y,a(v6,v5,w * u))
    ]]></literal>
    <justification jstring="[para(3522(a,2),12836(a,1,3))].">
      <j1 rule="para" parents="3522 12836"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,a(z,y,x)) = a(x,y,z) * (u * a(w,v5,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12836(a,1),10565(a,1,2))].">
      <j1 rule="para" parents="12836 10565"/>
    </justification>
  </clause>

  <clause id="12845">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,z)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(11577(a,2),12836(a,1,3))].">
      <j1 rule="para" parents="11577 12836"/>
    </justification>
  </clause>

  <clause id="12846">
    <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(12836(a,1),12111(a,1,1,2))].">
      <j1 rule="para" parents="12836 12111"/>
    </justification>
  </clause>

  <clause id="12847">
    <literal><![CDATA[
      a(x,y,z) * a(u,x,a(z,y,x)) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(12836(a,1),12509(a,1,2))].">
      <j1 rule="para" parents="12836 12509"/>
    </justification>
  </clause>

  <clause id="12848">
    <literal><![CDATA[
      a(x * y,x,a(z,u,x)) = a(y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(2363,a,12840,a)].">
      <j1 rule="hyper" parents="2363 12840"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) / z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12792,a(flip),b,12833,a)].">
      <j1 rule="hyper" parents="65 12792 12833"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(41,a,12330,a,b,12833,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 12330 12833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      L(a(x,y,z),z,x * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(43,a,12459,a,b,12850,a(flip))].">
      <j1 rule="hyper" parents="43 12459 12850"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      a(L(x * L(x,y,z),x,z * y),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(12850(a,2),1915(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12850 1915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12853">
    <literal><![CDATA[
      L(a(x \ y,x,z),z,y) = L(z,x,x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(2350,a,12851,a)].">
      <j1 rule="hyper" parents="2350 12851"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      L(a(x,y,z),z,y * x) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(2349,a,12851,a)].">
      <j1 rule="hyper" parents="2349 12851"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      L(R(a(x,y,z),u,w),z,x * y) = R(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(12851(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12851 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),z,x * y) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(12851(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12851 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12857">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(y * x,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,12854,a(flip),b,12524,a)].">
      <j1 rule="hyper" parents="132 12854 12524"/>
    </justification>
  </clause>

  <clause id="12858">
    <literal><![CDATA[
      L(R(a(x,y,z) \ 1,u,w),z,x * y) = R(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(12835(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12835 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12859">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,x * y) = L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(12835(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12835 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12860">
    <literal><![CDATA[
      (x * y) \ ((y * (T(x,y) * z)) / z) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,5005,a,b,12849,a)].">
      <j1 rule="hyper" parents="65 5005 12849"/>
    </justification>
  </clause>

  <clause id="12862">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) * v6 = a(y * x,z,a(v5,w,u)) * v6
    ]]></literal>
    <justification jstring="[hyper(136,a,12838,a,b,11,a)].">
      <j1 rule="hyper" parents="136 12838 11"/>
    </justification>
  </clause>

  <clause id="12863">
    <literal><![CDATA[
      a(x,y,a(z,y,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,12242,a(flip),b,12847,a),flip(a)].">
      <j1 rule="hyper" parents="131 12242 12847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      L(a(x,y,y),y,z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,12863,a)].">
      <j1 rule="hyper" parents="54 12863"/>
    </justification>
  </clause>

  <clause id="12865">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12665,a,b,12864,a)].">
      <j1 rule="hyper" parents="65 12665 12864"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) = a(x,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12526,a(flip),b,12857,a),flip(a)].">
      <j1 rule="hyper" parents="65 12526 12857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12867">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) = a(x,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,12866,a)].">
      <j1 rule="hyper" parents="65 12836 12866"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      (R(x,y,z) \ x) * a(x,y,z) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,12513,a,b,12867,a)].">
      <j1 rule="hyper" parents="65 12513 12867"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      a(x,y,z) * a(y,x,a(z,y,x)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12867(a,1),12511(a,1,2))].">
      <j1 rule="para" parents="12867 12511"/>
    </justification>
  </clause>

  <clause id="12870">
    <literal><![CDATA[
      L(a(x,y,z),x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12847,a(flip),b,12869,a)].">
      <j1 rule="hyper" parents="65 12847 12869"/>
    </justification>
  </clause>

  <clause id="12871">
    <literal><![CDATA[
      x \ R(x,a(y,z,u),y) = a(x,a(y,z,u),y) * 1
    ]]></literal>
    <justification jstring="[para(11783(a,1),12869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11783 12869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12872">
    <literal><![CDATA[
      L(a(x,y,z),x,z * y) = L(a(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,12460,a,b,12870,a)].">
      <j1 rule="hyper" parents="325 12460 12870"/>
    </justification>
  </clause>

  <clause id="12873">
    <literal><![CDATA[
      x \ R(x,L(x,y,z),u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11760,a(flip),b,12870,a),flip(a)].">
      <j1 rule="hyper" parents="65 11760 12870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      L(a(L(x \ 1,y,z),x,u),x \ 1,L(x,y,z)) = L(x \ 1,y,z) \ R(L(x \ 1,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7466,a(flip),b,12870,a)].">
      <j1 rule="hyper" parents="65 7466 12870"/>
    </justification>
  </clause>

  <clause id="12875">
    <literal><![CDATA[
      L(R(a(x,y,z),u,w),x,y) = R(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(12870(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12870 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),x,y) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(12870(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12870 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12877">
    <literal><![CDATA[
      L(a(x,y,y \ z),x,y) = x \ (((x * y) * (y \ z)) / z)
    ]]></literal>
    <justification jstring="[para(108(a,2),12870(a,2,2))].">
      <j1 rule="para" parents="108 12870"/>
    </justification>
  </clause>

  <clause id="12878">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),x,L(y,z,u)) = x \ R(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(7454(a,1),12870(a,1,1))].">
      <j1 rule="para" parents="7454 12870"/>
    </justification>
  </clause>

  <clause id="12879">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(12870(a,1),12450(a,2,1))].">
      <j1 rule="para" parents="12870 12450"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[para(12870(a,1),12459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12870 12459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      L(x \ R(x,L(x,y,z),u),w,v5) = a(L(x,w,v5),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,11570,a(flip),b,12880,a)].">
      <j1 rule="hyper" parents="325 11570 12880"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      x \ (y * R(y \ x,y,z)) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,469,a(flip),b,12880,a)].">
      <j1 rule="hyper" parents="325 469 12880"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      R(x,y,z) * (x \ y) = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12880,a,b,9360,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 12880 9360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      (x * y) * a(y,x,z) = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12880,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="137 12880 102"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      (a(x,y,z) \ u) * R(a(x,y,z),u,w) = u * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(7289,a,12883,a)].">
      <j1 rule="hyper" parents="7289 12883"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      x * (y * a(x,y,z)) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,12883,a(flip),b,958,a)].">
      <j1 rule="hyper" parents="137 12883 958"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      R(R(1 / x,x,y),y,z) * (x * y) = y * a(R(1 / x,x,y),y,z)
    ]]></literal>
    <justification jstring="[para(365(a,1),12883(a,1,2))].">
      <j1 rule="para" parents="365 12883"/>
    </justification>
  </clause>

  <clause id="12888">
    <literal><![CDATA[
      x * (a(x,y,z) * y) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(7219,a,12886,a)].">
      <j1 rule="hyper" parents="7219 12886"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      (x * y) * a(x,y,z) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,11582,a,b,12886,a)].">
      <j1 rule="hyper" parents="65 11582 12886"/>
    </justification>
  </clause>

  <clause id="12890">
    <literal><![CDATA[
      L(L(x,y,a(z,y,x)),y * a(z,y,x),z) = (R(z,y,x) * y) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(12886(a,1),11644(a,2,1))].">
      <j1 rule="para" parents="12886 11644"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * x = R(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(37,a,10579,a,b,12888,a(flip))].">
      <j1 rule="hyper" parents="37 10579 12888"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      L(x,y,z) * (R(z,y,x) * y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(12889(a,1),10606(a,1,2))].">
      <j1 rule="para" parents="12889 10606"/>
    </justification>
  </clause>

  <clause id="12893">
    <literal><![CDATA[
      a(x,y,z) * a(y,x,a(x,y,z)) = L(a(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,12509,a,b,12872,a)].">
      <j1 rule="hyper" parents="325 12509 12872"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,5794,a(flip),b,12879,a),flip(a)].">
      <j1 rule="hyper" parents="325 5794 12879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12895">
    <literal><![CDATA[
      L(a(x,y,z * L(u,w,v5)) \ 1,x,y) = R(x,y,z * R(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(11354(a,1),12894(a,1,1,1))].">
      <j1 rule="para" parents="11354 12894"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      x \ R(x,a(y,z,u),y) = a(x,a(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,8,a(flip),b,12871,a),flip(a)].">
      <j1 rule="hyper" parents="325 8 12871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12897">
    <literal><![CDATA[
      (x \ ((x * y) * z)) \ (y * z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,12400,a(flip),b,12831,a),flip(a)].">
      <j1 rule="hyper" parents="325 12400 12831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      a(a(x,y,z),z,u) \ 1 = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12206,a(flip),b,12897,a),flip(a)].">
      <j1 rule="hyper" parents="65 12206 12897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ 1 = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(10613(a,1),12898(a,1,1))].">
      <j1 rule="para" parents="10613 12898"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12586,a(flip),b,12899,a)].">
      <j1 rule="hyper" parents="65 12586 12899"/>
    </justification>
  </clause>

  <clause id="12901">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(41,a,12554,a,b,12899,a),flip(a)].">
      <j1 rule="hyper" parents="41 12554 12899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      x * a(x,y,a(z,u,y)) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(137,a,12899,a(flip),b,12586,a(flip))].">
      <j1 rule="hyper" parents="137 12899 12586"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      a(x * y,z,a(u,w,z)) = a(z,a(u,w,z),y * x)
    ]]></literal>
    <justification jstring="[hyper(10136,a,12901,a),flip(a)].">
      <j1 rule="hyper" parents="10136 12901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      (x * (y * a(z,u,y))) / a(z,u,y) = x * (a(y,a(z,u,y),x) \ y)
    ]]></literal>
    <justification jstring="[para(12901(a,2),11707(a,2,2,1))].">
      <j1 rule="para" parents="12901 11707"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      x * a(y,a(z,u,y),w) = x * a(w,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(12901(a,2),12842(a,1,2))].">
      <j1 rule="para" parents="12901 12842"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * y = R(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(12901(a,1),12891(a,1,1))].">
      <j1 rule="para" parents="12901 12891"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * x = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(40,a,7207,a,b,12900,a)].">
      <j1 rule="hyper" parents="40 7207 12900"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      x * (a(a(y,z,x),x,x \ u) \ (x \ u)) = u * a(x \ u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(12900(a,1),12425(a,2,2))].">
      <j1 rule="para" parents="12900 12425"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ y = y * a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(12900(a,1),12588(a,1,1))].">
      <j1 rule="para" parents="12900 12588"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ x = x * a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[para(12901(a,2),12912(a,1,1))].">
      <j1 rule="para" parents="12901 12912"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      a(a(x,y,z),z,u) \ z = z * a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10613(a,2),12913(a,1,1))].">
      <j1 rule="para" parents="10613 12913"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      a(a(x,y,z),u,z) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,9163,a(flip),b,12852,a),flip(a)].">
      <j1 rule="hyper" parents="65 9163 12852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      L(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,12915,a)].">
      <j1 rule="hyper" parents="54 12915"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      (a(x,y,z) * y) \ (x \ ((x * y) * z)) = z
    ]]></literal>
    <justification jstring="[hyper(65,a,11642,a,b,12916,a)].">
      <j1 rule="hyper" parents="65 11642 12916"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      L(x * y,z,a(y,y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(65,a,9054,a(flip),b,12916,a)].">
      <j1 rule="hyper" parents="65 9054 12916"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(201,a,12916,a(flip),b,11642,a)].">
      <j1 rule="hyper" parents="201 12916 11642"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      (x * a(y,z,u)) * u = (x * u) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,12916,a(flip),b,7320,a)].">
      <j1 rule="hyper" parents="137 12916 7320"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      (a(x,y,z) * u) * z = (u * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,12916,a(flip),b,7268,a)].">
      <j1 rule="hyper" parents="137 12916 7268"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ u) * z) = u * z
    ]]></literal>
    <justification jstring="[hyper(137,a,12916,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="137 12916 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      L(R(x,y,z),u,a(w,v5,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12916(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12916 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12916(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12916 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(z,w,v5) = a(x,y,z) * (u * L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(12916(a,1),412(a,1,2,1))].">
      <j1 rule="para" parents="12916 412"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      (x * a(y,z,u)) * u = a(y,z,u) * (x * u)
    ]]></literal>
    <justification jstring="[para(12916(a,1),7215(a,1,2))].">
      <j1 rule="para" parents="12916 7215"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      (a(x,x,y) \ z) * T(y * x,z) = a(x,x,y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(12918(a,1),728(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12918 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      L(L(x,y,z),x,L(a(u,w,x),v5,v6)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12776,a(flip),b,12924,a)].">
      <j1 rule="hyper" parents="65 12776 12924"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ y = L(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(43,a,11941,a,b,12924,a)].">
      <j1 rule="hyper" parents="43 11941 12924"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,12917,a(flip),b,7220,a(flip))].">
      <j1 rule="hyper" parents="201 12917 7220"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      a(x,y,z) = ((x \ ((x * y) * z)) / z) / y
    ]]></literal>
    <justification jstring="[hyper(135,a,12919,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="135 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      a(x,y,z) = y \ ((x \ ((x * y) * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(132,a,12919,a,b,7190,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 12919 7190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) * u) / (y * u) = R(a(x,y,z),y,u)
    ]]></literal>
    <justification jstring="[para(12919(a,2),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12919 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      a(x,y,z) * (y * K((x \ ((x * y) * z)) / z,u)) = T(a(x,y,z) * y,u)
    ]]></literal>
    <justification jstring="[para(12919(a,2),6671(a,1,2,2,1))].">
      <j1 rule="para" parents="12919 6671"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      (x \ y) / ((x * z) \ y) = z * a(x,z,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),12931(a,1,1,2))].">
      <j1 rule="para" parents="10 12931"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),y) = ((x \ ((x * y) * z)) / z) \ y
    ]]></literal>
    <justification jstring="[para(12931(a,2),225(a,2,1))].">
      <j1 rule="para" parents="12931 225"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      (x * y) / L(y,x,z) = x * a(z,x,L(y,x,z))
    ]]></literal>
    <justification jstring="[para(307(a,1),12931(a,1,1))].">
      <j1 rule="para" parents="307 12931"/>
    </justification>
  </clause>

  <clause id="12941">
    <literal><![CDATA[
      a(x,y,(z \ ((z * ((u \ w) * u)) * v5)) / v5) = a(x,y,w * a(z,(u \ w) * u,v5))
    ]]></literal>
    <justification jstring="[para(12931(a,2),10050(a,1,3))].">
      <j1 rule="para" parents="12931 10050"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) * a(y,y \ 1,(x \ ((x * y) * z)) / z) = (y \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12933(a,2),12375(a,2,2))].">
      <j1 rule="para" parents="12933 12375"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      x * ((y * a(x,y,z)) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,12920,a,b,11624,a)].">
      <j1 rule="hyper" parents="137 12920 11624"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      (x * a(y,z,u)) / u = (x / u) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,154,a(flip),b,12920,a)].">
      <j1 rule="hyper" parents="135 154 12920"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      (x * (y * a(x,z,u))) * u = ((x * y) * u) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(11582(a,1),12920(a,1,1))].">
      <j1 rule="para" parents="11582 12920"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      (a(x,y,z) \ y) * z = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,12828,a,b,12922,a),flip(a)].">
      <j1 rule="hyper" parents="36 12828 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * y = a(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(37,a,12800,a,b,12946,a)].">
      <j1 rule="hyper" parents="37 12800 12946"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,12799,a,b,12947,a)].">
      <j1 rule="hyper" parents="65 12799 12947"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      L(x,a(y,x,z),a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7470,a,12947,a(flip))].">
      <j1 rule="hyper" parents="7470 12947"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      x \ (a(y,x,z) \ x) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,12947,a(flip),b,8489,a(flip))].">
      <j1 rule="hyper" parents="132 12947 8489"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ y = a(x,y,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(12554(a,1),12947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12554 12947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      x * (a(y,z,x) \ z) = L(x,z,y) * z
    ]]></literal>
    <justification jstring="[para(12947(a,1),12802(a,1,2))].">
      <j1 rule="para" parents="12947 12802"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * y = a(x,y,z) * (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,12949,a(flip),b,7473,a)].">
      <j1 rule="hyper" parents="137 12949 7473"/>
    </justification>
  </clause>

  <clause id="12954">
    <literal><![CDATA[
      L(x,y,z) * ((x \ y) * a(u,w,x)) = (a(z,y,x) \ y) * a(u,w,x)
    ]]></literal>
    <justification jstring="[para(12948(a,1),10583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12948 10583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,8534,a,b,12950,a)].">
      <j1 rule="hyper" parents="65 8534 12950"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      a(x,y,z) \ (z * y) = L(z,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,10587,a,b,12952,a)].">
      <j1 rule="hyper" parents="65 10587 12952"/>
    </justification>
  </clause>

  <clause id="12957">
    <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(12398(a,1),12952(a,2,1))].">
      <j1 rule="para" parents="12398 12952"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      x * (y * a(y,a(z,u,y),x)) = L(x,y,a(z,u,y)) * y
    ]]></literal>
    <justification jstring="[para(12914(a,1),12952(a,1,2))].">
      <j1 rule="para" parents="12914 12952"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      a(x,y,z) * ((y * x) * z) = (y * R(x,y,z)) * z
    ]]></literal>
    <justification jstring="[para(12884(a,1),12926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12884 12926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      L(x,a(y,z,x),u) \ x = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(41,a,1779,a,b,12929,a)].">
      <j1 rule="hyper" parents="41 1779 12929"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      x * a(y,x,L(z,x,y)) = z * (L(z,x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(8390,a,12940,a),flip(a)].">
      <j1 rule="hyper" parents="8390 12940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      x * (L(x,y,z) \ y) = y * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(12821(a,1),12961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12821 12961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      L(x,y,z) = (y * a(z,y,x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(12962(a,1),8359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12962 8359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      (x * (a(x,y,a(z,u,w)) * y)) \ (x * y) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(12951(a,1),11621(a,1,1,2))].">
      <j1 rule="para" parents="12951 11621"/>
    </justification>
  </clause>

  <clause id="12966">
    <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="[para(12951(a,1),11941(a,1,1))].">
      <j1 rule="para" parents="12951 11941"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      a(L(x,y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,8796,a,b,12959,a)].">
      <j1 rule="hyper" parents="37 8796 12959"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      a(a(L(x,y,z),u,u),y,z) = a(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(11560(a,2),12967(a,1,1))].">
      <j1 rule="para" parents="11560 12967"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      L(x,L(y,z,u),a(L(y,z,u),z,u)) = L(x,a(y,z,u),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12967(a,1),11756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12967 11756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      a(L(x,y,z),a(L(x,y,z),y,z),u) = a(a(x,y,z),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12967(a,1),11785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12967 11785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      L(x,y,L(z,y,x)) \ x = L(a(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(12967(a,1),12418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12967 12418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      L(x,y,L(z,y,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,12418,a(flip),b,12971,a),flip(a)].">
      <j1 rule="hyper" parents="41 12418 12971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = L(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(308(a,1),12972(a,1,3))].">
      <j1 rule="para" parents="308 12972"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      (x \ y) / ((x * z) \ y) = z * a(x,z,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(12824(a,1),12938(a,2,2))].">
      <j1 rule="para" parents="12824 12938"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      ((x \ (((x * y) * z) * a(x,u,z))) / z) / (y * a(x,u,z)) = a(x,y * a(x,u,z),z)
    ]]></literal>
    <justification jstring="[para(12945(a,1),12932(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12945 12932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) = a(y,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,12509,a,b,12893,a)].">
      <j1 rule="hyper" parents="36 12509 12893"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      (L(x,y,z) / y) \ (x / y) = a(z,y,y \ (x / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),12829(a,1,2))].">
      <j1 rule="para" parents="10 12829"/>
    </justification>
  </clause>

  <clause id="12979">
    <literal><![CDATA[
      (L(x,y,z) / y) \ (x / y) = a(z,y,y \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(325,a,10110,a(flip),b,12978,a),flip(a)].">
      <j1 rule="hyper" parents="325 10110 12978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      (L(x,y,z) / y) \ (x / y) = a(z,y,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12008,a(flip),b,12979,a),flip(a)].">
      <j1 rule="hyper" parents="325 12008 12979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      L(L(x,y,y) \ L(L(x,y,y),y,z),L(x,y,y),y) = ((L(x,y,z) / y) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(12981(a,2),12398(a,2,1))].">
      <j1 rule="para" parents="12981 12398"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      x \ R(x,L(y,z,u),y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10594,a,12878,a),flip(a)].">
      <j1 rule="hyper" parents="10594 12878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      x \ R(x,y,L(y,z,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1735(a,1),12983(a,1,2))].">
      <j1 rule="para" parents="1735 12983"/>
    </justification>
  </clause>

  <clause id="12986">
    <literal><![CDATA[
      x * a(x,y,L(y,z,u)) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(148,a,12985,a)].">
      <j1 rule="hyper" parents="148 12985"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) * x = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,7207,a,b,12985,a)].">
      <j1 rule="hyper" parents="40 7207 12985"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      R(x,y,y) \ R(x,y,L(y,z,z)) = a(z,z,a(x,y,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12986(a,1),12669(a,1,2))].">
      <j1 rule="para" parents="12986 12669"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = R(x,y,y) \ R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12986(a,1),12785(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12986 12785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      R(x,y,L(y,y,z)) = a(x,y,y) * x
    ]]></literal>
    <justification jstring="[para(12865(a,1),12987(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12865 12987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      R(x,y,L(y,y,z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1900,a(flip),b,12990,a),flip(a)].">
      <j1 rule="hyper" parents="325 1900 12990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      R(x,y,z \ (z / (y \ 1))) = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(1721(a,1),12991(a,1,3))].">
      <j1 rule="para" parents="1721 12991"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      R(x,y,z \ ((y \ 1) \ z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8717,a(flip),b,12992,a)].">
      <j1 rule="hyper" parents="65 8717 12992"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      R(x,y,z \ (y \ z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8991,a(flip),b,12993,a)].">
      <j1 rule="hyper" parents="65 8991 12993"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      (x * (a(y,z,u) * L(u,w,v5))) \ (a(y,z,u) * (x * L(u,w,v5))) = a(x,a(y,z,u),L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(12925(a,1),7270(a,1,2))].">
      <j1 rule="para" parents="12925 7270"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      a(x,y,z) * (y * a(x,y,z)) = z * (L(L(z,y,x),y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12542,a(flip),b,12953,a),flip(a)].">
      <j1 rule="hyper" parents="65 12542 12953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(x,y,z) * w)) = u * (a(u,w,a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(41,a,11735,a,b,12965,a)].">
      <j1 rule="hyper" parents="41 11735 12965"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * (y * (z \ 1)) = y * (L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(7484(a,1),12832(a,1,1))].">
      <j1 rule="para" parents="7484 12832"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      a(x,y,z) * (y * (z \ 1)) = y * (L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(12821(a,1),13000(a,1,1))].">
      <j1 rule="para" parents="12821 13000"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      (x \ y) * (L(z,x \ y,x) \ 1) = x \ (y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(65,a,11681,a(flip),b,13001,a),flip(a)].">
      <j1 rule="hyper" parents="65 11681 13001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ y = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12955,a(flip),b,12939,a),flip(a)].">
      <j1 rule="hyper" parents="65 12955 12939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      x * a(R(1 / y,y,x),x,z) = (R(1 / y,x,z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(765,a,12887,a),flip(a)].">
      <j1 rule="hyper" parents="765 12887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      x * a(R(1 / y,y,x),x,z) = (y \ R(y,x,z)) * x
    ]]></literal>
    <justification jstring="[para(1080(a,1),13004(a,2,1))].">
      <j1 rule="para" parents="1080 13004"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      x * a(L(1 / y,y,x),x,z) = (y \ R(y,x,z)) * x
    ]]></literal>
    <justification jstring="[para(8679(a,1),13005(a,1,2))].">
      <j1 rule="para" parents="8679 13005"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      x * a(L(y \ 1,y,x),x,z) = (y \ R(y,x,z)) * x
    ]]></literal>
    <justification jstring="[para(1872(a,1),13006(a,1,2))].">
      <j1 rule="para" parents="1872 13006"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      x * a(L(y,y,x),x,z) = (y \ R(y,x,z)) * x
    ]]></literal>
    <justification jstring="[para(1903(a,1),13007(a,1,2))].">
      <j1 rule="para" parents="1903 13007"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      a(L(x,x,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5051,a(flip),b,13008,a),flip(a)].">
      <j1 rule="hyper" parents="36 5051 13008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,x,z) = a(y \ x,x,z)
    ]]></literal>
    <justification jstring="[hyper(1887,a,13009,a),flip(a)].">
      <j1 rule="hyper" parents="1887 13009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      a(L(x,x,y),x \ y,z) = x \ R(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11087,a(flip),b,13009,a)].">
      <j1 rule="hyper" parents="65 11087 13009"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      a(L(T(x \ 1,x),x,y),y * x,z) = (x \ 1) \ R(x \ 1,y * x,z)
    ]]></literal>
    <justification jstring="[para(5688(a,1),13009(a,1,1))].">
      <j1 rule="para" parents="5688 13009"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      L(x,a(L(y,y,z),z,u),a(L(y,y,z),z,u)) = R(x,y \ R(y,z,u),a(L(y,y,z),z,u))
    ]]></literal>
    <justification jstring="[para(13009(a,1),9014(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13009 9014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      a(L(a(x,y,y),a(x,y,y),z),z,u) * y = R(a(x,y,y),z,u) * L(y,y,x)
    ]]></literal>
    <justification jstring="[para(13009(a,2),12682(a,1,1))].">
      <j1 rule="para" parents="13009 12682"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      a(L(L(x,y,z),x,L(u,y,z)),u,w) = L(x,y,z) \ R(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(12776(a,1),13009(a,1,1))].">
      <j1 rule="para" parents="12776 13009"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      R(x \ y,x,z) \ (x \ y) = a(y \ x,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(13010(a,1),5794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13010 5794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      R(L(x \ (y \ x),y,z),x,u) \ (x \ (y \ (a(z,y,y) \ x))) = a((y \ (a(z,y,y) \ x)) \ x,x,u) \ 1
    ]]></literal>
    <justification jstring="[para(12761(a,1),13017(a,1,1,1))].">
      <j1 rule="para" parents="12761 13017"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      a(x,y,z) \ (u * (z * a(x,y,z))) = u * (a(z,a(x,y,z),u) \ z)
    ]]></literal>
    <justification jstring="[hyper(7210,a,12907,a)].">
      <j1 rule="hyper" parents="7210 12907"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      (x \ y) * a(z,y,x) = L(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(132,a,7191,a(flip),b,12954,a),flip(a)].">
      <j1 rule="hyper" parents="132 7191 12954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(x,y,z) * w)) = R(u,w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(325,a,12888,a(flip),b,12999,a),flip(a)].">
      <j1 rule="hyper" parents="325 12888 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w * a(x,y,z))) = R(u,w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(65,a,7303,a(flip),b,13021,a)].">
      <j1 rule="hyper" parents="65 7303 13021"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      (x * y) \ (a(z,u,w) \ (x * (y * a(z,u,w)))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,13023,a,b,12889,a)].">
      <j1 rule="hyper" parents="132 13023 12889"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      a(x,y,z) \ (u * (z * a(x,y,z))) = u * (z * a(z,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(12913(a,1),13019(a,2,2))].">
      <j1 rule="para" parents="12913 13019"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      a(x,y,z) \ (u * (z * a(x,y,z))) = L(u,z,a(x,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(325,a,12958,a(flip),b,13025,a),flip(a)].">
      <j1 rule="hyper" parents="325 12958 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      R(x,y,a(z,u,y)) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(37,a,13023,a(flip),b,13026,a(flip))].">
      <j1 rule="hyper" parents="37 13023 13026"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      x \ R(x,y,a(z,u,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,13027,a,b,12902,a)].">
      <j1 rule="hyper" parents="132 13027 12902"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      R(x,y,z * R(u,w,v5)) = R(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(41,a,12894,a(flip),b,12895,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 12894 12895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      R(x,y,y * R(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,8998,a(flip),b,13029,a),flip(a)].">
      <j1 rule="hyper" parents="325 8998 13029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      R(x,y,z \ R(z,u,w)) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8783,a,b,13029,a)].">
      <j1 rule="hyper" parents="65 8783 13029"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      a(L(x \ 1,x,y),y * x,z) = (x \ 1) \ R(x \ 1,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(1878,a,13013,a)].">
      <j1 rule="hyper" parents="1878 13013"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      a(L(x,x,y),y * x,z) = (x \ 1) \ R(x \ 1,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,1903,a(flip),b,13032,a)].">
      <j1 rule="hyper" parents="65 1903 13032"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      a(L(x,x,y),y * x,z) = x \ R(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1081,a(flip),b,13034,a),flip(a)].">
      <j1 rule="hyper" parents="325 1081 13034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      a(L(L(x,y,z),x,L(u,y,z)),u,w) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,11554,a(flip),b,13016,a),flip(a)].">
      <j1 rule="hyper" parents="325 11554 13016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      a(L(L(x,x,L(y,z,u)),z,u),y,w) = L(x \ R(x,y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(1860,a,13036,a)].">
      <j1 rule="hyper" parents="1860 13036"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      (x / (L(x,y,z) \ x)) * a(z,y,x) = (a(y,x,a(z,y,x)) \ 1) * x
    ]]></literal>
    <justification jstring="[para(12823(a,1),12803(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12823 12803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      (x / (L(x,y,z) \ x)) * a(z,y,x) = a(y,x,a(z,y,x)) * x
    ]]></literal>
    <justification jstring="[para(12554(a,1),13039(a,2,1))].">
      <j1 rule="para" parents="12554 13039"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = a(y,x,a(z,y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,13041,a)].">
      <j1 rule="hyper" parents="334 13041"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = R(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(325,a,12909,a(flip),b,13042,a),flip(a)].">
      <j1 rule="hyper" parents="325 12909 13042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      a(x,y,z) * (y * K(x \ (x * y),u)) = T(a(x,y,z) * y,u)
    ]]></literal>
    <justification jstring="[para(9662(a,1),12936(a,1,2,2))].">
      <j1 rule="para" parents="9662 12936"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      a(x,y,z) * (y * K(y,u)) = T(a(x,y,z) * y,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13045(a,1,2,2,1))].">
      <j1 rule="para" parents="9 13045"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      T(a(x,y,z) * y,u) = a(x,y,z) * T(y,u)
    ]]></literal>
    <justification jstring="[para(2094(a,2),13046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2094 13046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      T(a(x,y,z) * y,u) = T(y,u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,7190,a(flip),b,13049,a),flip(a)].">
      <j1 rule="hyper" parents="325 7190 13049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      T(a(x,y,y) * y,y * x) = 1 / R((y * x) \ x,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,11933,a,b,13050,a),flip(a)].">
      <j1 rule="hyper" parents="325 11933 13050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      x * T(a(y,x,x) * x,x * y) = y \ (x * (y * x))
    ]]></literal>
    <justification jstring="[para(13050(a,2),11913(a,1,2))].">
      <j1 rule="para" parents="13050 11913"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      T(a(x,y,y) * y,y * x) = 1 / (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(10475(a,1),13051(a,2,2))].">
      <j1 rule="para" parents="10475 13051"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      x * (1 / (y \ (x \ y))) = y \ (x * (y * x))
    ]]></literal>
    <justification jstring="[para(13053(a,1),13052(a,1,2))].">
      <j1 rule="para" parents="13053 13052"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      (x \ y) \ (y * x) = y \ (x * (y * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11838,a(flip),b,13054,a)].">
      <j1 rule="hyper" parents="65 11838 13054"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      (((x \ y) \ (y * x)) \ 1) * ((y \ (x * (y * x))) * ((x * (y * x)) \ y)) = (x * (y * x)) \ y
    ]]></literal>
    <justification jstring="[para(13055(a,2),1419(a,1,1,1))].">
      <j1 rule="para" parents="13055 1419"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      R(x \ y,x \ y,(y * x) * (x \ y)) * (y * x) = ((x \ y) * (x \ y)) * (y \ (x * (y * x)))
    ]]></literal>
    <justification jstring="[para(13055(a,1),12010(a,2,2))].">
      <j1 rule="para" parents="13055 12010"/>
    </justification>
  </clause>

  <clause id="13058">
    <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(7498(a,1),12957(a,1,2,1))].">
      <j1 rule="para" parents="7498 12957"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,x,a(z,y,x)) \ x) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(12822(a,1),13058(a,1,2,1))].">
      <j1 rule="para" parents="12822 13058"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * a(x,a(z,y,x),y)) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(12912(a,1),13059(a,1,2))].">
      <j1 rule="para" parents="12912 13059"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      x * (a(x,a(y,z,x),z) * (x \ L(x,z,y))) = (a(y,z,x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,8512,a(flip),b,13060,a)].">
      <j1 rule="hyper" parents="65 8512 13060"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      a(x,a(y,z,x),z) * L(x,z,y) = (a(y,z,x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,9315,a(flip),b,13061,a)].">
      <j1 rule="hyper" parents="65 9315 13061"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      a(x,a(y,z,x),z) * L(x,z,y) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,10572,a(flip),b,13062,a),flip(a)].">
      <j1 rule="hyper" parents="325 10572 13062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      L(x,y,z) * a(x,a(z,y,x),y) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(7209,a,13063,a)].">
      <j1 rule="hyper" parents="7209 13063"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      L(x,y,z) * a(y,x,a(x,y,z)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,12908,a(flip),b,13064,a)].">
      <j1 rule="hyper" parents="65 12908 13064"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      ((x * y) * z) \ (y * (T(x,y) * z)) = (x * y) \ ((y * (T(x,y) * z)) / z)
    ]]></literal>
    <justification jstring="[para(5243(a,1),12810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5243 12810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      ((x * y) * z) \ (y * (T(x,y) * z)) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(325,a,12860,a(flip),b,13066,a),flip(a)].">
      <j1 rule="hyper" parents="325 12860 13066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      L(x,((y * z) * u) \ ((y * u) * z),w) = L(x,a(z,y,u) \ 1,w)
    ]]></literal>
    <justification jstring="[para(13067(a,1),11094(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13067 11094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11021,a(flip),b,13068,a),flip(a)].">
      <j1 rule="hyper" parents="65 11021 13068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      L(L(x,y,a(z,y,x)),y * a(z,y,x),z) = L(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,9934,a(flip),b,12890,a),flip(a)].">
      <j1 rule="hyper" parents="325 9934 12890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      L(x,y * a(z,y,x),z) = L(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(12916(a,1),13071(a,1,1))].">
      <j1 rule="para" parents="12916 13071"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      a(x,y * a(x,y,z),z) \ (y * a(x,y,z)) = L(z,y,L(x,y,z)) * (z \ (y * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(13072(a,1),12948(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13072 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      a(a(x,y,L(y,a(x,y,y),z)),z,u) * y = R(a(x,y,y),z,u) * L(y,y,x)
    ]]></literal>
    <justification jstring="[para(12665(a,2),13015(a,1,1,1))].">
      <j1 rule="para" parents="12665 13015"/>
    </justification>
  </clause>

  <clause id="13075">
    <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(12690(a,1),13074(a,1,1,1,3)),flip(a)].">
      <j1 rule="para" parents="12690 13074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      L(x,x,y) * R(a(y,x,x),z,u) = a(a(y,x,x),z,u) * x
    ]]></literal>
    <justification jstring="[hyper(7289,a,13075,a)].">
      <j1 rule="hyper" parents="7289 13075"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * ((w \ v5) * w)) * z))) = a(x,y,v5 * a(u,(w \ v5) * w,z))
    ]]></literal>
    <justification jstring="[hyper(10137,a,12941,a)].">
      <j1 rule="hyper" parents="10137 12941"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      a(x,y,L(L((z \ u) * z,w,v5),v5,w)) = a(x,y,u * a(w,(z \ u) * z,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,12184,a(flip),b,13077,a)].">
      <j1 rule="hyper" parents="65 12184 13077"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = a(x,y,z * a(w,(v5 \ z) * v5,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10520,a(flip),b,13078,a)].">
      <j1 rule="hyper" parents="65 10520 13078"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[para(176(a,1),13079(a,2,3,2,2))].">
      <j1 rule="para" parents="176 13079"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) * a(x,u,z)) / z) / (y * a(x,u,z)) = a(x,y * a(x,u,z),z)
    ]]></literal>
    <justification jstring="[para(11625(a,1),12976(a,1,1,1))].">
      <j1 rule="para" parents="11625 12976"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),y,y),L(x,y,y),y) = ((L(x,y,z) / y) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(4458(a,1),12982(a,1,1))].">
      <j1 rule="para" parents="4458 12982"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) * a(x,u,z)) / (y * a(x,u,z)) = a(x,y * a(x,u,z),z)
    ]]></literal>
    <justification jstring="[para(12944(a,1),13082(a,1,1))].">
      <j1 rule="para" parents="12944 13082"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      ((T(x,y) * z) \ (z * u)) \ (T(T(x,z),y) \ u) = a(z,T(T(x,z),y),u \ T(x,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10058,a(flip),b,12807,a),flip(a)].">
      <j1 rule="hyper" parents="325 10058 12807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      ((T(x,y) * z) \ (z * u)) \ (T(T(x,z),y) \ u) = a(z,T(T(x,z),y),u \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,10058,a(flip),b,13085,a),flip(a)].">
      <j1 rule="hyper" parents="325 10058 13085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      ((T(x,y) * z) \ (z * u)) \ (T(T(x,z),y) \ u) = a(z,x,u \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,10011,a(flip),b,13087,a),flip(a)].">
      <j1 rule="hyper" parents="325 10011 13087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      L(a(x,y,z \ y),u,T(T(y,x),w) \ z) = L(T(T(y,x),w) \ z,y,x) \ (T(T(y,x),w) \ z)
    ]]></literal>
    <justification jstring="[para(13089(a,1),10965(a,1,1))].">
      <j1 rule="para" parents="13089 10965"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      L(x,a(L(y,y,z),z,u),a(L(y,y,z),z,u)) = R(x,y \ R(y,z,u),y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(13009(a,1),13014(a,2,3))].">
      <j1 rule="para" parents="13009 13014"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      L(x,a(L(y,y,z),z,u),a(L(y,y,z),z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12787,a(flip),b,13092,a),flip(a)].">
      <j1 rule="hyper" parents="325 12787 13092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),a(L(y,y,z),z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13009(a,1),13093(a,1,2))].">
      <j1 rule="para" parents="13009 13093"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y \ R(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13009(a,1),13094(a,1,3))].">
      <j1 rule="para" parents="13009 13094"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      L(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(2367,a,13095,a)].">
      <j1 rule="hyper" parents="2367 13095"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) * a(y,y \ 1,z \ (x \ ((x * y) * z))) = (y \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(10046(a,1),12942(a,1,2))].">
      <j1 rule="para" parents="10046 12942"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      a(x,y * a(x,y,z),z) \ (y * a(x,y,z)) = L(z,y,L(x,y,z)) * ((z \ y) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(10580(a,1),13073(a,2,2))].">
      <j1 rule="para" parents="10580 13073"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) * a(y,y \ 1,L(L(y,x,z),z,x)) = (y \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12184(a,1),13097(a,1,2))].">
      <j1 rule="para" parents="12184 13097"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) * K(y,y \ 1) = (y \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5679(a,1),13099(a,1,2))].">
      <j1 rule="para" parents="5679 13099"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      (x \ ((x * T(y,y \ 1)) * z)) / z = (y \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12149,a(flip),b,13100,a)].">
      <j1 rule="hyper" parents="65 12149 13100"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      T(x,x \ 1) \ ((x \ 1) \ a(y,x,z)) = a(y,T(x,x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(132,a,13101,a(flip),b,12931,a(flip))].">
      <j1 rule="hyper" parents="132 13101 12931"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,x,z)) = a(y,T(x,x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,4858,a(flip),b,13103,a)].">
      <j1 rule="hyper" parents="65 4858 13103"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,x,z)) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,9991,a(flip),b,13104,a),flip(a)].">
      <j1 rule="hyper" parents="325 9991 13104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      L(a(x,y,z),y,y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12452,a(flip),b,13105,a)].">
      <j1 rule="hyper" parents="65 12452 13105"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      a(x,x,a(y,x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,13105,a(flip),b,11961,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 13105 11961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      a(a(x,y,z),y,y) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12741,a,b,13108,a)].">
      <j1 rule="hyper" parents="65 12741 13108"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      L(x \ L(x,y,z),y,y) = 1 \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(13108(a,1),12578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13108 12578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      K(x,y \ ((a(z,y,u) * y) \ ((a(z,y,u) * (y * y)) * w))) = K(x,1 \ w)
    ]]></literal>
    <justification jstring="[para(13109(a,1),8609(a,2,2,1))].">
      <j1 rule="para" parents="13109 8609"/>
    </justification>
  </clause>

  <clause id="13112">
    <literal><![CDATA[
      a(L(L(x,x,L(y,y,y)),y,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(43,a,13037,a(flip),b,13107,a),flip(a)].">
      <j1 rule="hyper" parents="43 13037 13107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13113">
    <literal><![CDATA[
      L(x \ L(x,y,z),y,y) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,67,a(flip),b,13110,a),flip(a)].">
      <j1 rule="hyper" parents="325 67 13110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13115">
    <literal><![CDATA[
      L(x \ L(x,y,z),L(x,y,y),y) = ((L(x,y,z) / y) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(13113(a,1),13083(a,1,1))].">
      <j1 rule="para" parents="13113 13083"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      a(L(L(x,x,y),y,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(6555(a,1),13112(a,1,1,1))].">
      <j1 rule="para" parents="6555 13112"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      a((x \ y) * y,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5079,a,13116,a)].">
      <j1 rule="hyper" parents="5079 13116"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      R(x,y,z) = x * a((x \ y) * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,5036,a(flip),b,13116,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 5036 13116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      a(x * (y \ x),x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(2363,a,13117,a)].">
      <j1 rule="hyper" parents="2363 13117"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      R(x,y,z) = x * a(y * (x \ y),y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,2337,a,b,13117,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 2337 13117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      (x / y) \ R(x / y,x,z) = a(y * x,x,z)
    ]]></literal>
    <justification jstring="[para(85(a,1),13117(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="85 13117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      a((x * ((x \ y) * y)) * y,y,z) = ((x \ y) \ (x \ 1)) \ R((x \ y) \ (x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(12374(a,1),13117(a,1,1,1))].">
      <j1 rule="para" parents="12374 13117"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ R((x \ ((x * y) * z)) / z,y,u) = a((a(x,y,z) \ 1) * y,y,u)
    ]]></literal>
    <justification jstring="[para(13003(a,1),13117(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13003 13117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      a(L(x,y,z) * (u \ L(x,y,z)),x,L(x,y,z)) = u \ R(u,L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(7455,a,13120,a)].">
      <j1 rule="hyper" parents="7455 13120"/>
    </justification>
  </clause>

  <clause id="13126">
    <literal><![CDATA[
      R(x,y,z) = a(y * (x \ y),y,z) * x
    ]]></literal>
    <justification jstring="[hyper(7225,a,13120,a),flip(a)].">
      <j1 rule="hyper" parents="7225 13120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      a(x * (y \ x),x,a(z,u,x)) = a(y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,13028,a(flip),b,13120,a),flip(a)].">
      <j1 rule="hyper" parents="325 13028 13120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      a(a(x,y,z) * (u \ a(x,y,z)),a(x,y,z),x) = a(u,a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,12896,a(flip),b,13120,a),flip(a)].">
      <j1 rule="hyper" parents="325 12896 13120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      L(x,y,z) * L(a(u * (x \ u),u,w),y,z) = L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(13120(a,2),11549(a,1,2,1))].">
      <j1 rule="para" parents="13120 11549"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      a((L(x,y,z) \ 1) * ((x \ 1) \ (1 / L(x,y,z))),1 / L(x,y,z),u) = (1 / x) \ R(1 / x,1 / L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12619(a,1),13120(a,1,1))].">
      <j1 rule="para" parents="12619 13120"/>
    </justification>
  </clause>

  <clause id="13131">
    <literal><![CDATA[
      (x * (y \ R(y,x,z))) \ (x * z) = L(z,x,x * (y \ x))
    ]]></literal>
    <justification jstring="[para(13120(a,1),12963(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13120 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      a(x * (y \ x),x,(z * ((u \ w) * v5)) \ v6) * y = R(y,x,(z * ((w / u) * v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(10446(a,1),13126(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10446 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      a(x * (y \ x),x,L(z,u,w) * v5) * y = R(y,x,R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(11359(a,1),13126(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11359 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      a(x * (y \ x),x,L(z,u,u) * w) * y = R(y,x,(u \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[para(11994(a,1),13126(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11994 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      R(x,y,z \ L(u * w,u,u)) = a(y * (x \ y),y,z \ (u \ w)) * x
    ]]></literal>
    <justification jstring="[para(12502(a,1),13126(a,2,1))].">
      <j1 rule="para" parents="12502 13126"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,y,z) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(4245,a,13122,a)].">
      <j1 rule="hyper" parents="4245 13122"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      x \ (y * R(y \ x,y,z)) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(4243,a,13122,a)].">
      <j1 rule="hyper" parents="4243 13122"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      (x * y) \ (x * R(x \ (x * y),x,z)) = a(L(y,x,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2341,a(flip),b,13137,a),flip(a)].">
      <j1 rule="hyper" parents="325 2341 13137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      a(x \ y,x,z) = a(y * x,x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12882,a(flip),b,13137,a)].">
      <j1 rule="hyper" parents="65 12882 13137"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      a(x * y,y,a(z,u,y)) = a(y,a(z,u,y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12901,a,b,13139,a),flip(a)].">
      <j1 rule="hyper" parents="65 12901 13139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      (x * y) \ ((z / x) \ (z * y)) = a(z * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11632,a,b,13139,a)].">
      <j1 rule="hyper" parents="65 11632 13139"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      a((x \ y) * y,y \ x,z) = a(y * (y \ x),y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12704,a(flip),b,13139,a)].">
      <j1 rule="hyper" parents="65 12704 13139"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      (x / y) \ (x * z) = (y * z) * a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,13139,a(flip),b,11632,a),flip(a)].">
      <j1 rule="hyper" parents="137 13139 11632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      a((x * ((x \ y) * z)) * y,y,u) = a(L(z,x \ y,x),y,u)
    ]]></literal>
    <justification jstring="[para(101(a,1),13139(a,1,1)),flip(a)].">
      <j1 rule="para" parents="101 13139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z * w)) \ (u * w)) = a(x,y,a(u * z,z,w))
    ]]></literal>
    <justification jstring="[para(13139(a,1),10323(a,2,3))].">
      <j1 rule="para" parents="13139 10323"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      a(x * y,y,z) \ x = ((x / y) * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(13139(a,1),11748(a,1,1))].">
      <j1 rule="para" parents="13139 11748"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u \ w) \ (w * z))) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[para(13139(a,1),11842(a,2,3))].">
      <j1 rule="para" parents="13139 11842"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      a(x,y,a(z \ ((u * u) * w),z,v5)) = a(x,y,a(v5,z,z * w))
    ]]></literal>
    <justification jstring="[para(13139(a,2),12843(a,1,3))].">
      <j1 rule="para" parents="13139 12843"/>
    </justification>
  </clause>

  <clause id="13149">
    <literal><![CDATA[
      x * (a(a(y,z,x),x,x \ u) \ (x \ u)) = u * a(u * x,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(13139(a,1),12911(a,2,2))].">
      <j1 rule="para" parents="13139 12911"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      a(x * (y \ K(z,u)),y \ K(z,u),w) = a(x / y,y \ K(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12162,a(flip),b,13141,a),flip(a)].">
      <j1 rule="hyper" parents="65 12162 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      a(x,y,L(z,a(u * w,w,w),v5)) = a(x,y,L(z,(u / w) \ (u * w),v5))
    ]]></literal>
    <justification jstring="[para(13141(a,1),11454(a,1,3,2))].">
      <j1 rule="para" parents="13141 11454"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      (x / y) \ (a(z,z,u) \ x) = (y * (u \ L(u,z,z))) * a(x * y,y,u \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(12730(a,1),13143(a,1,2))].">
      <j1 rule="para" parents="12730 13143"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      a(x * y,x,z) \ y = ((y / x) * (x * z)) / z
    ]]></literal>
    <justification jstring="[para(2337(a,1),13146(a,1,1))].">
      <j1 rule="para" parents="2337 13146"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      a(x,a(y,z,x),x \ u) = a(x,a(y,z,x),x * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12904,a(flip),b,13140,a),flip(a)].">
      <j1 rule="hyper" parents="65 12904 13140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      a(x,a(y,z,x),x * u) \ (x \ u) = L(x \ u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(13154(a,1),12585(a,1,1))].">
      <j1 rule="para" parents="13154 12585"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      a((x \ y) * y,y \ x,z) = a(x,y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),13142(a,2,1))].">
      <j1 rule="para" parents="10 13142"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      a(x * (y \ x),x \ y,z) = a(y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(2363,a,13156,a)].">
      <j1 rule="hyper" parents="2363 13156"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      (x * y) \ (x * R(y,x,z)) = a(L(y,x,x),x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),13138(a,1,2,2,1))].">
      <j1 rule="para" parents="9 13138"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      x \ (R(y,x,z) * (y \ x)) = a(L(y,x,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,9359,a(flip),b,13158,a)].">
      <j1 rule="hyper" parents="65 9359 13158"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      x \ (x * a(y,x,z)) = a(L(y,x,x),x,z)
    ]]></literal>
    <justification jstring="[para(12883(a,1),13159(a,1,2))].">
      <j1 rule="para" parents="12883 13159"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      a(L(x,y,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(332,a,13160,a),flip(a)].">
      <j1 rule="hyper" parents="332 13160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      a(x,y,a(((z * z) \ u) \ w,u,v5)) = a(x,y,a(v5,u,u * w))
    ]]></literal>
    <justification jstring="[para(554(a,2),13148(a,1,3,1))].">
      <j1 rule="para" parents="554 13148"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      a(x,y,a((z / (u * u)) \ w,z,v5)) = a(x,y,a(v5,z,z * w))
    ]]></literal>
    <justification jstring="[para(4604(a,2),13163(a,1,3))].">
      <j1 rule="para" parents="4604 13163"/>
    </justification>
  </clause>

  <clause id="13165">
    <literal><![CDATA[
      a(x,y,a(z / (u / (w * w)),u,v5)) = a(x,y,a(v5,u,u * z))
    ]]></literal>
    <justification jstring="[para(1870(a,2),13164(a,1,3))].">
      <j1 rule="para" parents="1870 13164"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      L(a(x * (y \ x),x,z),u,w) \ L(R(y,x,z),u,w) = L(y,u,w)
    ]]></literal>
    <justification jstring="[hyper(132,a,13129,a(flip),b,7227,a)].">
      <j1 rule="hyper" parents="132 13129 7227"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(y,y,y)) = ((L(x,y,z) / y) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12781,a(flip),b,13115,a)].">
      <j1 rule="hyper" parents="65 12781 13115"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      R(x,y,R(z,u,w) * v5) = R(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,13126,a,b,13133,a),flip(a)].">
      <j1 rule="hyper" parents="65 13126 13133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      a(x,y,R(z,z,L(u,w,v5) * v6) * (L(u,w,v5) * v6)) = a(x,y,z \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(13168(a,1),11395(a,1,3,1))].">
      <j1 rule="para" parents="13168 11395"/>
    </justification>
  </clause>

  <clause id="13170">
    <literal><![CDATA[
      a(x * (y \ K(z,u)),y \ 1,w) = a(x / y,y \ K(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(10165,a,13150,a)].">
      <j1 rule="hyper" parents="10165 13150"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      a(x / y,y \ K(z,u),w) = a(x * y,y \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8452,a(flip),b,13170,a),flip(a)].">
      <j1 rule="hyper" parents="65 8452 13170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      a(x / y,y \ 1,z) = a(x * y,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(10165,a,13171,a)].">
      <j1 rule="hyper" parents="10165 13171"/>
    </justification>
  </clause>

  <clause id="13174">
    <literal><![CDATA[
      a(x * (y \ x),(y \ x) \ 1,z) = a(y,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),13172(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 13172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) = ((L(x,y,z) / y) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,6555,a(flip),b,13167,a)].">
      <j1 rule="hyper" parents="65 6555 13167"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      ((L(x,y,z) / y) \ (x / y)) \ 1 = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12398,a(flip),b,13175,a),flip(a)].">
      <j1 rule="hyper" parents="65 12398 13175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) \ 1 = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(12981(a,1),13177(a,1,1))].">
      <j1 rule="para" parents="12981 13177"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(286,a,13178,a),flip(a)].">
      <j1 rule="hyper" parents="286 13178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      a(x,y,L(L(z,y,y),u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10508,a,13179,a)].">
      <j1 rule="hyper" parents="10508 13179"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      a(x,y,y * (z * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10173,a,13179,a)].">
      <j1 rule="hyper" parents="10173 13179"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      a(x,y,y \ z) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11997,a(flip),b,13179,a)].">
      <j1 rule="hyper" parents="65 11997 13179"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      a(x,y,y \ z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11996,a(flip),b,13179,a)].">
      <j1 rule="hyper" parents="65 11996 13179"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      a(x,y,(x * y) \ z) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12824,a,b,13183,a)].">
      <j1 rule="hyper" parents="65 12824 13183"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      (x * y) \ ((y * z) * (z \ x)) = K(y,x) * a(y,z,z * x)
    ]]></literal>
    <justification jstring="[para(13183(a,1),6162(a,2,2))].">
      <j1 rule="para" parents="13183 6162"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      a(x,y,y * (x \ z)) * z = (x * y) * (y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(13183(a,1),7259(a,1,1))].">
      <j1 rule="para" parents="13183 7259"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      T(x,y) * a(z,u,u * (z \ x)) = (z * u) * (u \ (z \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(13183(a,1),10240(a,1,2))].">
      <j1 rule="para" parents="13183 10240"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      x \ ((x * y) * (y \ z)) = z * a(x,y,y * z)
    ]]></literal>
    <justification jstring="[para(13183(a,1),11623(a,2,2))].">
      <j1 rule="para" parents="13183 11623"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      (x * (x \ y)) * (a(x,x,x \ y) * z) = a(x,x,x * y) * (y * z)
    ]]></literal>
    <justification jstring="[para(13183(a,1),11743(a,2,1))].">
      <j1 rule="para" parents="13183 11743"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      L(a(x,y,y * z),x,y) = x \ (((x * y) * (y \ z)) / z)
    ]]></literal>
    <justification jstring="[para(13183(a,1),12877(a,1,1))].">
      <j1 rule="para" parents="13183 12877"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      (x \ y) / ((x * z) \ y) = z * a(x,z,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(13183(a,1),12975(a,2,2))].">
      <j1 rule="para" parents="13183 12975"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      R(x,y,(z * u) * (u \ z)) = R(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(13184(a,1),8275(a,2,3))].">
      <j1 rule="para" parents="13184 8275"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      L(x,y,a(z,u,z * u)) = L(x,y,a(u,u,u \ z))
    ]]></literal>
    <justification jstring="[para(13184(a,1),10537(a,1,3))].">
      <j1 rule="para" parents="13184 10537"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w * u)) * y,x,a(z,u,u \ w)) = L(y,a(z,u,u \ w),x)
    ]]></literal>
    <justification jstring="[para(13184(a,1),12966(a,1,1,1,3))].">
      <j1 rule="para" parents="13184 12966"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      x \ (a(y,z,x) \ ((x * u) * (u \ a(y,z,x)))) = a(x,u,u * a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,10588,a,b,13191,a(flip))].">
      <j1 rule="hyper" parents="36 10588 13191"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      L(x,y,a(z,z,z \ u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9054,a(flip),b,13197,a),flip(a)].">
      <j1 rule="hyper" parents="65 9054 13197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      L(x \ y,z,a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(65,a,12916,a(flip),b,13200,a),flip(a)].">
      <j1 rule="hyper" parents="65 12916 13200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      L(x,y,a(z,z,z * u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),13200(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="9 13200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      L(x,y,a(z * u,z,z)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10715,a,b,13202,a)].">
      <j1 rule="hyper" parents="65 10715 13202"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      x * a(a(y * z,y,y),x,x) = L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12743,a,b,13203,a)].">
      <j1 rule="hyper" parents="65 12743 13203"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      R(x,y,(z * u) * (u \ z)) = R(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,9047,a(flip),b,13196,a),flip(a)].">
      <j1 rule="hyper" parents="325 9047 13196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      x \ (((x * y) * (y \ z)) / z) = x \ R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12870,a(flip),b,13194,a),flip(a)].">
      <j1 rule="hyper" parents="65 12870 13194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      x \ R(x,y,y \ z) = x \ R(x,y,y * z)
    ]]></literal>
    <justification jstring="[para(108(a,1),13206(a,1,2))].">
      <j1 rule="para" parents="108 13206"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      R(x,y,y \ z) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(49,a,13207,a)].">
      <j1 rule="hyper" parents="49 13207"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,z * x)
    ]]></literal>
    <justification jstring="[hyper(939,a,13208,a)].">
      <j1 rule="hyper" parents="939 13208"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      R(x,y,y * z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(136,a,13208,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="136 13208 108"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      x * R(a(y,z,u),w,w * x) = (a(y,z,u) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(13208(a,1),7288(a,1,2))].">
      <j1 rule="para" parents="13208 7288"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      a(L(R(x,y,y * z),z,z),u,w) = a(z * ((x * y) * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[para(13212(a,1),3515(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13212 3515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      R(x,y,z * y) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(8690(a,1),13212(a,1,1))].">
      <j1 rule="para" parents="8690 13212"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      (((x / (y * z)) / z) * z) * (z \ y) = (x / (z * (y * z))) * y
    ]]></literal>
    <justification jstring="[para(310(a,1),13215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 13215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      (x / (y * (z * y))) * z = (x / (z * y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(327,a,13216,a),flip(a)].">
      <j1 rule="hyper" parents="327 13216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      a(x,x,x * y) * (y * z) = y * (a(x,x,x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(528,a,13192,a),flip(a)].">
      <j1 rule="hyper" parents="528 13192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      a(x,x,x * y) * (y * z) = y * (a(x,x,x * y) * z)
    ]]></literal>
    <justification jstring="[para(13183(a,1),13221(a,2,2,1))].">
      <j1 rule="para" parents="13183 13221"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      (((x \ y) / y) * x) * (y * z) = y * (a(x,x,x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12005,a(flip),b,13223,a)].">
      <j1 rule="hyper" parents="65 12005 13223"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      a(L(L(x,y,y * z),z,z),u,w) = a(z * ((x * y) * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8685,a(flip),b,13214,a)].">
      <j1 rule="hyper" parents="65 8685 13214"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      R(x,y,(z \ (z \ u)) * w) = R(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13126,a,b,13134,a),flip(a)].">
      <j1 rule="hyper" parents="65 13126 13134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      R(x,y,L(z * u,z,z) * w) = R(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),13226(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="9 13226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      R(x,y,z \ L(u * w,u,u)) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(325,a,13126,a,b,13135,a),flip(a)].">
      <j1 rule="hyper" parents="325 13126 13135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      R(x,y,z \ L(u * w,w,w)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9877,a,b,13228,a)].">
      <j1 rule="hyper" parents="65 9877 13228"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      R(x,y,z \ (L(u,w,w) * w)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8986,a(flip),b,13229,a)].">
      <j1 rule="hyper" parents="65 8986 13229"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      a(x,y,L(z,a(u * w,w,w),v5)) = a(x,y,L(z,(w \ u) \ (u * w),v5))
    ]]></literal>
    <justification jstring="[para(10824(a,1),13151(a,2,3))].">
      <j1 rule="para" parents="10824 13151"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      a(x,y,L(z,a(u * w,w,w),v5)) = a(x,y,L(z,u \ (w * (u * w)),v5))
    ]]></literal>
    <justification jstring="[para(13055(a,1),13231(a,2,3,2))].">
      <j1 rule="para" parents="13055 13231"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      K(x,y \ ((a(z,y,u) * y) \ ((y * y) * (a(z,y,u) * w)))) = K(x,1 \ w)
    ]]></literal>
    <justification jstring="[para(7232(a,1),13111(a,1,2,2,2))].">
      <j1 rule="para" parents="7232 13111"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      a(L(x,y,z) * (u \ L(x,y,z)),x,L(x,y,z)) = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,12983,a(flip),b,13125,a),flip(a)].">
      <j1 rule="hyper" parents="325 12983 13125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13235">
    <literal><![CDATA[
      x * (a(a(y,z,x),x,x * u) \ (x \ u)) = u * a(u * x,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(13183(a,1),13149(a,1,2,1))].">
      <j1 rule="para" parents="13183 13149"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      x \ R(T(x,a(y,z,x)),u,u * a(y,z,x)) = a(x,u,u * a(y,z,x))
    ]]></literal>
    <justification jstring="[para(13209(a,1),13199(a,1,2))].">
      <j1 rule="para" parents="13209 13199"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      x \ R(x,y,y * a(z,u,x)) = a(x,y,y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(7179(a,1),13236(a,1,2,1))].">
      <j1 rule="para" parents="7179 13236"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      K(x,(((a(y,z,u) * z) * z) \ (z * z)) * (a(y,z,u) * w)) = K(x,1 \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8323,a(flip),b,13233,a)].">
      <j1 rule="hyper" parents="65 8323 13233"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      x * (a(x,a(y,z,x),x * u) \ (x \ u)) = u * a(u * x,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(10613(a,1),13235(a,1,2,1))].">
      <j1 rule="para" parents="10613 13235"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      K(x,((y * (a(z,y,u) * y)) \ (y * y)) * (a(z,y,u) * w)) = K(x,1 \ w)
    ]]></literal>
    <justification jstring="[para(7684(a,1),13238(a,1,2,1,1))].">
      <j1 rule="para" parents="7684 13238"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,x)) = y * a(y * x,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(13155(a,1),13239(a,1,2))].">
      <j1 rule="para" parents="13155 13239"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,x)) = y * a(y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[para(12840(a,1),13241(a,2,2))].">
      <j1 rule="para" parents="12840 13241"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      K(x,(a(y,z,u) * z) \ ((z \ 1) \ (a(y,z,u) * w))) = K(x,1 \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8446,a(flip),b,13240,a)].">
      <j1 rule="hyper" parents="65 8446 13240"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      K(x,y \ (a(z,y,u) \ ((y \ 1) \ (a(z,y,u) * w)))) = K(x,1 \ w)
    ]]></literal>
    <justification jstring="[hyper(8262,a,13243,a)].">
      <j1 rule="hyper" parents="8262 13243"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      K(x,y \ (a(z,y,u) \ ((y \ 1) \ (a(z,y,u) * w)))) = K(x,w)
    ]]></literal>
    <justification jstring="[para(67(a,1),13244(a,2,2))].">
      <j1 rule="para" parents="67 13244"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      K(x,a(y,z,u) * (z \ ((z \ 1) \ (a(y,z,u) * w)))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12653,a(flip),b,13245,a)].">
      <j1 rule="hyper" parents="65 12653 13245"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      K(x,y \ ((y \ 1) \ (a(z,y,u) * w))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12816,a(flip),b,13246,a)].">
      <j1 rule="hyper" parents="65 12816 13246"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7343,a(flip),b,13247,a)].">
      <j1 rule="hyper" parents="65 7343 13247"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7400,a,13249,a)].">
      <j1 rule="hyper" parents="7400 13249"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = T(x,w) / x
    ]]></literal>
    <justification jstring="[hyper(325,a,2117,a(flip),b,13249,a),flip(a)].">
      <j1 rule="hyper" parents="325 2117 13249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      K(x,y \ (a(z,u,w) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,12653,a,b,13249,a)].">
      <j1 rule="hyper" parents="65 12653 13249"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      T((x * a(y,z,u)) * K(w,x),w) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(13250(a,1),1589(a,1,1,2))].">
      <j1 rule="para" parents="13250 1589"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,2117,a(flip),b,13253,a(flip))].">
      <j1 rule="hyper" parents="39 2117 13253"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7395,a,13258,a)].">
      <j1 rule="hyper" parents="7395 13258"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      x * T(y,a(z,u,w) * x) = y * x
    ]]></literal>
    <justification jstring="[hyper(137,a,13258,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="137 13258 22"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12649,a,b,13258,a)].">
      <j1 rule="hyper" parents="65 12649 13258"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,4870,a(flip),b,13259,a),flip(a)].">
      <j1 rule="hyper" parents="65 4870 13259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(y,z,u)) = w * (T(x,w) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13259(a,1),7267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13259 7267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      T(a(x,y,z) / u,u \ 1) = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[hyper(2900,a,13262,a)].">
      <j1 rule="hyper" parents="2900 13262"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      T(x / (a(y,z,u) \ w),w) = (a(y,z,u) \ w) \ x
    ]]></literal>
    <justification jstring="[hyper(376,a,13261,a),flip(a)].">
      <j1 rule="hyper" parents="376 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(w,u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(137,a,13261,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 13261 22"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) * x,y) = (a(z,u,w) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(13261(a,1),8896(a,1,2))].">
      <j1 rule="para" parents="13261 8896"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      (x / (a(y,z,u) * w)) * w = w * ((a(y,z,u) * w) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,250,a(flip),b,13260,a),flip(a)].">
      <j1 rule="hyper" parents="65 250 13260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(13260(a,1),7266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13260 7266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      K(x,x \ y) * (x \ (a(z,u,w) \ y)) = (a(z,u,w) \ y) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,13254,a(flip),b,2460,a)].">
      <j1 rule="hyper" parents="136 13254 2460"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      (1 / (1 / x)) \ a(y,z,u) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,7449,a(flip),b,13264,a)].">
      <j1 rule="hyper" parents="65 7449 13264"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      1 / (1 / (x \ a(y,z,u))) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(201,a,82,a(flip),b,13278,a),flip(a)].">
      <j1 rule="hyper" parents="201 82 13278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      a(x,y,z) / (u \ 1) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),13278(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 13278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      ((1 / x) \ 1) * ((1 / x) \ (((1 / x) \ 1) \ a(y,z,u))) = ((1 / x) * (1 / x)) \ (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(13278(a,1),9846(a,2,2))].">
      <j1 rule="para" parents="13278 9846"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      1 / (1 / (K(x,y) \ a(z,u,w))) = a(z,u,w) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2848,a(flip),b,13280,a),flip(a)].">
      <j1 rule="hyper" parents="325 2848 13280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) \ 1 = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(13280(a,1),200(a,1,1,1))].">
      <j1 rule="para" parents="13280 200"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      T((1 / x) \ a(y,z,u),x \ 1) = (x \ 1) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[para(13281(a,1),115(a,1,1))].">
      <j1 rule="para" parents="13281 115"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      T(a(x,y,z) * (u * K(w,u)),w) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(7912(a,1),13257(a,1,1))].">
      <j1 rule="para" parents="7912 13257"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      a(x,x,y) \ ((y * x) * z) = (y * x) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12927,a(flip),b,13269,a)].">
      <j1 rule="hyper" parents="65 12927 13269"/>
    </justification>
  </clause>

  <clause id="13288">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ w) = (w / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,250,a(flip),b,13269,a)].">
      <j1 rule="hyper" parents="65 250 13269"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) = T(u,w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1583(a,1),13286(a,1,1,2))].">
      <j1 rule="para" parents="1583 13286"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      T(a(x,y,y * (x \ z)) * z,u) = (x * y) * (y \ (x \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(325,a,13189,a(flip),b,13289,a),flip(a)].">
      <j1 rule="hyper" parents="325 13189 13289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,w)) = (a(z,u,w) * y) * x
    ]]></literal>
    <justification jstring="[hyper(137,a,13289,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="137 13289 22"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) * x,y) = (y * x) / (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(13289(a,2),8430(a,1,2))].">
      <j1 rule="para" parents="13289 8430"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (u * w) = (a(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[hyper(7319,a,13292,a)].">
      <j1 rule="hyper" parents="7319 13292"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(37,a,109,a,b,13294,a)].">
      <j1 rule="hyper" parents="37 109 13294"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) * u) / (y * u) = L(a(x,y,z),y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12934,a,b,13295,a)].">
      <j1 rule="hyper" parents="65 12934 13295"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (L(R(x,x,w),y,z) * u) = L(a(x,x,L(w,y,z)),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12061,a,b,13295,a)].">
      <j1 rule="hyper" parents="65 12061 13295"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      L(a(x,x,y),x * y,z) = ((x * y) * z) \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11905,a(flip),b,13295,a),flip(a)].">
      <j1 rule="hyper" parents="65 11905 13295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13299">
    <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(13295(a,1),1470(a,1,1,2))].">
      <j1 rule="para" parents="13295 1470"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (L(a(x,y,z) \ 1,u,w) \ v5) = a(x,y,z) * (R(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(13295(a,2),1523(a,2,2,1))].">
      <j1 rule="para" parents="13295 1523"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 = v5 * R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13295(a,2),7227(a,2,2))].">
      <j1 rule="para" parents="13295 7227"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),x,y) = R(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13295(a,1),12875(a,1,1))].">
      <j1 rule="para" parents="13295 12875"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),z,x * y) = R(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(13295(a,1),12855(a,1,1))].">
      <j1 rule="para" parents="13295 12855"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(a(x,y,z),u,w) = u * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13295(a,1),12885(a,1,2))].">
      <j1 rule="para" parents="13295 12885"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      x * L(a(y,z,u),w,w * x) = (a(y,z,u) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(13295(a,1),13213(a,1,2))].">
      <j1 rule="para" parents="13295 13213"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) * w = w * R(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(12665(a,2),13303(a,1,1))].">
      <j1 rule="para" parents="12665 13303"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) * L(y,y,x) = a(a(x,y,y),z,u) * y
    ]]></literal>
    <justification jstring="[hyper(325,a,13076,a(flip),b,13308,a),flip(a)].">
      <j1 rule="hyper" parents="325 13076 13308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12876,a(flip),b,13304,a),flip(a)].">
      <j1 rule="hyper" parents="65 12876 13304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      (x / (y * a(z,u,w))) * y = y * ((a(z,u,w) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7472,a,13271,a)].">
      <j1 rule="hyper" parents="7472 13271"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      1 / (1 / (K(x,y) * a(z,u,w))) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2618(a,1),13283(a,1,2,2))].">
      <j1 rule="para" parents="2618 13283"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      x \ ((x \ 1) \ a(y,z,u)) = x * ((1 / x) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13285(a,1),12603(a,1,2))].">
      <j1 rule="para" parents="13285 12603"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      1 / (1 / (a(x,y,z) * K(u,w))) = a(x,y,z) * K(u,w)
    ]]></literal>
    <justification jstring="[para(7190(a,2),13313(a,1,2,2))].">
      <j1 rule="para" parents="7190 13313"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12856,a(flip),b,13305,a),flip(a)].">
      <j1 rule="hyper" parents="65 12856 13305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      x * (y * L(L(x,z,u) \ x,x,y)) = ((L(x,z,u) \ x) * x) * y
    ]]></literal>
    <justification jstring="[para(13317(a,1),10599(a,1,2,2))].">
      <j1 rule="para" parents="13317 10599"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(37,a,12682,a,b,13309,a(flip))].">
      <j1 rule="hyper" parents="37 12682 13309"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) * y) = (a(z,u,w) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13270,a(flip),b,13293,a),flip(a)].">
      <j1 rule="hyper" parents="65 13270 13293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) * w) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(136,a,7473,a(flip),b,13321,a)].">
      <j1 rule="hyper" parents="136 7473 13321"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      a(x,x,L(y,x * y,z)) = ((x * y) * z) \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12056,a,b,13298,a)].">
      <j1 rule="hyper" parents="65 12056 13298"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(37,a,109,a,b,13322,a)].">
      <j1 rule="hyper" parents="37 109 13322"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      T((x * y) * (y \ (x \ z)),u) = (x * y) * (y \ (x \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(13188(a,1),13291(a,1,1))].">
      <j1 rule="para" parents="13188 13291"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      T((x * y) * (y \ (x \ y)),x) = (y * x) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,6254,a(flip),b,13326,a),flip(a)].">
      <j1 rule="hyper" parents="325 6254 13326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = (x * y) * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(10470(a,1),13327(a,1,1))].">
      <j1 rule="para" parents="10470 13327"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      (x * y) * (x \ (y \ x)) = x * K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6251,a(flip),b,13328,a),flip(a)].">
      <j1 rule="hyper" parents="65 6251 13328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13330">
    <literal><![CDATA[
      (x * y) * (x \ (y \ x)) = x * K(x * y,y)
    ]]></literal>
    <justification jstring="[para(4651(a,2),13329(a,2,2))].">
      <j1 rule="para" parents="4651 13329"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      R(x,y,x \ (y \ x)) \ (x * K(x * y,y)) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(132,a,13330,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="132 13330 109"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * y = y * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12811,a(flip),b,13306,a)].">
      <j1 rule="hyper" parents="65 12811 13306"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(7272,a,13332,a),flip(a)].">
      <j1 rule="hyper" parents="7272 13332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ y = y * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12951,a,b,13332,a)].">
      <j1 rule="hyper" parents="65 12951 13332"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,12841,a(flip),b,13332,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 12841 13332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),a(y,z,u),w) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13332(a,1),12113(a,1,1))].">
      <j1 rule="para" parents="13332 12113"/>
    </justification>
  </clause>

  <clause id="13337">
    <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(13332(a,1),12966(a,1,1))].">
      <j1 rule="para" parents="13332 12966"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      a(a(x,y,z),u * w,v5) = a(v5,w * u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10160,a,13333,a)].">
      <j1 rule="hyper" parents="10160 13333"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,12554,a,b,13333,a)].">
      <j1 rule="hyper" parents="325 12554 13333"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11785,a(flip),b,13333,a)].">
      <j1 rule="hyper" parents="65 11785 13333"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(13333(a,2),12554(a,1,1))].">
      <j1 rule="para" parents="13333 12554"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ y) * x = y * L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(13333(a,1),12946(a,1,1,1))].">
      <j1 rule="para" parents="13333 12946"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      a(a(x,y,z),u * w,v5) = a(v5,w * u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(10160,a,13335,a)].">
      <j1 rule="hyper" parents="10160 13335"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,13333,a,b,13335,a)].">
      <j1 rule="hyper" parents="325 13333 13335"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11785,a(flip),b,13335,a)].">
      <j1 rule="hyper" parents="65 11785 13335"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      (x \ ((x * y) * a(z,u,w))) \ (y * a(z,u,w)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12897,a,b,13339,a)].">
      <j1 rule="hyper" parents="65 12897 13339"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      (x * y) \ (L(x,y,a(z,u,w)) * y) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12412,a,b,13342,a)].">
      <j1 rule="hyper" parents="65 12412 13342"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      1 * a(x,y * z,a(u,w,v5)) = a(a(u,w,v5),z * y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,7,a,b,13338,a)].">
      <j1 rule="hyper" parents="325 7 13338"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      a(x,y * ((z * z) \ u),a(w,v5,v6)) = a(a(v6,v5,w),u * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7568,a(flip),b,13344,a),flip(a)].">
      <j1 rule="hyper" parents="65 7568 13344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      a(a(x,y,z),(u \ w) * (((v5 * v5) \ v6) * v6),v7) = a(v7,(v6 * v6) * (u \ (w / (v5 * v5))),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(937(a,1),13344(a,1,2))].">
      <j1 rule="para" parents="937 13344"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      (x * a(a(y,z,u),x,w)) * w = x * L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13334(a,1),13343(a,1,1))].">
      <j1 rule="para" parents="13334 13343"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w * a(x,y,z))) = L(u,w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(40,a,13024,a,b,13352,a)].">
      <j1 rule="hyper" parents="40 13024 13352"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      1 * a(x,y * (z \ 1),a(u,w,v5)) = a(a(u,w,v5),z * y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,7570,a(flip),b,13353,a),flip(a)].">
      <j1 rule="hyper" parents="325 7570 13353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      (x * y) * a(a(z,u,w),x,y) = x * L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12920,a(flip),b,13356,a)].">
      <j1 rule="hyper" parents="65 12920 13356"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,u,a(x,y,z))) = (a(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[para(13356(a,1),12943(a,1,2))].">
      <j1 rule="para" parents="13356 12943"/>
    </justification>
  </clause>

  <clause id="13362">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * u) * w) = u * L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11624,a,b,13360,a)].">
      <j1 rule="hyper" parents="65 11624 13360"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ x) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,12390,a,b,13360,a(flip))].">
      <j1 rule="hyper" parents="36 12390 13360"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(140,a,13363,a),flip(a)].">
      <j1 rule="hyper" parents="140 13363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) \ 1 = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,4168,a,b,13363,a)].">
      <j1 rule="hyper" parents="65 4168 13363"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(13363(a,1),12357(a,1,1))].">
      <j1 rule="para" parents="13363 12357"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      L((a(x,y,z) * u) \ w,u,a(x,y,z)) = u \ (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(526,a,13366,a),flip(a)].">
      <j1 rule="hyper" parents="526 13366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      L((x * a(y,z,u)) \ w,x,a(y,z,u)) = x \ (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(43,a,7274,a,b,13366,a),flip(a)].">
      <j1 rule="hyper" parents="43 7274 13366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      (x * L(y,x,a(z,u,w))) * a(z,u,w) = (x * a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(137,a,13366,a(flip),b,7320,a),flip(a)].">
      <j1 rule="hyper" parents="137 13366 7320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),y,a(z,u,w)) * (y * (a(z,u,w) * (x * a(a(z,u,w),x,y)))) = y * (a(z,u,w) * R(x * a(a(z,u,w),x,y),y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(13336(a,1),7448(a,1,1,1))].">
      <j1 rule="para" parents="13336 7448"/>
    </justification>
  </clause>

  <clause id="13373">
    <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(43,a,13366,a,b,13337,a)].">
      <j1 rule="hyper" parents="43 13366 13337"/>
    </justification>
  </clause>

  <clause id="13374">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(37,a,13023,a(flip),b,13357,a(flip))].">
      <j1 rule="hyper" parents="37 13023 13357"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      R(x,y,(z * u) * (u \ z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13205,a,b,13374,a)].">
      <j1 rule="hyper" parents="65 13205 13374"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ (u * (z * w))) = L(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11821,a,b,13374,a)].">
      <j1 rule="hyper" parents="65 11821 13374"/>
    </justification>
  </clause>

  <clause id="13377">
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11685,a,b,13374,a)].">
      <j1 rule="hyper" parents="65 11685 13374"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      R(x,y,z \ (u \ (z \ u))) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11667,a,b,13374,a)].">
      <j1 rule="hyper" parents="65 11667 13374"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      L(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,11622,a(flip),b,13374,a),flip(a)].">
      <j1 rule="hyper" parents="65 11622 13374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) = R(y,y,z) / ((x \ y) * a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11608,a(flip),b,13374,a),flip(a)].">
      <j1 rule="hyper" parents="65 11608 13374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      L(x / (y \ 1),y \ 1,a(z,u,y)) = (x * a(z,u,y)) / (y \ a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10573,a(flip),b,13374,a),flip(a)].">
      <j1 rule="hyper" parents="65 10573 13374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (y * a(z,u,w)) = a(z,u,w) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,13374,a(flip),b,7260,a)].">
      <j1 rule="hyper" parents="136 13374 7260"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,w)) \ (y * a(z,u,w)) = (x \ y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(13374(a,1),481(a,1,1))].">
      <j1 rule="para" parents="13374 481"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      L(x,y * y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(13374(a,1),7325(a,1))].">
      <j1 rule="para" parents="13374 7325"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) \ L(y,y,z) = a(z,y,y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(13374(a,1),12727(a,1,1))].">
      <j1 rule="para" parents="13374 12727"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      L(R(x,y,z),u,a(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(13379(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13379 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      L(x * y,x * y,a(y,y,x)) \ (y \ x) = (1 / (x * y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(13375(a,1),12261(a,1,1))].">
      <j1 rule="para" parents="13375 12261"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      L(x,y * z,a(z,z,y)) * (z \ y) = (x * (y * z)) * ((y * z) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(13375(a,1),13212(a,1,1))].">
      <j1 rule="para" parents="13375 13212"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      L(x,x,a(x,x,y)) \ (y \ (x \ y)) = (1 / x) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(13377(a,1),12261(a,1,1))].">
      <j1 rule="para" parents="13377 12261"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      a(x,y * (z \ 1),a(u,w,v5)) = a(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(130,a,13359,a,b,13338,a(flip))].">
      <j1 rule="hyper" parents="130 13359 13338"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      a(x,(y * z) * y,a(u,w,v5)) = a(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10211,a(flip),b,13391,a),flip(a)].">
      <j1 rule="hyper" parents="65 10211 13391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13393">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ ((a(x,y,z) \ x) * u) = x * L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,11618,a,b,13362,a)].">
      <j1 rule="hyper" parents="65 11618 13362"/>
    </justification>
  </clause>

  <clause id="13394">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(a(z,u,w),x,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13191,a(flip),b,13362,a),flip(a)].">
      <j1 rule="hyper" parents="65 13191 13362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      x * a(y,a(y,z,u),x) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,11804,a(flip),b,13362,a(flip))].">
      <j1 rule="hyper" parents="36 11804 13362"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * u = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(7226,a,13395,a)].">
      <j1 rule="hyper" parents="7226 13395"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      x * a(x,y,a(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13341(a,1),13395(a,1,2))].">
      <j1 rule="para" parents="13341 13395"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      L(x,L(y,z,u),a(L(y,z,u),z,u)) = a(a(y,z,u),L(y,z,u),x) * x
    ]]></literal>
    <justification jstring="[para(12970(a,1),13396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12970 13396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * x = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13341(a,1),13396(a,1,1))].">
      <j1 rule="para" parents="13341 13396"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      x * a(x,y * z,a(y * z,y,y)) = L(x,y * z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13203,a(flip),b,13398,a),flip(a)].">
      <j1 rule="hyper" parents="325 13203 13398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,x)) = L(y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13242,a,b,13398,a)].">
      <j1 rule="hyper" parents="65 13242 13398"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) = x \ L(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(1336,a,13404,a),flip(a)].">
      <j1 rule="hyper" parents="1336 13404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      L(x * y,y,a(y,z,u)) = L(x,y,a(u,z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(816,a,13404,a),flip(a)].">
      <j1 rule="hyper" parents="816 13404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      L(x * y,x,a(x,z,u)) = x * L(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),13404(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 13404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      L(x \ a(x,y,z),x,a(x,u,w)) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11580(a,1),13407(a,2,2))].">
      <j1 rule="para" parents="11580 13407"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      L(a(x,y,z) * x,x,a(x,u,w)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[para(11580(a,1),13408(a,2,1))].">
      <j1 rule="para" parents="11580 13408"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * x) \ 1 = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7240,a(flip),b,13410,a)].">
      <j1 rule="hyper" parents="65 7240 13410"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ 1 = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11589(a,1),13412(a,1,1))].">
      <j1 rule="para" parents="11589 13412"/>
    </justification>
  </clause>

  <clause id="13414">
    <literal><![CDATA[
      (a(x,y,z) / x) \ 1 = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,13284,a,b,13413,a)].">
      <j1 rule="hyper" parents="41 13284 13413"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      (1 / x) * (y \ (x \ y)) = x \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(11670(a,1),13390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11670 13390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(a(z,u,w),x,y * x)
    ]]></literal>
    <justification jstring="[para(10045(a,1),13394(a,2,2))].">
      <j1 rule="para" parents="10045 13394"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(x * y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13335(a,1),13394(a,2,2))].">
      <j1 rule="para" parents="13335 13394"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) * y = x * a(y * x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(612,a,13417,a)].">
      <j1 rule="hyper" parents="612 13417"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      R(x,y,y) \ (x * K(x * y,y)) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(12994(a,1),13331(a,1,1))].">
      <j1 rule="para" parents="12994 13331"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      (R(x,y,y) \ x) * K(x * y,y) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(8307,a,13420,a)].">
      <j1 rule="hyper" parents="8307 13420"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(y,z,u)) = (a(y,z,u) * x) * w
    ]]></literal>
    <justification jstring="[hyper(325,a,13292,a(flip),b,13263,a),flip(a)].">
      <j1 rule="hyper" parents="325 13292 13263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      (a(x,y,z) * (T(u,a(x,y,z)) * w)) / w = w \ ((w * u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,11739,a(flip),b,13350,a)].">
      <j1 rule="hyper" parents="41 11739 13350"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      T(a(x,y,z) * (T(u,a(x,y,z)) / w),w) = (w \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10876,a(flip),b,13383,a)].">
      <j1 rule="hyper" parents="65 10876 13383"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      (1 / (x * y)) * (y \ x) = (x * y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(12918(a,1),13388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12918 13388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      a(a(x,y,z),L(x,y,z),u) * u = L(u,a(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12969,a(flip),b,13399,a),flip(a)].">
      <j1 rule="hyper" parents="65 12969 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      (x * a(y,z,u)) / (u \ a(y,z,u)) = L(x / (u \ 1),u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10958,a,13381,a),flip(a)].">
      <j1 rule="hyper" parents="10958 13381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)) * y,x,a(u,z,z \ u)) = L(y,a(u,z,z \ u),x)
    ]]></literal>
    <justification jstring="[para(10348(a,1),13198(a,1,1,1))].">
      <j1 rule="para" parents="10348 13198"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)) * y,x,a(u,z,u * z)) = L(y,a(u,z,z \ u),x)
    ]]></literal>
    <justification jstring="[para(13184(a,1),13432(a,1,3))].">
      <j1 rule="para" parents="13184 13432"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)) * y,x,a(z,z,u)) = L(y,a(u,z,z \ u),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9054,a(flip),b,13433,a)].">
      <j1 rule="hyper" parents="65 9054 13433"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      L(x,a(y,z,z \ y),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12966,a(flip),b,13434,a),flip(a)].">
      <j1 rule="hyper" parents="65 12966 13434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      L(x,a(y,z,y * z),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(13184(a,1),13435(a,1,2))].">
      <j1 rule="para" parents="13184 13435"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1316,a(flip),b,13299,a),flip(a)].">
      <j1 rule="hyper" parents="65 1316 13299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,x * y) = R(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(13437(a,1),12858(a,1,1))].">
      <j1 rule="para" parents="13437 12858"/>
    </justification>
  </clause>

  <clause id="13439">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u * w) * w = ((a(x,y,z) \ 1) * u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(13437(a,1),13212(a,1,1))].">
      <j1 rule="para" parents="13437 13212"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12859,a(flip),b,13438,a),flip(a)].">
      <j1 rule="hyper" parents="65 12859 13438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (L(R(x,x,w),y,z) * u) = a(x,x,L(L(w,y,z),L(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12056,a,b,13297,a),flip(a)].">
      <j1 rule="hyper" parents="325 12056 13297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      a((x * ((x \ y) * y)) * y,y,z) = (x \ y) \ ((x \ 1) * R((x \ 1) \ (x \ y),y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1403,a(flip),b,13123,a),flip(a)].">
      <j1 rule="hyper" parents="325 1403 13123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      R(x,y,(z * ((u / w) * v5)) \ v6) = R(x,y,(z * ((w \ u) * v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,13126,a,b,13132,a),flip(a)].">
      <j1 rule="hyper" parents="65 13126 13132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      (x / y) \ (a(z,z,u) \ x) = (a(z,z,u) \ y) * a(x * y,y,u \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(12730(a,1),13152(a,2,1))].">
      <j1 rule="para" parents="12730 13152"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      (x / y) \ (a(z,z,u) \ x) = (a(z,z,u) \ y) * a(x * y,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(7492(a,1),13444(a,2,2))].">
      <j1 rule="para" parents="7492 13444"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      L(a(x,x,y),z,u * z) \ z = (u / z) \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,13020,a(flip),b,13445,a)].">
      <j1 rule="hyper" parents="325 13020 13445"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      a(x,x,L(y,z,u * z)) \ z = (u / z) \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(12056(a,2),13446(a,1,1))].">
      <j1 rule="para" parents="12056 13446"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      a(x,x,L(y,z / u,z * (z / u))) \ (z / u) = (u * K(u \ z,u)) \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(2691(a,1),13447(a,2,1))].">
      <j1 rule="para" parents="2691 13447"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      a(x,y,(1 / z) \ (L(u,w,v5) * v6)) = a(x,y,z \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(1289(a,1),13169(a,1,3))].">
      <j1 rule="para" parents="1289 13169"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      a(x,y,z \ (R(u,w,v5) * v6)) = a(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,10366,a(flip),b,13449,a),flip(a)].">
      <j1 rule="hyper" parents="65 10366 13449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) * L(v6,v6,R(u,w,v5)))) = a(x,y,z \ (R(u,w,v5) / (v6 \ 1)))
    ]]></literal>
    <justification jstring="[para(1720(a,1),13450(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1720 13450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      a((x * ((x \ y) * y)) * y,y,z) = (x \ y) \ (x \ (1 * R(1 \ y,y,z)))
    ]]></literal>
    <justification jstring="[para(1402(a,1),13442(a,2,2))].">
      <j1 rule="para" parents="1402 13442"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      a((x * ((x \ y) * y)) * y,y,z) = (x \ y) \ (x \ (1 * R(y,y,z)))
    ]]></literal>
    <justification jstring="[para(67(a,1),13452(a,2,2,2,2,1))].">
      <j1 rule="para" parents="67 13452"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      a((x * ((x \ y) * y)) * y,y,z) = (x \ y) \ (x \ R(y,y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),13453(a,2,2,2))].">
      <j1 rule="para" parents="7 13453"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      (x \ y) \ (x \ R(y,y,z)) = a(L(y,x \ y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13144,a(flip),b,13454,a),flip(a)].">
      <j1 rule="hyper" parents="65 13144 13454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) * L(v6,v6,R(u,w,v5)))) = a(x,y,z \ ((v6 \ 1) \ R(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10110,a(flip),b,13451,a),flip(a)].">
      <j1 rule="hyper" parents="325 10110 13451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) * L(v6,v6,R(u,w,v5)))) = a(x,y,z \ (v6 \ R(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10463,a(flip),b,13456,a),flip(a)].">
      <j1 rule="hyper" parents="325 10463 13456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) * L(v6,v6,L(u,w,v5)))) = a(x,y,z \ (v6 \ R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(9931(a,1),13457(a,1,3,2,2))].">
      <j1 rule="para" parents="9931 13457"/>
    </justification>
  </clause>

  <clause id="13459">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) / (v6 \ 1))) = a(x,y,z \ (v6 \ R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1720(a,1),13458(a,1,3,2))].">
      <j1 rule="para" parents="1720 13458"/>
    </justification>
  </clause>

  <clause id="13460">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ L(w,v5,v6))) = a(x,y,z \ (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(10280,a,13459,a)].">
      <j1 rule="hyper" parents="10280 13459"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      a(x,y,z \ (u \ R(w,v5,v6))) = a(x,y,z \ (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(10464,a,13460,a),flip(a)].">
      <j1 rule="hyper" parents="10464 13460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      a(x * (y \ x),x,z \ (u \ L(w,v5,v6))) * y = R(y,x,z \ (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(13461(a,1),13126(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13461 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      R(x,y,z \ (u \ R(w,v5,v6))) = R(x,y,z \ (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13126,a,b,13462,a),flip(a)].">
      <j1 rule="hyper" parents="65 13126 13462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      R(x,y,z \ (u \ L(w \ v5,w,w))) = R(x,y,z \ (u \ (v5 * (w \ 1))))
    ]]></literal>
    <justification jstring="[hyper(65,a,8744,a(flip),b,13463,a),flip(a)].">
      <j1 rule="hyper" parents="65 8744 13463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((1 / w) * v5))) = R(x,y,z \ (u \ (v5 * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(649(a,1),13464(a,1,3,2,2))].">
      <j1 rule="para" parents="649 13464"/>
    </justification>
  </clause>

  <clause id="13466">
    <literal><![CDATA[
      R(x,y,z \ (u \ (w * (v5 \ 1)))) = R(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8773,a(flip),b,13465,a),flip(a)].">
      <j1 rule="hyper" parents="65 8773 13465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      R(x,y,(z * ((u \ 1) * (z \ w))) \ (w * u)) = R(x,y,((u \ 1) * (z \ w)) \ (z \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11829,a(flip),b,13466,a)].">
      <j1 rule="hyper" parents="65 11829 13466"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      a(x,x,L(y,z / u,z * (u \ z))) \ (z / u) = (u * K(u \ z,u)) \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(2322(a,1),13448(a,1,1,3))].">
      <j1 rule="para" parents="2322 13448"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      a(x,x,L(y,z \ u,u * (z \ u))) \ (u / z) = (z * K(z \ u,z)) \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(10814(a,1),13468(a,1,1,3))].">
      <j1 rule="para" parents="10814 13468"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      a(x,y * a(x,y,z),z) \ (y * a(x,y,z)) = (a(L(x,y,z),y,z) \ y) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,12954,a(flip),b,13098,a),flip(a)].">
      <j1 rule="hyper" parents="325 12954 13098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      a(x,y * a(x,y,z),z) \ (y * a(x,y,z)) = (a(x,y,z) \ y) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12967(a,1),13470(a,2,1,1))].">
      <j1 rule="para" parents="12967 13470"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      a(x,y * a(x,y,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,12475,a,b,13471,a),flip(a)].">
      <j1 rule="hyper" parents="41 12475 13471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      L(x,y,L((z * a(u,z,w)) * a(u,z,w),w,u)) = L(x,y,L(z * a(u,z,w),u,w))
    ]]></literal>
    <justification jstring="[para(13472(a,1),11793(a,1,3,1,2))].">
      <j1 rule="para" parents="13472 11793"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) * (u * a(z,u,w)),w,z)) = L(x,y,L(u * a(z,u,w),z,w))
    ]]></literal>
    <justification jstring="[hyper(2353,a,13473,a)].">
      <j1 rule="hyper" parents="2353 13473"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      L(x,y,L(z * (L(L(z,u,w),u,w) \ u),z,w)) = L(x,y,L(u * a(w,u,z),w,z))
    ]]></literal>
    <justification jstring="[para(12998(a,1),13475(a,1,3,1))].">
      <j1 rule="para" parents="12998 13475"/>
    </justification>
  </clause>

  <clause id="13477">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w),u,w)) = L(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12339,a(flip),b,13476,a),flip(a)].">
      <j1 rule="hyper" parents="65 12339 13476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      R(x,y,(z * ((u \ 1) * (z \ w))) \ (w * u)) = R(x,y,(u * (z \ w)) \ (z \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8795,a(flip),b,13467,a),flip(a)].">
      <j1 rule="hyper" parents="325 8795 13467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      L(T(a(x,y,z),(y * z) * x) \ 1,x,y * z) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12432(a,2,1,2))].">
      <j1 rule="para" parents="9 12432"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      L(T(a(x,y,z),(y * z) * x) \ 1,x,y * z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,5794,a(flip),b,13480,a),flip(a)].">
      <j1 rule="hyper" parents="325 5794 13480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y * z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(7186(a,1),13481(a,1,1,1))].">
      <j1 rule="para" parents="7186 13481"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ L(a(x,y,z),x,y * z) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(13483(a,1),1764(a,1,1))].">
      <j1 rule="para" parents="13483 1764"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (x \ R(x,y,z)) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12461(a,1),13484(a,1,2))].">
      <j1 rule="para" parents="12461 13484"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      R(x,y,z) * R(x \ 1,y,z) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8955,a(flip),b,13486,a)].">
      <j1 rule="hyper" parents="65 8955 13486"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      R(x,y,z) * (x \ R(x,y,z)) = x * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,13486,a(flip),b,11765,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 13486 11765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      R(x,y,z) / (a(x,y,z) * a(x,y,z)) = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(13487(a,1),8962(a,1,2))].">
      <j1 rule="para" parents="13487 8962"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      x * (a(x,y,z) * a(x,y,z)) = R(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12469,a(flip),b,13488,a),flip(a)].">
      <j1 rule="hyper" parents="65 12469 13488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13492">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(x,y,z) \ R(x,y,z)) = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8980,a,13489,a)].">
      <j1 rule="hyper" parents="8980 13489"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      R((a(x,y,z) \ 1) * (a(x,y,z) \ x),y,z) = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1098,a,b,13492,a)].">
      <j1 rule="hyper" parents="65 1098 13492"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      R(x * (y \ L(L(y,z,x),z,x)),z,y) = x * (R(x,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(12544(a,1),13493(a,1,1))].">
      <j1 rule="para" parents="12544 13493"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      a(x,y,R(z / u,u,z \ (w \ v5)) \ (w \ v5)) = a(x,y,u * (z \ (L(v5,w,w) * w)))
    ]]></literal>
    <justification jstring="[para(13230(a,1),12506(a,1,3,1))].">
      <j1 rule="para" parents="13230 12506"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      a(x,y,z * (u \ (L(w,v5,v5) * v5))) = a(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(480(a,1),13499(a,1,3)),flip(a)].">
      <j1 rule="para" parents="480 13499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,K(v5,v6) / u)) * v7) = a(x,y,v7 * (z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11520,a,b,13500,a)].">
      <j1 rule="hyper" parents="65 11520 13500"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,u \ K(v5,v6))) * v7) = a(x,y,v7 * (z \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(1551(a,1),13501(a,1,3,1,2))].">
      <j1 rule="para" parents="1551 13501"/>
    </justification>
  </clause>

  <clause id="13503">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,K(v5,v6) / u,u)) * v7) = a(x,y,v7 * (z \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(7541(a,1),13502(a,1,3,1,2))].">
      <j1 rule="para" parents="7541 13502"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,u \ 1,u)) * v5) = a(x,y,v5 * (z \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(343(a,1),13503(a,1,3,1,2,2))].">
      <j1 rule="para" parents="343 13503"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      L(a(L(x,y,z),x,u),x \ 1,L(x,y,z)) = L(x \ 1,y,z) \ R(L(x \ 1,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(1903(a,1),12874(a,1,1))].">
      <j1 rule="para" parents="1903 12874"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      L(a(x,L(x,y,z),u),x \ 1,L(x,y,z)) = L(x \ 1,y,z) \ R(L(x \ 1,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(7452(a,1),13506(a,1,1))].">
      <j1 rule="para" parents="7452 13506"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      L(x \ 1,y,z) \ R(L(x \ 1,y,z),x,u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11760,a(flip),b,13507,a),flip(a)].">
      <j1 rule="hyper" parents="65 11760 13507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      L((x \ 1) \ R(x \ 1,x,y),z,u) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11554,a(flip),b,13508,a)].">
      <j1 rule="hyper" parents="65 11554 13508"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      L(x \ R(x,x,y),z,u) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(1081(a,1),13510(a,1,1))].">
      <j1 rule="para" parents="1081 13510"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = L(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(11590(a,1),13511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11590 13511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,12056,a,b,13512,a),flip(a)].">
      <j1 rule="hyper" parents="325 12056 13512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      x \ R(x,L(x,y,z),u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12873,a,b,13513,a)].">
      <j1 rule="hyper" parents="65 12873 13513"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      a(L(x,y,z),x,u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7452,a,b,13513,a)].">
      <j1 rule="hyper" parents="65 7452 13513"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      a(x \ y,x \ y,L(z,x,x)) = a(x * y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7453,a(flip),b,13513,a),flip(a)].">
      <j1 rule="hyper" parents="65 7453 13513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,L(x,y,z) \ 1,L(u,y,z)) = a(L(x,y,z) \ 1,x \ 1,u)
    ]]></literal>
    <justification jstring="[para(12341(a,1),13513(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12341 13513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13518">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ y = L(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(13513(a,1),12597(a,1,1))].">
      <j1 rule="para" parents="13513 12597"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      a(x,L(x,x,L(y,z,u)),w) = a(x,x,L(w,L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(12692(a,1),13513(a,1,2))].">
      <j1 rule="para" parents="12692 13513"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      a(x,x,L(y,z,a(u,w,x))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(12916(a,1),13513(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12916 13513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),v5) = L(a(x,x,L(v5,u,w)),y,z)
    ]]></literal>
    <justification jstring="[para(13514(a,1),12881(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13514 12881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13522">
    <literal><![CDATA[
      L(x,y,L(y,y,z)) = a(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12239(a,1),13518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12239 13518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13523">
    <literal><![CDATA[
      L(x,y,L(y,y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1782,a(flip),b,13522,a),flip(a)].">
      <j1 rule="hyper" parents="325 1782 13522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13524">
    <literal><![CDATA[
      L(x,y,z \ (y \ z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,8595,a(flip),b,13523,a)].">
      <j1 rule="hyper" parents="65 8595 13523"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) = ((1 / (y \ (x \ y))) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,700,a(flip),b,13524,a),flip(a)].">
      <j1 rule="hyper" parents="65 700 13524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13526">
    <literal><![CDATA[
      a(x / y,x / y,L(z,y * (x / y),x)) = a(y * x,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12297,a,b,13516,a)].">
      <j1 rule="hyper" parents="65 12297 13516"/>
    </justification>
  </clause>

  <clause id="13527">
    <literal><![CDATA[
      a(x,x,L(y,L(x,z,u),w)) = a(x,x,L(y,x,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13513,a(flip),b,13519,a),flip(a)].">
      <j1 rule="hyper" parents="65 13513 13519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),v5) = a(x,x,L(L(v5,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,12056,a,b,13521,a),flip(a)].">
      <j1 rule="hyper" parents="325 12056 13521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      a(x,x,L(y,L(x,z,u),w)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,12239,a(flip),b,13527,a),flip(a)].">
      <j1 rule="hyper" parents="325 12239 13527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (L(R(x,x,w),y,z) * u) = a(x,x,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13441,a,b,13529,a)].">
      <j1 rule="hyper" parents="65 13441 13529"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),z,u)) \ (((x \ 1) * x) * y) = (R(x,z,u) \ 1) * (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(13528(a,1),11212(a,1,1))].">
      <j1 rule="para" parents="13528 11212"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      (x * a(y,y,L(L(x,z,u),z,u))) * L(y,z,u) = (y \ ((1 / L(y,z,u)) \ x)) * y
    ]]></literal>
    <justification jstring="[para(13528(a,1),11974(a,1,1,2))].">
      <j1 rule="para" parents="13528 11974"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      L(L(x,a(y,z,z),L(z,u,w)),L(z,u,w),L(z,u,w)) = a(z,z,L(L(x,u,w),u,w)) \ x
    ]]></literal>
    <justification jstring="[para(13528(a,1),12676(a,2,1))].">
      <j1 rule="para" parents="13528 12676"/>
    </justification>
  </clause>

  <clause id="13535">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) = ((x \ y) \ (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(11825(a,1),13525(a,2,1))].">
      <j1 rule="para" parents="11825 13525"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      ((x \ y) \ (y * x)) \ 1 = (1 / x) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(660,a,13535,a),flip(a)].">
      <j1 rule="hyper" parents="660 13535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13537">
    <literal><![CDATA[
      ((x \ y) \ (y * x)) \ 1 = x \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,13415,a(flip),b,13536,a),flip(a)].">
      <j1 rule="hyper" parents="325 13415 13536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13538">
    <literal><![CDATA[
      (x \ (y \ (x \ y))) * ((y \ (x * (y * x))) * ((x * (y * x)) \ y)) = (x * (y * x)) \ y
    ]]></literal>
    <justification jstring="[para(13537(a,1),13056(a,1,1))].">
      <j1 rule="para" parents="13537 13056"/>
    </justification>
  </clause>

  <clause id="13539">
    <literal><![CDATA[
      a(x / y,x / y,L(z,x,x)) = a(y * x,y \ x,z)
    ]]></literal>
    <justification jstring="[para(10816(a,1),13526(a,1,3))].">
      <j1 rule="para" parents="10816 13526"/>
    </justification>
  </clause>

  <clause id="13540">
    <literal><![CDATA[
      a(x / y,y \ x,L(z,x,x)) = a(y * x,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(10163,a,13539,a)].">
      <j1 rule="hyper" parents="10163 13539"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      a(x \ y,x \ y,L(z,y,y)) = a(x * y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(2574,a,13540,a)].">
      <j1 rule="hyper" parents="2574 13540"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      a(L(x,y \ x,y),(x \ y) \ y,z) = a((x \ y) \ y,(x \ y) \ y,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12706,a,b,13542,a)].">
      <j1 rule="hyper" parents="325 12706 13542"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,L(x,y,z) \ 1,L(u,y,z)) = a(L(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1847,a(flip),b,13517,a),flip(a)].">
      <j1 rule="hyper" parents="325 1847 13517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      a(L(x,y \ x,y),(x \ y) \ y,z) = a((x \ y) \ y,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,9992,a(flip),b,13543,a),flip(a)].">
      <j1 rule="hyper" parents="325 9992 13543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      a(L(x,y \ x,y),(x \ y) \ y,z) = a(x,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,1871,a(flip),b,13546,a),flip(a)].">
      <j1 rule="hyper" parents="325 1871 13546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      a(L(x,y \ x,y),x,z) = a(x,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(10150,a,13548,a)].">
      <j1 rule="hyper" parents="10150 13548"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      (x \ y) * a(y,y,L(z,x,x)) = x \ R(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,13549,a(flip),b,13455,a)].">
      <j1 rule="hyper" parents="137 13549 13455"/>
    </justification>
  </clause>

  <clause id="13553">
    <literal><![CDATA[
      (x \ ((1 / L(x,y,z)) \ u)) * x = (u * a(x,x,u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12044(a,1),13533(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12044 13533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      a(x,x,y) * (y * L(x,z,u)) = (x \ ((1 / L(x,z,u)) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,11832,a(flip),b,13553,a)].">
      <j1 rule="hyper" parents="325 11832 13553"/>
    </justification>
  </clause>

  <clause id="13556">
    <literal><![CDATA[
      (x \ ((1 / L(x,y,z)) \ u)) * x = u * (L(x,y,z) * a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10566,a(flip),b,13554,a),flip(a)].">
      <j1 rule="hyper" parents="65 10566 13554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13557">
    <literal><![CDATA[
      x * (L(y,z,u) * a(y,y,x)) = (1 / L(y,z,u)) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,6868,a(flip),b,13556,a),flip(a)].">
      <j1 rule="hyper" parents="65 6868 13556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      a(x,x,y) \ (((x \ 1) * x) * y) = (R(x,z,u) \ 1) * (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(12044(a,1),13532(a,1,1))].">
      <j1 rule="para" parents="12044 13532"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * (R(x,y,z) * u) = (x \ 1) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,7300,a(flip),b,13558,a),flip(a)].">
      <j1 rule="hyper" parents="65 7300 13558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      L(L(x,a(y,z,z),L(z,u,w)),L(z,u,w),L(z,u,w)) = a(z,z,x) \ x
    ]]></literal>
    <justification jstring="[para(12044(a,1),13534(a,2,1))].">
      <j1 rule="para" parents="12044 13534"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      L(L(x,a(y,z,z),L(z,u,w)),L(z,u,w),L(z,u,w)) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1782,a(flip),b,13561,a),flip(a)].">
      <j1 rule="hyper" parents="325 1782 13561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(464(a,1),13562(a,1,1))].">
      <j1 rule="para" parents="464 13562"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,x) = (1 / L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(660,a,13564,a),flip(a)].">
      <j1 rule="hyper" parents="660 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13566">
    <literal><![CDATA[
      a(L(x,y,y),L(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(13564(a,1),13161(a,1,1))].">
      <j1 rule="para" parents="13564 13161"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      L(L(T(x,y),z,u) \ w,x,x) = (1 / L(T(x,y),z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(10845,a,13565,a)].">
      <j1 rule="hyper" parents="10845 13565"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      (x * x) * ((1 / L(x,y,z)) * u) = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(137,a,13565,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="137 13565 18"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      ((R(x,y,y) * (L(y,y,x) * z)) / z) \ (x * y) = a(x,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11833,a,b,13566,a)].">
      <j1 rule="hyper" parents="65 11833 13566"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      L(x,y,z) \ L(u,x \ 1,x) = (1 / L(T(x,x \ 1),y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,9741,a(flip),b,13567,a)].">
      <j1 rule="hyper" parents="65 9741 13567"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      ((x * x) / L(x,y,z)) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,439,a(flip),b,13568,a)].">
      <j1 rule="hyper" parents="65 439 13568"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(8357(a,1),13571(a,1,1))].">
      <j1 rule="para" parents="8357 13571"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(4168(a,2),13572(a,1,1))].">
      <j1 rule="para" parents="4168 13572"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * x) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(7818(a,2),13572(a,1,1))].">
      <j1 rule="para" parents="7818 13572"/>
    </justification>
  </clause>

  <clause id="13575">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (L(a(x,y,z),u,w) \ v5)) = L(a(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(12453(a,1),13572(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12453 13572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      x \ ((L(1 / x,y,z) \ 1) * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(530,a,13573,a)].">
      <j1 rule="hyper" parents="530 13573"/>
    </justification>
  </clause>

  <clause id="13577">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ (((L(1 / T(x,y),z,u) \ 1) \ T(x,y)) * w)) = L(w,(L(1 / T(x,y),z,u) \ 1) \ x,L(1 / T(x,y),z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(10967,a,13573,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10967 13573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      x * L(L(y,z,u) \ y,y,x) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(36,a,13318,a,b,13574,a(flip))].">
      <j1 rule="hyper" parents="36 13318 13574"/>
    </justification>
  </clause>

  <clause id="13579">
    <literal><![CDATA[
      x \ ((L(x,y,z) \ x) \ (x * (x * (L(x,y,z) \ u)))) = L(1 / u,x,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(13574(a,1),12356(a,1,2,2))].">
      <j1 rule="para" parents="13574 12356"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      x * L(a(y,y,z),z,x) = z * (L(z,y,y) \ x)
    ]]></literal>
    <justification jstring="[para(824(a,1),13578(a,1,2,1))].">
      <j1 rule="para" parents="824 13578"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      x * a(y,y,L(z,z,x)) = z * (L(z,y,y) \ x)
    ]]></literal>
    <justification jstring="[para(12056(a,2),13580(a,1,2))].">
      <j1 rule="para" parents="12056 13580"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) * (u * (u \ z)) = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(7276,a,13581,a)].">
      <j1 rule="hyper" parents="7276 13581"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) * z = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(7226,a,13581,a)].">
      <j1 rule="hyper" parents="7226 13581"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      (a(x,x,L(a(y,z,z),a(y,z,z),u)) * u) \ ((L(a(y,z,z),x,x) \ u) * z) = L(z,z,y)
    ]]></literal>
    <justification jstring="[para(13584(a,2),12687(a,1,1))].">
      <j1 rule="para" parents="13584 12687"/>
    </justification>
  </clause>

  <clause id="13586">
    <literal><![CDATA[
      x \ ((y \ ((1 / y) \ x)) * z) = x * (L(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(11987(a,1),13576(a,1,2,1))].">
      <j1 rule="para" parents="11987 13576"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      x \ ((x * a(y,y,x)) * z) = x * (L(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11977,a(flip),b,13586,a)].">
      <j1 rule="hyper" parents="65 11977 13586"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      L(x,y,z) \ L(u,x \ 1,x) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(6585(a,1),13570(a,2,1))].">
      <j1 rule="para" parents="6585 13570"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (K(x,x \ 1) * u) = L(x,y,z) \ (x * ((1 / x) * u))
    ]]></literal>
    <justification jstring="[para(4214(a,1),13588(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4214 13588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13590">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(v5,a(x,y,z) \ 1,a(x,y,z)) = L(a(x,y,z) \ 1,u,w) * v5
    ]]></literal>
    <justification jstring="[para(12450(a,2),13588(a,2,1))].">
      <j1 rule="para" parents="12450 13588"/>
    </justification>
  </clause>

  <clause id="13591">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (K(x,x \ 1) * u) = x * (L(x,y,z) \ ((1 / x) * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,1256,a(flip),b,13589,a),flip(a)].">
      <j1 rule="hyper" parents="325 1256 13589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13592">
    <literal><![CDATA[
      (L(x,y,z) \ K(x,x \ 1)) * u = x * (L(x,y,z) \ ((1 / x) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,9593,a(flip),b,13591,a)].">
      <j1 rule="hyper" parents="65 9593 13591"/>
    </justification>
  </clause>

  <clause id="13593">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((1 / x) * u)) = (1 / L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(4172(a,1),13592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4172 13592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      (1 / L(x,y,z)) * ((1 / x) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 13593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12619,a(flip),b,13594,a)].">
      <j1 rule="hyper" parents="65 12619 13594"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      L(x * a(y,y,x),y,L(y,z,u)) = (L(y,z,u) \ y) \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(13594(a,1),11969(a,2,2))].">
      <j1 rule="para" parents="13594 11969"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12350,a,b,13595,a)].">
      <j1 rule="hyper" parents="65 12350 13595"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = x * (L(x,y,a(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(13366(a,1),13597(a,1,2,1))].">
      <j1 rule="para" parents="13366 13597"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      L(x * a(y,y,x),y,L(y,z,u)) = y * ((L(y,z,u) \ y) \ (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(325,a,10601,a(flip),b,13596,a),flip(a)].">
      <j1 rule="hyper" parents="325 10601 13596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      (a(x,x,a(y,z,L(z,a(y,z,z),u))) * u) \ ((L(a(y,z,z),x,x) \ u) * z) = L(z,z,y)
    ]]></literal>
    <justification jstring="[para(12665(a,2),13585(a,1,1,1,3))].">
      <j1 rule="para" parents="12665 13585"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(v5,a(x,y,z),a(x,y,z)) = L(a(x,y,z) \ 1,u,w) * v5
    ]]></literal>
    <justification jstring="[para(10952(a,1),13590(a,1,2))].">
      <j1 rule="para" parents="10952 13590"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      (a(x,x,a(y,z,z)) * u) \ ((L(a(y,z,z),x,x) \ u) * z) = L(z,z,y)
    ]]></literal>
    <justification jstring="[para(12690(a,1),13600(a,1,1,1,3,3))].">
      <j1 rule="para" parents="12690 13600"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      (a(x,x,a(y,z,z)) * u) \ ((a(y,z,L(z,x,x)) \ u) * z) = L(z,z,y)
    ]]></literal>
    <justification jstring="[para(12665(a,2),13602(a,1,2,1,1))].">
      <j1 rule="para" parents="12665 13602"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      (a(x,x,a(y,z,z)) * u) \ (u * L(z,z,L(y,x,x))) = L(z,z,y)
    ]]></literal>
    <justification jstring="[para(12686(a,1),13603(a,1,2))].">
      <j1 rule="para" parents="12686 13603"/>
    </justification>
  </clause>

  <clause id="13605">
    <literal><![CDATA[
      x \ (x * ((L(x,y,z) \ x) \ (x * (L(x,y,z) \ u)))) = L(1 / u,x,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(10601(a,1),13579(a,1,2))].">
      <j1 rule="para" parents="10601 13579"/>
    </justification>
  </clause>

  <clause id="13606">
    <literal><![CDATA[
      x \ (x * (x * ((L(x,y,z) \ x) \ (L(x,y,z) \ u)))) = L(1 / u,x,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(10601(a,1),13605(a,1,2,2))].">
      <j1 rule="para" parents="10601 13605"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) \ (L(x,y,z) \ u)) = L(1 / u,x,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(332,a,13606,a)].">
      <j1 rule="hyper" parents="332 13606"/>
    </justification>
  </clause>

  <clause id="13609">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) \ (L(x,y,z) \ u)) = L(1 / u,x,x * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1570(a,1),13607(a,2,1))].">
      <j1 rule="para" parents="1570 13607"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = a(x,a(w,v5,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7476,a,12997,a)].">
      <j1 rule="hyper" parents="7476 12997"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      L(x \ y,x \ y,a(x,x,y)) * (y * x) = ((x \ y) * (x \ y)) * (y \ (x * (y * x)))
    ]]></literal>
    <justification jstring="[para(13375(a,1),13057(a,1,1))].">
      <j1 rule="para" parents="13375 13057"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) * (y \ (x * (y * x))) = (x \ y) * (y * x)
    ]]></literal>
    <justification jstring="[para(13201(a,1),13619(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13201 13619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13621">
    <literal><![CDATA[
      a(x,y,L(z,u \ (w * (u * w)),v5)) = a(x,y,L(z,(w \ u) * (u * w),v5))
    ]]></literal>
    <justification jstring="[para(13620(a,1),11453(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13620 11453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13623">
    <literal><![CDATA[
      L(a(x,y,z \ y),u,T(y,x) \ z) = L(T(T(y,x),w) \ z,y,x) \ (T(T(y,x),w) \ z)
    ]]></literal>
    <justification jstring="[hyper(4561,a,13091,a)].">
      <j1 rule="hyper" parents="4561 13091"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      L(a(x,y,z \ y),u,y \ z) = L(T(T(y,x),w) \ z,y,x) \ (T(T(y,x),w) \ z)
    ]]></literal>
    <justification jstring="[hyper(4561,a,13623,a)].">
      <j1 rule="hyper" parents="4561 13623"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      L(a(x,y,z \ y),u,y \ z) = ((T(y,w) * x) \ (x * z)) \ (T(T(y,x),w) \ z)
    ]]></literal>
    <justification jstring="[para(10842(a,1),13625(a,2,1))].">
      <j1 rule="para" parents="10842 13625"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      L(a(x,y,z \ y),u,y \ z) = a(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,13089,a(flip),b,13628,a),flip(a)].">
      <j1 rule="hyper" parents="325 13089 13628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ R((x \ ((x * y) * z)) / z,y,u) = a(a(x,y,z) \ y,y,u)
    ]]></literal>
    <justification jstring="[para(12947(a,1),13124(a,2,1))].">
      <j1 rule="para" parents="12947 13124"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      L(a(x,y,y * L(y,z,u)),y,y \ L(y,z,u)) = ((x * (y \ L(y,z,u))) \ (x * L(y,z,u))) \ y
    ]]></literal>
    <justification jstring="[para(9165(a,1),12420(a,1,1))].">
      <j1 rule="para" parents="9165 12420"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * ((x \ L(x,y,y)) \ x) = (x \ L(x,y,y)) \ L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13518(a,1),12751(a,2,2))].">
      <j1 rule="para" parents="13518 12751"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * ((x \ L(x,y,y)) \ x) = L(x,y,L(y,z,u)) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,12722,a(flip),b,13632,a),flip(a)].">
      <j1 rule="hyper" parents="325 12722 13632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * ((x \ L(x,y,y)) \ x) = L(x * a(y,y,x),y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12243,a,b,13633,a),flip(a)].">
      <j1 rule="hyper" parents="325 12243 13633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * (x * a(y,y,x)) = L(x * a(y,y,x),y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12722(a,1),13634(a,1,2))].">
      <j1 rule="para" parents="12722 13634"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ (y * a(x,x,y)) = L(y * a(x,x,y),x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12738,a(flip),b,13635,a)].">
      <j1 rule="hyper" parents="65 12738 13635"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      a(x,x \ (y * (x * y)),x * L(x,y,y)) \ z = z * ((x \ (y * (x * y))) * ((y * (x * y)) \ x))
    ]]></literal>
    <justification jstring="[para(249(a,1),12767(a,1,1,3))].">
      <j1 rule="para" parents="249 12767"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      a(x,y,((z * u) \ (z * w)) * (u \ w)) = a(x,y,a(z,u,w \ u))
    ]]></literal>
    <justification jstring="[para(13629(a,1),12809(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13629 12809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      x * ((1 / x) \ (((1 / x) \ 1) \ a(y,z,u))) = ((1 / x) * (1 / x)) \ (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(546,a,13282,a)].">
      <j1 rule="hyper" parents="546 13282"/>
    </justification>
  </clause>

  <clause id="13642">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ (a(y,z,u) / x) = x * ((1 / x) \ (x \ a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(85(a,1),13641(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="85 13641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ (a(y,z,u) / x) = (x * x) * (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,648,a(flip),b,13642,a),flip(a)].">
      <j1 rule="hyper" parents="325 648 13642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      (x \ (1 / x)) \ (a(y,z,u) / x) = (x * x) * (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[para(277(a,1),13643(a,1,1))].">
      <j1 rule="para" parents="277 13643"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      ((1 / x) \ x) * (a(y,z,u) / x) = (x * x) * (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,778,a(flip),b,13644,a)].">
      <j1 rule="hyper" parents="65 778 13644"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      (a(x,y,z) * ((1 / (1 / u)) * u)) / u = (u * u) * (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7547,a,b,13645,a)].">
      <j1 rule="hyper" parents="65 7547 13645"/>
    </justification>
  </clause>

  <clause id="13647">
    <literal><![CDATA[
      (a(x,y,z) * (u * (1 / (1 / u)))) / u = (u * u) * (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(282(a,1),13646(a,1,1,2))].">
      <j1 rule="para" parents="282 13646"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      (a(x,y,z) * ((1 / u) \ u)) / u = (u * u) * (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(3288(a,1),13647(a,1,1,2))].">
      <j1 rule="para" parents="3288 13647"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      (x * x) * (x \ a(y,z,u)) = a(y,z,u) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(65,a,9857,a(flip),b,13648,a),flip(a)].">
      <j1 rule="hyper" parents="65 9857 13648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      (x \ K(y,z)) \ (((x \ K(y,z)) * x) * (x \ a(u,w,v5))) = x \ (a(u,w,v5) / (1 / x))
    ]]></literal>
    <justification jstring="[para(13649(a,1),4404(a,2,2))].">
      <j1 rule="para" parents="13649 4404"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      (x \ K(y,z)) \ (((x \ K(y,z)) \ 1) \ a(u,w,v5)) = x \ (a(u,w,v5) / (1 / x))
    ]]></literal>
    <justification jstring="[para(10948(a,1),13650(a,1,2))].">
      <j1 rule="para" parents="10948 13650"/>
    </justification>
  </clause>

  <clause id="13652">
    <literal><![CDATA[
      (x \ K(y,z)) * ((1 / (x \ K(y,z))) * a(u,w,v5)) = x \ (a(u,w,v5) / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13314,a(flip),b,13651,a)].">
      <j1 rule="hyper" parents="65 13314 13651"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      (x \ K(y,z)) * ((K(z,y) * x) * a(u,w,v5)) = x \ (a(u,w,v5) / (1 / x))
    ]]></literal>
    <justification jstring="[para(2627(a,1),13652(a,1,2,1))].">
      <j1 rule="para" parents="2627 13652"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      (x \ K(y,z)) * (K(z,y) * (x * a(u,w,v5))) = x \ (a(u,w,v5) / (1 / x))
    ]]></literal>
    <justification jstring="[para(287(a,1),13653(a,1,2))].">
      <j1 rule="para" parents="287 13653"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      x \ (a(y,z,u) / (1 / x)) = (x \ 1) * (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9647,a,13654,a),flip(a)].">
      <j1 rule="hyper" parents="9647 13654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      a(x,(y * y) * (z \ (u / (w * w))),a(v5,v6,v7)) = a(a(v7,v6,v5),z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10444,a(flip),b,13355,a),flip(a)].">
      <j1 rule="hyper" parents="65 10444 13355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      a(x,(y * y) * (z \ ((u * u) \ w)),a(v5,v6,v7)) = a(a(v7,v6,v5),z \ w,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,10245,a(flip),b,13656,a)].">
      <j1 rule="hyper" parents="65 10245 13656"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      a(x,y \ ((z * z) \ u),a(w,v5,v6)) = a(a(v6,v5,w),y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12213,a(flip),b,13658,a)].">
      <j1 rule="hyper" parents="65 12213 13658"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      L(a(x,y,y * L(y,z,u)),y,y * L(y,z,u)) = ((x * (y \ L(y,z,u))) \ (x * L(y,z,u))) \ y
    ]]></literal>
    <justification jstring="[hyper(2366,a,13631,a)].">
      <j1 rule="hyper" parents="2366 13631"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      x * ((y \ (z * (y * z))) * ((z * (y * z)) \ y)) = 1 \ x
    ]]></literal>
    <justification jstring="[para(7704(a,1),13637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7704 13637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      x * ((y \ (z * (y * z))) * ((z * (y * z)) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,67,a(flip),b,13661,a),flip(a)].">
      <j1 rule="hyper" parents="325 67 13661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      (x * (y * x)) \ y = x \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13538,a(flip),b,13662,a)].">
      <j1 rule="hyper" parents="65 13538 13662"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) \ (x * L(y,z,u))) \ y = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10594,a,13660,a),flip(a)].">
      <j1 rule="hyper" parents="10594 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) \ x = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1758(a,1),13666(a,1,1))].">
      <j1 rule="para" parents="1758 13666"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ 1 = y \ L(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13668(a,1),6998(a,1,1))].">
      <j1 rule="para" parents="13668 6998"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      x \ L(x,x \ L(x,y,z),u) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12642,a(flip),b,13669,a),flip(a)].">
      <j1 rule="hyper" parents="65 12642 13669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,x,u) = L(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(40,a,12806,a,b,13669,a(flip))].">
      <j1 rule="hyper" parents="40 12806 13669"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      L(x,y,z) \ L(x * L(x,y,z),x,u) = L(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1339,a,b,13671,a)].">
      <j1 rule="hyper" parents="65 1339 13671"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w) \ (T(x,y) \ z),x \ z,x) = (z \ (x * L(x \ z,u,w))) \ 1
    ]]></literal>
    <justification jstring="[para(8812(a,1),12332(a,2,1,2))].">
      <j1 rule="para" parents="8812 12332"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w) \ (T(x,y) \ z),x \ z,x) = L(z \ x,u,w) \ (z \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,2023,a(flip),b,13673,a),flip(a)].">
      <j1 rule="hyper" parents="325 2023 13673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      L(L(x \ y,z,u) \ (x \ y),x \ y,x) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(8599(a,1),13674(a,1,1))].">
      <j1 rule="para" parents="8599 13674"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      L(x \ y,y,z) \ (x \ y) = a(z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12383,a,b,13676,a),flip(a)].">
      <j1 rule="hyper" parents="65 12383 13676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) = x * (L(y \ x,z,u) \ (y \ x))
    ]]></literal>
    <justification jstring="[para(13676(a,1),13578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13676 13578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      a(x,y,y \ (z \ y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,8658,a(flip),b,13677,a),flip(a)].">
      <j1 rule="hyper" parents="65 8658 13677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      a(x,y,y \ z) \ (z \ y) = L(z \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,7205,a,b,13677,a)].">
      <j1 rule="hyper" parents="41 7205 13677"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      L((x / (y \ 1)) \ x,x,z) \ ((x / (y \ 1)) \ x) = a(z,x,L(y,y,x))
    ]]></literal>
    <justification jstring="[para(1721(a,2),13677(a,2,3))].">
      <j1 rule="para" parents="1721 13677"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      a(x,y,(z \ y) * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,13184,a(flip),b,13679,a)].">
      <j1 rule="hyper" parents="65 13184 13679"/>
    </justification>
  </clause>

  <clause id="13683">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,13183,a(flip),b,13679,a)].">
      <j1 rule="hyper" parents="65 13183 13679"/>
    </justification>
  </clause>

  <clause id="13684">
    <literal><![CDATA[
      a(x,a(y,z,x),x \ (u \ x)) = L(u,x,a(y,z,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,10613,a(flip),b,13679,a)].">
      <j1 rule="hyper" parents="65 10613 13679"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),x \ (u \ x)) = L(u,x,x * L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,8810,a(flip),b,13679,a)].">
      <j1 rule="hyper" parents="65 8810 13679"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = a(z,y,(L(x,u,w) \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,12327,a(flip),b,13682,a)].">
      <j1 rule="hyper" parents="325 12327 13682"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,y * (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(7285,a,13683,a),flip(a)].">
      <j1 rule="hyper" parents="7285 13683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      a(x,y,y * (a(z,z,u) \ y)) = a(z,z,u) \ a(z,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,12458,a(flip),b,13683,a),flip(a)].">
      <j1 rule="hyper" parents="325 12458 13683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = a(z,y,y * (L(x,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12327,a(flip),b,13683,a)].">
      <j1 rule="hyper" parents="325 12327 13683"/>
    </justification>
  </clause>

  <clause id="13690">
    <literal><![CDATA[
      a(x * L(y,z,u),w,w * (v5 \ w)) \ v5 = L(v5,w,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(11282(a,1),13687(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11282 13687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) \ z = L(z,y,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(13161(a,1),13687(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13161 13687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      a(x,y,y * z) \ (z \ y) = L(z \ y,y,x)
    ]]></literal>
    <justification jstring="[para(13183(a,1),13680(a,1,1))].">
      <j1 rule="para" parents="13183 13680"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      L(x,y,L(z,y,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13687,a,b,13691,a),flip(a)].">
      <j1 rule="hyper" parents="65 13687 13691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      L(x,y,y \ z) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11990,a(flip),b,13694,a)].">
      <j1 rule="hyper" parents="65 11990 13694"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      L(x,y,y \ z) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11989,a(flip),b,13694,a)].">
      <j1 rule="hyper" parents="65 11989 13694"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      L(x,y \ z,z * (y \ z)) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(1576,a,13696,a),flip(a)].">
      <j1 rule="hyper" parents="1576 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = L(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12974,a,b,13696,a)].">
      <j1 rule="hyper" parents="65 12974 13696"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      L(x * a(y \ z,x,y),y,z * y) = z \ (((z / y) * x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11805,a(flip),b,13696,a),flip(a)].">
      <j1 rule="hyper" parents="65 11805 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      L(x,y \ 1,z * (y \ 1)) = L(x,y \ 1,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5127,a(flip),b,13696,a),flip(a)].">
      <j1 rule="hyper" parents="65 5127 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      L(x,y,x * y) \ 1 = y \ ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(13696(a,1),12562(a,1,1))].">
      <j1 rule="para" parents="13696 12562"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      L(a(x \ y,x,z),z,y) = L(z,x,y * x) \ z
    ]]></literal>
    <justification jstring="[para(13696(a,1),12853(a,2,1))].">
      <j1 rule="para" parents="13696 12853"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      L(K(x,y) / z,K(x,y) / z,u) = L(K(x,y) * (z \ 1),z,z * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11328,a,b,13697,a)].">
      <j1 rule="hyper" parents="65 11328 13697"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,u * w)) * v5) = a(x,y,v5 * (z \ (w \ ((u / w) \ 1))))
    ]]></literal>
    <justification jstring="[para(13702(a,1),10655(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="13702 10655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      (x * K(x \ y,x)) \ (a(z,z,u) \ y) = a(z,z,L(u,x \ y,x)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(13698(a,1),13469(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="13698 13469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      L(x,y,(x \ z) * y) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,4194,a(flip),b,13699,a),flip(a)].">
      <j1 rule="hyper" parents="65 4194 13699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      L(a(x * y,y,z),z,x) = L(z,y,x * y) \ z
    ]]></literal>
    <justification jstring="[para(13139(a,1),13703(a,1,1))].">
      <j1 rule="para" parents="13139 13703"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      x / L(y,z,z * (y \ x)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(201,a,2321,a,b,13709,a(flip))].">
      <j1 rule="hyper" parents="201 2321 13709"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      L(L(x,y,z * y) \ x,x,z) = a(z * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(43,a,12417,a,b,13710,a)].">
      <j1 rule="hyper" parents="43 12417 13710"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      x / a(y,y,L(z,u,u * (a(y,y,z) \ x))) = (x / (u * a(y,y,z))) * u
    ]]></literal>
    <justification jstring="[para(12056(a,2),13711(a,1,2))].">
      <j1 rule="para" parents="12056 13711"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      L(x,y \ 1,y \ z) = L(x,y \ 1,y * z)
    ]]></literal>
    <justification jstring="[hyper(2352,a,13701,a),flip(a)].">
      <j1 rule="hyper" parents="2352 13701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      L(T(1 / x,x * y) \ z,x \ 1,x * y) = y \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11076,a(flip),b,13714,a),flip(a)].">
      <j1 rule="hyper" parents="65 11076 13714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      a(x,a(y,z,x),x \ (u \ x)) = a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,12584,a(flip),b,13684,a),flip(a)].">
      <j1 rule="hyper" parents="325 12584 13684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      L(L(x,y,a(z,u,y)) \ x,w,v5) = a(y,a(z,u,y),y \ (L(x,w,v5) \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12327,a(flip),b,13684,a)].">
      <j1 rule="hyper" parents="325 12327 13684"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ y) * y) = L(a(x,y,(z \ y) * y),u,w)
    ]]></literal>
    <justification jstring="[para(13682(a,2),13686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13682 13686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      a(x,y,y * (L(z,u,w) \ y)) = L(a(x,y,y * (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(13683(a,2),13689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13683 13689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      a(x,y,y * (y * a(z,z,u))) = a(z,z,u) \ a(z,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,12731,a(flip),b,13688,a)].">
      <j1 rule="hyper" parents="65 12731 13688"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),y,y)) = a(z,z,u) \ a(z,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(10117,a,13720,a)].">
      <j1 rule="hyper" parents="10117 13720"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13179,a(flip),b,13721,a),flip(a)].">
      <j1 rule="hyper" parents="65 13179 13721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12479,a,b,13722,a)].">
      <j1 rule="hyper" parents="65 12479 13722"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      L(x \ y,z,u) \ (x \ y) = y \ (L(x / y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(9370,a,13678,a),flip(a)].">
      <j1 rule="hyper" parents="9370 13678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      a(x,y,((z \ u) \ y) * y) = u \ (L(z / u,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13682,a,b,13724,a)].">
      <j1 rule="hyper" parents="65 13682 13724"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      a(x,y,(a(z,u,(w \ u) * u) \ y) * y) = w \ (L(L(w,u,z) / w,y,x) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[para(13682(a,2),13725(a,1,3,1,1))].">
      <j1 rule="para" parents="13682 13725"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),x \ (u \ x)) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,12531,a(flip),b,13685,a),flip(a)].">
      <j1 rule="hyper" parents="325 12531 13685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      L(L(x,y,y * L(y,z,u)) \ x,w,v5) = a(y,y \ L(y,z,u),y \ (L(x,w,v5) \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12327,a(flip),b,13685,a)].">
      <j1 rule="hyper" parents="325 12327 13685"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      L(x,y,z * R(u,w,v5)) = L(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,13687,a,b,13690,a),flip(a)].">
      <j1 rule="hyper" parents="65 13687 13690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x,x * L(x,y,z)) = R(x,y,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(5408,a,13729,a),flip(a)].">
      <j1 rule="hyper" parents="5408 13729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      L(x,y * L(y,z,u),a(y,z,u)) = L(x,a(y,z,u),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11438,a,b,13729,a)].">
      <j1 rule="hyper" parents="65 11438 13729"/>
    </justification>
  </clause>

  <clause id="13732">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * L(u,w,v5)) = L(x,y,R(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12771,a(flip),b,13729,a),flip(a)].">
      <j1 rule="hyper" parents="65 12771 13729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      L(x,y,(z * u) * R(L(w,u,z),v5,v6)) = L(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(412(a,1),13729(a,2,3))].">
      <j1 rule="para" parents="412 13729"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ v5) = L(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,12755,a(flip),b,13732,a),flip(a)].">
      <j1 rule="hyper" parents="65 12755 13732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ w,v5) \ x,x,L(y,z,u) \ w) = a(v5,R(y,z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12394,a(flip),b,13734,a),flip(a)].">
      <j1 rule="hyper" parents="65 12394 13734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w,v5) \ v6,L(u,w,v5) \ v6) * (L(u,w,v5) \ v6)) = a(x,y,(R(u,w,v5) \ v6) \ z)
    ]]></literal>
    <justification jstring="[para(13734(a,1),12196(a,1,3,1))].">
      <j1 rule="para" parents="13734 12196"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      L(K(x,y) * (z \ 1),z,z * u) = L(K(x,y) / z,z \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10877,a(flip),b,13704,a),flip(a)].">
      <j1 rule="hyper" parents="65 10877 13704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      L(x,R(K(y,z) * (u \ 1),u,u * w) \ v5,v6) = L(x,L(K(y,z) / u,u \ 1,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(13737(a,1),11427(a,2,2,1))].">
      <j1 rule="para" parents="13737 11427"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x,x * L(x,y,z)) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,961,a(flip),b,13730,a),flip(a)].">
      <j1 rule="hyper" parents="325 961 13730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      x * (R(x,y,z) \ ((x \ R(x,y,z)) * u)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),13740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 13740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      x * (R(x,y,z) \ (u * (x \ R(x,y,z)))) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5051(a,1),13741(a,1,2,2))].">
      <j1 rule="para" parents="5051 13741"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      x * (R(R(x,y,z),u,x \ R(x,y,z)) * (R(x,y,z) \ (u * (x \ R(x,y,z))))) = L(R(x,y,z) * u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(972(a,2),13742(a,1,2))].">
      <j1 rule="para" parents="972 13742"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      L(x \ 1,y,z) \ ((y / (x \ 1)) \ y) = a(z,y,L(x,x,y))
    ]]></literal>
    <justification jstring="[para(85(a,1),13681(a,1,1,1))].">
      <j1 rule="para" parents="85 13681"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = L(z \ 1,y,x) \ (z \ 1)
    ]]></literal>
    <justification jstring="[para(85(a,1),13744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="85 13744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(325,a,1518,a(flip),b,13745,a),flip(a)].">
      <j1 rule="hyper" parents="325 1518 13745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,v5) \ L(L(x,y,z) \ x,u,w) = a(v5,x,L(L(x,y,z) \ x,u,w))
    ]]></literal>
    <justification jstring="[para(10559(a,1),13747(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10559 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,v5) \ L(a(x,y,z) \ 1,u,w) = a(v5,z,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(10593(a,1),13747(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10593 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,L(y,u,w))) = L(L(z,u,w),y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[para(12776(a,1),13747(a,1,3))].">
      <j1 rule="para" parents="12776 13747"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      (L(x,y,y * (z \ y)) \ x) * z = R(z,y,L(x,x,y))
    ]]></literal>
    <justification jstring="[para(13747(a,1),13126(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13747 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,z)),w) = R(x,L(u,z,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(13747(a,1),13324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13747 13324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,L(w,w,u))) = L(x,y,L(w,u,z) \ w) \ x
    ]]></literal>
    <justification jstring="[para(13747(a,1),13364(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="13747 13364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,w,u))) = R(x,y,L(w,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(13747(a,1),13374(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13747 13374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      (L(L(a(x,y,z) \ 1,u,w),z,z * (v5 \ z)) \ L(a(x,y,z) \ 1,u,w)) * v5 = R(v5,z,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(10593(a,1),13752(a,2,3))].">
      <j1 rule="para" parents="10593 13752"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      (L(x \ L(x,y,z),x,L(L(x,u,w) * (v5 \ L(x,u,w)),u,w)) \ (x \ L(x,y,z))) * v5 = R(v5,L(x,u,w),L(x \ L(x,y,z),x \ L(x,y,z),L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(12781(a,1),13752(a,1,1,1))].">
      <j1 rule="para" parents="12781 13752"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      (L(R(x,y,z),a(x,u,w),a(x,u,w) * (v5 \ a(x,u,w))) \ R(x,y,z)) * v5 = R(v5,a(x,u,w),R(x,y,z))
    ]]></literal>
    <justification jstring="[para(13386(a,1),13752(a,2,3))].">
      <j1 rule="para" parents="13386 13752"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,w,u))) = R(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1260,a(flip),b,13755,a),flip(a)].">
      <j1 rule="hyper" parents="325 1260 13755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) = L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(13747(a,1),13759(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13747 13759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13761">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,1570,a(flip),b,13760,a),flip(a)].">
      <j1 rule="hyper" parents="325 1570 13760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,1039,a,b,13761,a)].">
      <j1 rule="hyper" parents="65 1039 13761"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,L(w,w,u))) = L(x,y,w * L(w,u,z)) \ x
    ]]></literal>
    <justification jstring="[para(1570(a,1),13754(a,2,1))].">
      <j1 rule="para" parents="1570 13754"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) \ x = x \ L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(13747(a,1),13765(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13747 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) \ x = x \ L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1570(a,1),13766(a,2,2))].">
      <j1 rule="para" parents="1570 13766"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      L(x \ 1,y,z * L(z,u,w)) = L(x,y,z * L(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(1529,a,13767,a),flip(a)].">
      <j1 rule="hyper" parents="1529 13767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) \ (L(x,y,z) \ u)) = L((1 / u) \ 1,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13609,a,b,13768,a)].">
      <j1 rule="hyper" parents="325 13609 13768"/>
    </justification>
  </clause>

  <clause id="13770">
    <literal><![CDATA[
      ((1 / x) * (x * y)) \ ((x * y) * z) = y \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10856,a(flip),b,13715,a)].">
      <j1 rule="hyper" parents="65 10856 13715"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      L(x,y,y) \ ((y * x) * z) = x \ (((1 / y) \ x) * z)
    ]]></literal>
    <justification jstring="[para(650(a,1),13770(a,1,1))].">
      <j1 rule="para" parents="650 13770"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      L(x,y,z * (u * R(w,v5,v6))) = L(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(413(a,1),13733(a,1,3))].">
      <j1 rule="para" parents="413 13733"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      L(x,y,z * (((u * u) * w) * L(v5,v6,v7))) = L(x,y,z * ((u * u) * (w * R(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(33(a,1),13772(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="33 13772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,L(y,u,w))) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,12327,a(flip),b,13751,a),flip(a)].">
      <j1 rule="hyper" parents="325 12327 13751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      L(L(a(x,y,z),x,u) \ a(x,y,z),w,v5) = a(u,x,L(a(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(11761(a,1),13774(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11761 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      L(L(x,a(y,z,x),u) \ x,w,v5) = a(u,a(y,z,x),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(12928(a,1),13774(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12928 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) = L(a(x,u,a(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(12960(a,1),13776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12960 13776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      a(x,y,L(a(y,z,u),w,v5)) = L(a(x,y,a(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(12507(a,1),13775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12507 13775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      a(x * y,z,L(a(z,x,y),z,z * R(z,x,y))) * R(z,x,y) = z * a(z,x,y)
    ]]></literal>
    <justification jstring="[para(13779(a,2),12592(a,1,1))].">
      <j1 rule="para" parents="13779 12592"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      a(x,a(y,z,x),x \ (L(u,w,v5) \ x)) = L(a(x,a(y,z,x),u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,12583,a(flip),b,13717,a),flip(a)].">
      <j1 rule="hyper" parents="65 12583 13717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,w,v5)) = L(a(x,a(y,z,x),u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,13716,a(flip),b,13781,a)].">
      <j1 rule="hyper" parents="65 13716 13781"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      L(a(x,a(y,z,x),u) \ 1,w,v5) = a(x,a(y,z,x),L(u,w,v5)) \ 1
    ]]></literal>
    <justification jstring="[para(13782(a,2),12450(a,2,1))].">
      <j1 rule="para" parents="13782 12450"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      L(a(x,a(y,z,x),u) \ 1,w,v5) = a(L(u,w,v5),x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,12899,a(flip),b,13783,a),flip(a)].">
      <j1 rule="hyper" parents="325 12899 13783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,u)) = L(a(x,u,a(w,v5,u)),y,z)
    ]]></literal>
    <justification jstring="[para(12899(a,1),13784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12899 13784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,u * w)) * v5) = a(x,y,(z \ (w \ (u / w))) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10709,a(flip),b,13707,a),flip(a)].">
      <j1 rule="hyper" parents="325 10709 13707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (w / u))) * v5) = a(x,y,(z \ L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11277,a(flip),b,13786,a),flip(a)].">
      <j1 rule="hyper" parents="65 11277 13786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (u \ w))) * v5) = a(x,y,(z \ L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,12303,a(flip),b,13787,a)].">
      <j1 rule="hyper" parents="65 12303 13787"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      a(x,R(y,z,u) \ w,v5) = a(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,12383,a,b,13735,a),flip(a)].">
      <j1 rule="hyper" parents="65 12383 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(w,R(y,z,u) \ v5,R(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(728(a,1),13789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="728 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      a(x,L(y * (z * z),z,z) \ u,w) = a(x,((y * z) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(2937(a,1),13789(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2937 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) \ (L(x,y,z) \ u)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(85(a,1),13769(a,2,1))].">
      <j1 rule="para" parents="85 13769"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      L(x * a(y,y,x),y,L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13599,a,b,13792,a)].">
      <j1 rule="hyper" parents="65 13599 13792"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) * R(z,x,y) = z * a(z,x,y)
    ]]></literal>
    <justification jstring="[para(9226(a,1),13780(a,1,1,3))].">
      <j1 rule="para" parents="9226 13780"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) * R(z,y,x) = z * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(2337(a,1),13794(a,1,1))].">
      <j1 rule="para" parents="2337 13794"/>
    </justification>
  </clause>

  <clause id="13797">
    <literal><![CDATA[
      a(x,y,a(y,x,z)) * R(y,x,z) = y * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(12977(a,1),13795(a,1,1))].">
      <j1 rule="para" parents="12977 13795"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      R(x,y,z) * a(y,x,a(x,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7209,a,13797,a)].">
      <j1 rule="hyper" parents="7209 13797"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),x \ (L(u,w,v5) \ x)) = L(a(x,x \ L(x,y,z),u),w,v5)
    ]]></literal>
    <justification jstring="[para(12531(a,1),13728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12531 13728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13800">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),L(u,w,v5)) = L(a(x,x \ L(x,y,z),u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,13727,a(flip),b,13799,a)].">
      <j1 rule="hyper" parents="65 13727 13799"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      L(a(x,x \ L(x,y,z),u) \ 1,w,v5) = a(x,x \ L(x,y,z),L(u,w,v5)) \ 1
    ]]></literal>
    <justification jstring="[para(13800(a,2),12450(a,2,1))].">
      <j1 rule="para" parents="13800 12450"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      L(x,y,z * (((u * u) * w) * L(v5,v6,v7))) = L(x,y,(w * R(v5,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,2356,a(flip),b,13773,a),flip(a)].">
      <j1 rule="hyper" parents="325 2356 13773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w * L(v5,v6,v7)))) = L(x,y,(w * R(v5,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[para(33(a,1),13802(a,1,3,2))].">
      <j1 rule="para" parents="33 13802"/>
    </justification>
  </clause>

  <clause id="13805">
    <literal><![CDATA[
      L(x,y,(z * R(u,w,v5)) * v6) = L(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,2356,a(flip),b,13804,a),flip(a)].">
      <j1 rule="hyper" parents="65 2356 13804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * R(z \ 1,v5,w)) * v6) = L(x,y,(z \ L(L(z,u,w),v5,w)) * v6)
    ]]></literal>
    <justification jstring="[para(11863(a,1),13805(a,2,3,1))].">
      <j1 rule="para" parents="11863 13805"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      L(L(x,y,(z * L(u,w,v5)) * v6) \ x,x,y) = a((z * R(u,w,v5)) * v6,y,x)
    ]]></literal>
    <justification jstring="[para(13805(a,1),12383(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13805 12383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      a((x * R(y,z,u)) * w,v5,v6) = a((x * L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,12383,a,b,13807,a),flip(a)].">
      <j1 rule="hyper" parents="65 12383 13807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      a((x * L(x,x,y)) * z,u,w) = a(a(x,x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12250,a(flip),b,13808,a),flip(a)].">
      <j1 rule="hyper" parents="65 12250 13808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,w) = a(a(y,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11721,a(flip),b,13809,a)].">
      <j1 rule="hyper" parents="65 11721 13809"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      L(x,y,(z \ L(R(z,u,w),v5,w)) * v6) = L(x,y,(z \ L(L(z,v5,w),u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(12476(a,1),13806(a,1,3,1))].">
      <j1 rule="para" parents="12476 13806"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      L(x,y,(z \ L(R(z,u,w),u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,11869,a(flip),b,13811,a),flip(a)].">
      <j1 rule="hyper" parents="325 11869 13811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      a(x,y,y * (a(z,u,(w \ u) * u) \ y)) = w \ (L(L(w,u,z) / w,y,x) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(10136,a,13726,a)].">
      <j1 rule="hyper" parents="10136 13726"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      L(x,R(y \ 1,y,y * z) \ (K(u,w) * v5),v6) = L(x,L(K(w,u) / y,y \ 1,z) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2780(a,1),13739(a,1,2))].">
      <j1 rule="para" parents="2780 13739"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      L(x,R(y \ 1,y,y * z) \ u,w) = L(x,L(K(v5,v6) / y,y \ 1,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(10895,a,13814,a)].">
      <j1 rule="hyper" parents="10895 13814"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      L(x,L(y \ 1,y,y * z) \ u,w) = L(x,L(K(v5,v6) / y,y \ 1,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11427,a(flip),b,13815,a)].">
      <j1 rule="hyper" parents="65 11427 13815"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      L(x,L(K(y,z) / u,u \ 1,w) \ v5,v6) = L(x,L(u \ 1,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,11442,a(flip),b,13817,a),flip(a)].">
      <j1 rule="hyper" parents="65 11442 13817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      L(x,L(y \ 1,y \ 1,z) \ u,w) = L(x,L(y \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(343(a,1),13818(a,1,2,1,1))].">
      <j1 rule="para" parents="343 13818"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,v5) \ L(L(x,y,z) \ x,u,w) = a(v5,x,L(x * L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10556,a(flip),b,13749,a),flip(a)].">
      <j1 rule="hyper" parents="325 10556 13749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,v5) \ L(a(x,y,z) \ 1,u,w) = a(v5,z,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10453,a(flip),b,13750,a),flip(a)].">
      <j1 rule="hyper" parents="325 10453 13750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,z,u) \ (a(x,y,z) \ 1),w,v5) = a(u,z,L(a(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,12327,a(flip),b,13821,a)].">
      <j1 rule="hyper" parents="65 12327 13821"/>
    </justification>
  </clause>

  <clause id="13823">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),w,v5)) = L(a(x,y,a(z,u,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(12522(a,1),13822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12522 13822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13824">
    <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(325,a,13785,a,b,13823,a)].">
      <j1 rule="hyper" parents="325 13785 13823"/>
    </justification>
  </clause>

  <clause id="13825">
    <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(325,a,13777,a,b,13823,a)].">
      <j1 rule="hyper" parents="325 13777 13823"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u * L(u,w,v5),u,w)) = a(x,u,L(a(v5,w,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12393,a,b,13824,a)].">
      <j1 rule="hyper" parents="65 12393 13824"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = a(x,y,L(a(w,v5,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13618,a,b,13825,a)].">
      <j1 rule="hyper" parents="65 13618 13825"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      a(x,L(y,z,u),a(u,w,y)) = a(x,y,a(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12845,a(flip),b,13827,a),flip(a)].">
      <j1 rule="hyper" parents="325 12845 13827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      a(a(x,y,z),L(x,u,z),w) = a(w,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13335,a,b,13828,a)].">
      <j1 rule="hyper" parents="65 13335 13828"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      L(x,a(y,z,u),L(y,z,u)) = a(x,y,a(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(13829(a,1),13430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13829 13430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      L(x,a(y,z,u),L(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,13400,a(flip),b,13831,a),flip(a)].">
      <j1 rule="hyper" parents="325 13400 13831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,x,u) \ (L(x,y,z) \ x),w,v5) = a(u,x,L(x * L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,12327,a(flip),b,13820,a)].">
      <j1 rule="hyper" parents="65 12327 13820"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),w,v5)) = L(a(x,y,y \ L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(13677(a,1),13836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13677 13836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),w,v5)) = L(a(x,y,y * L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(7498(a,1),13837(a,2,1))].">
      <j1 rule="para" parents="7498 13837"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),x,L(y,z,u))) = x \ R(x,y,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12559,a(flip),b,13838,a),flip(a)].">
      <j1 rule="hyper" parents="325 12559 13838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      x \ R(x,y,y \ R(y,z,u)) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10612,a(flip),b,13839,a),flip(a)].">
      <j1 rule="hyper" parents="65 10612 13839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      x \ R(x,y,y * R(y,z,u)) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13207,a(flip),b,13840,a)].">
      <j1 rule="hyper" parents="65 13207 13840"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      x \ L(x,y,y * L(y,z,u)) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13030(a,1),13842(a,1,2))].">
      <j1 rule="para" parents="13030 13842"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),x \ u) \ 1 = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12622,a,b,13843,a)].">
      <j1 rule="hyper" parents="65 12622 13843"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),u) \ 1 = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12529,a,b,13843,a)].">
      <j1 rule="hyper" parents="65 12529 13843"/>
    </justification>
  </clause>

  <clause id="13846">
    <literal><![CDATA[
      L(a(x,x \ L(x,y,z),u) \ 1,w,v5) = a(L(u,w,v5),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13801,a,b,13845,a)].">
      <j1 rule="hyper" parents="65 13801 13845"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),u) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,12642,a,b,13845,a),flip(a)].">
      <j1 rule="hyper" parents="41 12642 13845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      a(x \ y,x,x * L(x,z,u)) = a(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13845,a(flip),b,13844,a)].">
      <j1 rule="hyper" parents="65 13845 13844"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      a(x * y,y,y * L(y,z,u)) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1877,a,13848,a),flip(a)].">
      <j1 rule="hyper" parents="1877 13848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),u * x) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13847,a,b,13849,a)].">
      <j1 rule="hyper" parents="65 13847 13849"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      a(L(x,y,z),u,u * L(u,w,v5)) = L(a(x,u,u * L(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(13845(a,1),13846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13845 13846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13852">
    <literal><![CDATA[
      a(L(x,y,z),u,u * L(u,w,v5)) = a(x,u,L(u * L(u,w,v5),y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13838,a,b,13851,a),flip(a)].">
      <j1 rule="hyper" parents="325 13838 13851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13853">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ R(L(x,y,z) \ 1,u,w),y,z) = (x \ 1) \ R(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(12346(a,1),12354(a,2,2))].">
      <j1 rule="para" parents="12346 12354"/>
    </justification>
  </clause>

  <clause id="13854">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ R(L(x,y,z) \ 1,u,w),y,z) = x \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,1081,a(flip),b,13853,a),flip(a)].">
      <j1 rule="hyper" parents="325 1081 13853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      L(L(x,y,z) \ (1 * R(1 \ L(x,y,z),u,w)),y,z) = x \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(1403(a,1),13854(a,1,1))].">
      <j1 rule="para" parents="1403 13854"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      L(L(x,y,z) \ (1 * R(L(x,y,z),u,w)),y,z) = x \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(67(a,1),13856(a,1,1,2,2,1))].">
      <j1 rule="para" parents="67 13856"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      L(L(x,y,z) \ (1 * L(R(x,u,w),y,z)),y,z) = x \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(29(a,1),13857(a,1,1,2,2))].">
      <j1 rule="para" parents="29 13857"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      L(L(x,y,z) \ L(R(x,u,w),y,z),y,z) = x \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(7(a,1),13858(a,1,1,2))].">
      <j1 rule="para" parents="7 13858"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),u,w) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11555,a(flip),b,13859,a)].">
      <j1 rule="hyper" parents="65 11555 13859"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ 1,u,w) = L(x \ R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(13860(a,1),11879(a,1,1,1))].">
      <j1 rule="para" parents="13860 11879"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ 1 = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(5794(a,1),13861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5794 13861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ L(x,u,w) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11557,a,b,13862,a)].">
      <j1 rule="hyper" parents="65 11557 13862"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,y * z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1907(a,2),13862(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1907 13862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      (R(x,y,z) \ x) * ((R(x,y,z) \ x) * ((a(x,y,z) \ 1) \ u)) = (L(1 / (R(x,y,z) \ x),x,y * z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(13864(a,1),13573(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13864 13573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) \ v5) \ v6) = a(x,y,(L(z,u,w) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,11995,a(flip),b,13736,a),flip(a)].">
      <j1 rule="hyper" parents="65 11995 13736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ L(v5,R(z,u,w) \ 1,R(z,u,w))) \ v6) = a(x,y,((R(z,u,w) \ 1) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(389(a,1),13866(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="389 13866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(w,R(y,z,u) \ v5,R(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * w,v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,9993,a(flip),b,13790,a),flip(a)].">
      <j1 rule="hyper" parents="325 9993 13790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(w,R(y,z,u) \ v5,L(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * w,v6)
    ]]></literal>
    <justification jstring="[para(9931(a,1),13868(a,1,2,2,1))].">
      <j1 rule="para" parents="9931 13868"/>
    </justification>
  </clause>

  <clause id="13871">
    <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) * w,v6)
    ]]></literal>
    <justification jstring="[para(11427(a,1),13870(a,1,2,2,1))].">
      <j1 rule="para" parents="11427 13870"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ w) * T(v5,w),v6) = a(x,(R(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(728(a,1),13871(a,1,2))].">
      <j1 rule="para" parents="728 13871"/>
    </justification>
  </clause>

  <clause id="13873">
    <literal><![CDATA[
      a(x,(R(y,z,u) \ w) * v5,v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(10162,a,13872,a),flip(a)].">
      <j1 rule="hyper" parents="10162 13872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ w) * T(v5,v6),v7) = a(x,v5 * (R(y,z,u) \ w),v7)
    ]]></literal>
    <justification jstring="[hyper(65,a,10102,a(flip),b,13873,a),flip(a)].">
      <j1 rule="hyper" parents="65 10102 13873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      a(x,y * (R(z,u,w) \ v5),v6) = a(x,y * (L(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10102,a(flip),b,13875,a),flip(a)].">
      <j1 rule="hyper" parents="65 10102 13875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ L(v5,R(z,u,w) \ 1,R(z,u,w))) \ v6) = a(x,y,(v5 * R(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10385,a(flip),b,13867,a),flip(a)].">
      <j1 rule="hyper" parents="325 10385 13867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ L(v5,R(z,u,w) \ 1,L(z,u,w))) \ v6) = a(x,y,(v5 * R(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(9931(a,1),13877(a,1,3,1,2))].">
      <j1 rule="para" parents="9931 13877"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ L(v5,L(z,u,w) \ 1,L(z,u,w))) \ v6) = a(x,y,(v5 * R(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(11427(a,1),13878(a,1,3,1,2))].">
      <j1 rule="para" parents="11427 13878"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      a(x,y,((L(z,u,w) \ 1) * v5) \ v6) = a(x,y,(v5 * R(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(389(a,1),13879(a,1,3,1))].">
      <j1 rule="para" parents="389 13879"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) \ v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(10434,a,13880,a),flip(a)].">
      <j1 rule="hyper" parents="10434 13880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13882">
    <literal><![CDATA[
      a(x * (y \ x),x,(z * L(u,w,v5)) \ v6) * y = R(y,x,(z * R(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(13881(a,1),13126(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13881 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      R(x,y,(z * R(u,w,v5)) \ v6) = R(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,13126,a,b,13882,a),flip(a)].">
      <j1 rule="hyper" parents="65 13126 13882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13884">
    <literal><![CDATA[
      R(x,y,(z * L(u \ w,u,u)) \ v5) = R(x,y,(z * (w * (u \ 1))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,9685,a(flip),b,13883,a),flip(a)].">
      <j1 rule="hyper" parents="65 9685 13883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      R(x,y,(z * ((1 / u) * w)) \ v5) = R(x,y,(z * (w * (u \ 1))) \ v5)
    ]]></literal>
    <justification jstring="[para(649(a,1),13884(a,1,3,1,2))].">
      <j1 rule="para" parents="649 13884"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      R(x,y,(z * ((1 / u) * w)) \ v5) = R(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,11322,a(flip),b,13885,a),flip(a)].">
      <j1 rule="hyper" parents="325 11322 13885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      R(x,y,(z * ((u \ 1) * w)) \ v5) = R(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,13443,a(flip),b,13886,a)].">
      <j1 rule="hyper" parents="65 13443 13886"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      R(x,y,(z * ((z \ u) * w)) \ (u * w)) = R(x,y,(w * (z \ u)) \ (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13479,a(flip),b,13887,a),flip(a)].">
      <j1 rule="hyper" parents="65 13479 13887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (z * w))) = R(x,y,a(u,u \ w,z))
    ]]></literal>
    <justification jstring="[para(91(a,1),13888(a,1,3)),flip(a)].">
      <j1 rule="para" parents="91 13888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (z * w))) = L(x,y,a(u,u \ w,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13374,a(flip),b,13889,a),flip(a)].">
      <j1 rule="hyper" parents="325 13374 13889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(L(x * (L(x,y,z) \ x),u,z),y,z) = L(x * (L(x,y,z) \ x),u,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),12361(a,1,1))].">
      <j1 rule="para" parents="9 12361"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ x),u,z) = (L(x,y,z) \ x) * L(x,u,z)
    ]]></literal>
    <justification jstring="[para(12360(a,1),13891(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12360 13891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ x),u,z) = x * (L(x,y,z) \ L(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,9029,a(flip),b,13893,a),flip(a)].">
      <j1 rule="hyper" parents="325 9029 13893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      L(R(x \ L(x,y,z),L(L(x,y,z) \ x,u,w),v5),u,w) \ v5 = (L(x \ L(x,y,z),u,w) \ 1) * v5
    ]]></literal>
    <justification jstring="[hyper(305,a,12331,a)].">
      <j1 rule="hyper" parents="305 12331"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      L(R(x \ L(x,y,z),L(L(x,y,z) \ x,u,w),v5),u,w) \ v5 = L(L(x,y,z) \ x,u,w) * v5
    ]]></literal>
    <justification jstring="[para(12325(a,1),13896(a,2,1))].">
      <j1 rule="para" parents="12325 13896"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),L(L(x,y,z) \ x,u,w),v5),u,w) \ v5 = L(L(x,y,z) \ x,u,w) * v5
    ]]></literal>
    <justification jstring="[para(13440(a,1),13897(a,1,1,1))].">
      <j1 rule="para" parents="13440 13897"/>
    </justification>
  </clause>

  <clause id="13899">
    <literal><![CDATA[
      L(R(x \ (y \ x),x,z),y,u) \ (x \ (y \ (a(u,y,y) \ x))) = a((y \ (a(u,y,y) \ x)) \ x,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(29(a,1),13018(a,1,1))].">
      <j1 rule="para" parents="29 13018"/>
    </justification>
  </clause>

  <clause id="13900">
    <literal><![CDATA[
      L(L(x,a(x,y,z),a(x,y,z) * (u \ a(x,y,z))) \ x,w,v5) * u = R(u,a(x,y,z),R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(12575(a,1),13758(a,1,1))].">
      <j1 rule="para" parents="12575 13758"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      L(R(x \ (y \ x),x,z),y,u) \ L(x \ (y \ x),y,u) = a((y \ (a(u,y,y) \ x)) \ x,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(12761(a,1),13899(a,1,2))].">
      <j1 rule="para" parents="12761 13899"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      L(R(x \ (y \ x),x,z) \ (x \ (y \ x)),y,u) = a((y \ (a(u,y,y) \ x)) \ x,x,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,13863,a(flip),b,13901,a)].">
      <j1 rule="hyper" parents="65 13863 13901"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      a((x \ (a(y,x,x) \ z)) \ z,z,u) \ 1 = L(a((x \ z) \ z,z,u) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(13017(a,1),13902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13017 13902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      a((x \ (a(y,x,x) \ z)) \ z,z,u) \ 1 = L(a(x,z,u) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(1871(a,1),13903(a,2,1,1))].">
      <j1 rule="para" parents="1871 13903"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      a((L(x,x,y) \ z) \ z,z,u) \ 1 = L(a(x,z,u) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(12775(a,1),13904(a,1,1))].">
      <j1 rule="para" parents="12775 13904"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,u) = a(L(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1871(a,1),13906(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1871 13906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13908">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = L(a(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,12450,a(flip),b,13907,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 12450 13907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      a(L(x,x,y * z),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,12461,a(flip),b,13908,a),flip(a)].">
      <j1 rule="hyper" parents="325 12461 13908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      (x * (y \ R(y,x,z))) \ (x * z) = L(z,x,L(y,y,x * z))
    ]]></literal>
    <justification jstring="[para(13910(a,1),12963(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13910 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      L(x,y,L(z,z,y * x)) = L(x,y,y * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13131,a(flip),b,13911,a),flip(a)].">
      <j1 rule="hyper" parents="65 13131 13911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ u,w) = K(((y \ (z \ (x * (z * y)))) \ u) * K(z * y,x),w)
    ]]></literal>
    <justification jstring="[para(8923(a,1),12434(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8923 12434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ u,w) = K(((z \ (x * (z * y))) \ (y * u)) * K(z * y,x),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9802,a(flip),b,13913,a),flip(a)].">
      <j1 rule="hyper" parents="325 9802 13913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ u,w) = K(((x * (z * y)) \ (z * (y * u))) * K(z * y,x),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9802,a(flip),b,13914,a),flip(a)].">
      <j1 rule="hyper" parents="325 9802 13914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ u,w) = K(((z * y) \ (x \ (z * (y * u)))) * K(z * y,x),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9801,a(flip),b,13916,a),flip(a)].">
      <j1 rule="hyper" parents="325 9801 13916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13918">
    <literal><![CDATA[
      K(T(x * y,z) \ (z \ (x * (y * u))),w) = K((z * (L(z,y,x) \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,9459,a(flip),b,13917,a)].">
      <j1 rule="hyper" parents="325 9459 13917"/>
    </justification>
  </clause>

  <clause id="13919">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ u,w) = K(x \ ((z * y) \ (z * (y * u))),w)
    ]]></literal>
    <justification jstring="[hyper(8408,a,13918,a),flip(a)].">
      <j1 rule="hyper" parents="8408 13918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      K((x * (L(x,y,z) \ x)) \ u,w) = K(x \ L(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(18(a,2),13919(a,2,1,2))].">
      <j1 rule="para" parents="18 13919"/>
    </justification>
  </clause>

  <clause id="13921">
    <literal><![CDATA[
      K((L(x,y,z) \ x) \ (x \ u),w) = K(x \ L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(8267,a,13920,a)].">
      <j1 rule="hyper" parents="8267 13920"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      K(L(x,y,z) * (x \ (x \ u)),w) = K(x \ L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,8331,a(flip),b,13921,a)].">
      <j1 rule="hyper" parents="65 8331 13921"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      K(L(x \ 1,y,z) * u,w) = K(x \ L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9034,a(flip),b,13922,a)].">
      <j1 rule="hyper" parents="65 9034 13922"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      K((x \ 1) \ L(y,z,u),w) = K(L(x,z,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,6719,a(flip),b,13923,a),flip(a)].">
      <j1 rule="hyper" parents="65 6719 13923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      K(L(x,y,z) * u,w) = K(x * L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(8420,a,13924,a),flip(a)].">
      <j1 rule="hyper" parents="8420 13924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      K(x * L(y,z,u),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9799,a(flip),b,13925,a),flip(a)].">
      <j1 rule="hyper" parents="65 9799 13925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,(z * x) \ ((x * L(y,u,w)) * z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(13926(a,1),9812(a,1,1))].">
      <j1 rule="para" parents="13926 9812"/>
    </justification>
  </clause>

  <clause id="13930">
    <literal><![CDATA[
      x * (L(a(y,z,u),w,v5) * a(a(y,z,u),a(y,z,u),x)) = L(x,a(y,z,u),a(y,z,u)) * L(a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10566,a(flip),b,12627,a)].">
      <j1 rule="hyper" parents="65 10566 12627"/>
    </justification>
  </clause>

  <clause id="13931">
    <literal><![CDATA[
      a(x,x,y) * (z * L(z \ (a(x,x,y) \ z),u,w)) = z * (a(x,x,y) * L(v5 \ (a(x,x,y) \ v5),u,w))
    ]]></literal>
    <justification jstring="[para(8(a,1),12735(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="8 12735"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      x * (a(y,y,z) * L(u \ (a(y,y,z) \ u),w,v5)) = a(y,y,z) * (x * L(a(y,y,z) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(12720(a,1),13931(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12720 13931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      a(x,x,y) * (z * L(a(x,x,y) \ 1,u,w)) = z * (a(x,x,y) \ L(a(x,x,y),u,w))
    ]]></literal>
    <justification jstring="[para(1309(a,1),13932(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1309 13932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13935">
    <literal><![CDATA[
      a(x,x,y) * (z * L(a(x,x,y) \ 1,u,w)) = z * (a(x,x,y) \ a(x,x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(12056(a,2),13933(a,2,2,2))].">
      <j1 rule="para" parents="12056 13933"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      a(x,x,y) * (z * L(a(x,x,y) \ 1,u,w)) = z * a(w,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(13722(a,1),13935(a,2,2))].">
      <j1 rule="para" parents="13722 13935"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      a(x,x,y) * (a(x,x,L(y,z,u)) \ w) = w * a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(12732(a,1),13936(a,1,2))].">
      <j1 rule="para" parents="12732 13936"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ w) * a(x,x,y) = w * a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(7209,a,13937,a)].">
      <j1 rule="hyper" parents="7209 13937"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ (w * a(x,x,y)) = a(u,z,a(x,x,y)) * w
    ]]></literal>
    <justification jstring="[hyper(37,a,12921,a,b,13938,a),flip(a)].">
      <j1 rule="hyper" parents="37 12921 13938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      L(x * a(y,y,x),y,L(y,z,u)) = a(u,z,a(y,y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,13636,a(flip),b,13939,a)].">
      <j1 rule="hyper" parents="65 13636 13939"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      (1 / x) \ L(y,x,L(x,z,u)) = x * (a(u,z,a(x,x,y)) * y)
    ]]></literal>
    <justification jstring="[para(13940(a,1),11968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13940 11968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,((z * x) \ (x * L(y,u,w))) * z),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(8861(a,1),13929(a,1,2,1,1))].">
      <j1 rule="para" parents="8861 13929"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) * L(a(y,z,u),w,v5) = (1 / L(a(y,z,u),w,v5)) \ T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13557,a(flip),b,13930,a),flip(a)].">
      <j1 rule="hyper" parents="65 13557 13930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) * L(a(y,z,u),w,v5) = (L(a(y,z,u),w,v5) \ 1) \ T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7234(a,1),13944(a,2,1))].">
      <j1 rule="para" parents="7234 13944"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) * L(a(y,z,u),w,v5) = L(a(y,z,u) \ 1,w,v5) \ T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(12450(a,2),13945(a,2,1))].">
      <j1 rule="para" parents="12450 13945"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) * L(a(y,z,u),w,v5) = L(a(y,z,u) \ 1,w,v5) \ x
    ]]></literal>
    <justification jstring="[para(7179(a,1),13946(a,2,2))].">
      <j1 rule="para" parents="7179 13946"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,((z * x) \ x) * (L(y,u,w) * z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(10738(a,1),13942(a,1,2,1,1))].">
      <j1 rule="para" parents="10738 13942"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,((z * x) \ x) * (y * z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(8947(a,1),13949(a,1,2,1,1))].">
      <j1 rule="para" parents="8947 13949"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,(x \ (z \ x)) * (y * z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(8845(a,1),13950(a,1,2,1,1))].">
      <j1 rule="para" parents="8845 13950"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,T(z,x) \ (y * z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(8897(a,1),13951(a,1,2,1,1))].">
      <j1 rule="para" parents="8897 13951"/>
    </justification>
  </clause>

  <clause id="13954">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,T(K(x,z) * y,z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(2705(a,2),13953(a,1,2,1,1,2))].">
      <j1 rule="para" parents="2705 13953"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      K(x * y,z) * L(L(T(y,K(x,z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(9523(a,1),13954(a,1,2,1,1))].">
      <j1 rule="para" parents="9523 13954"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      L(K(x * y,z) * L(T(y,K(x,z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,8549,a,b,13955,a)].">
      <j1 rule="hyper" parents="65 8549 13955"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      L(L(K(x * y,z) * T(y,K(x,z)),x,z),u,w) = (z * x) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(8549(a,2),13956(a,1,1))].">
      <j1 rule="para" parents="8549 13956"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      L(L(x * K(y * x,z),y,z),u,w) = (z * y) \ ((y * L(x,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(3866(a,1),13958(a,1,1,1))].">
      <j1 rule="para" parents="3866 13958"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      L((x * y) \ ((y * z) * x),u,w) = (x * y) \ ((y * L(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(6687(a,1),13959(a,1,1))].">
      <j1 rule="para" parents="6687 13959"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * a(y * (x \ 1),x * (y \ (x \ y)),a(x,x,y)) = 1 / ((x \ y) \ (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(11683(a,1),12143(a,1,2))].">
      <j1 rule="para" parents="11683 12143"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * a(y * (x \ 1),a(x,x \ 1,y),a(x,x,y)) = 1 / ((x \ y) \ (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(11657(a,1),13961(a,1,2))].">
      <j1 rule="para" parents="11657 13961"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      R(R(x,y,y),y * y,L(a(z,u,x),y,x * y)) = ((x * y) * (y * a(z,u,x))) / (y * (y * a(z,u,x)))
    ]]></literal>
    <justification jstring="[para(100(a,1),12609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 12609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      R(R(x,y,y),y * y,L(a(z,u,x),y,x * y)) = R(x,y,y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,20,a,b,13963,a),flip(a)].">
      <j1 rule="hyper" parents="325 20 13963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      R(R(x,y,y),y * y,L(a(z,u,x),y,y)) = R(x,y,y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(12608(a,1),13964(a,1,3))].">
      <j1 rule="para" parents="12608 13964"/>
    </justification>
  </clause>

  <clause id="13966">
    <literal><![CDATA[
      (R(x,y,z) \ x) * ((R(x,y,z) \ x) * ((a(x,y,z) \ 1) \ u)) = (L(x \ R(x,y,z),x,y * z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(5795(a,1),13865(a,2,1,1,1))].">
      <j1 rule="para" parents="5795 13865"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      (R(x,y,z) \ x) * ((R(x,y,z) \ x) * ((a(x,y,z) \ 1) \ u)) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(1907(a,2),13966(a,2,1,1))].">
      <j1 rule="para" parents="1907 13966"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      a((L(x,y,z) \ 1) * ((x \ 1) \ (1 / L(x,y,z))),L(x,y,z) \ 1,u) = (1 / x) \ R(1 / x,1 / L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(10163,a,13130,a)].">
      <j1 rule="hyper" parents="10163 13130"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,z,z * (u \ z)) \ (a(x,y,z) \ 1),w,v5) * u = R(u,z,L(a(x,y,z) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(12327(a,1),13756(a,1,1))].">
      <j1 rule="para" parents="12327 13756"/>
    </justification>
  </clause>

  <clause id="13970">
    <literal><![CDATA[
      L(a(x * (y \ x),x,a(z,u,x)),w,v5) * y = R(y,x,L(a(z,u,x) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(12522(a,1),13969(a,1,1,1))].">
      <j1 rule="para" parents="12522 13969"/>
    </justification>
  </clause>

  <clause id="13971">
    <literal><![CDATA[
      R(x,y,L(a(z,u,y) \ 1,w,v5)) = L(a(x,y,a(z,u,y)),w,v5) * x
    ]]></literal>
    <justification jstring="[para(13127(a,1),13970(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13127 13970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13972">
    <literal><![CDATA[
      R(x,y,L(a(z,u,y) \ 1,w,v5)) = a(x,y,L(a(z,u,y),w,v5)) * x
    ]]></literal>
    <justification jstring="[para(13823(a,2),13971(a,2,1))].">
      <j1 rule="para" parents="13823 13971"/>
    </justification>
  </clause>

  <clause id="13973">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),w,v5)) * x = R(x,y,L(a(z,u,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,1765,a(flip),b,13972,a),flip(a)].">
      <j1 rule="hyper" parents="65 1765 13972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      a((L(x,y,z) \ 1) * ((x \ 1) \ (L(x,y,z) \ 1)),L(x,y,z) \ 1,u) = (1 / x) \ R(1 / x,1 / L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,5171,a(flip),b,13968,a)].">
      <j1 rule="hyper" parents="65 5171 13968"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      a((L(x,y,z) \ 1) * (L(x,y,z) \ x),L(x,y,z) \ 1,u) = (1 / x) \ R(1 / x,1 / L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1527(a,1),13974(a,1,1,2))].">
      <j1 rule="para" parents="1527 13974"/>
    </justification>
  </clause>

  <clause id="13976">
    <literal><![CDATA[
      a(x,y,(T(z * u,w * w) * v5) \ ((u * v5) * ((w * w) \ z))) = a(x,y,a(v5,u * (w * w),(w * w) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10710,a(flip),b,11919,a)].">
      <j1 rule="hyper" parents="65 10710 11919"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      a(x,y,a(z,u * (w * w),(w * w) \ v5)) = a(x,y,(T(v5 * u,w * w) * z) \ ((u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10351,a(flip),b,13976,a),flip(a)].">
      <j1 rule="hyper" parents="65 10351 13976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      a(x,y,a(z,u * (w * w),(w * w) \ v5)) = a(x,y,(z * (v5 * u)) \ ((u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,10255,a(flip),b,13978,a),flip(a)].">
      <j1 rule="hyper" parents="325 10255 13978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13982">
    <literal><![CDATA[
      a(x,y,a(z,u * (w * w),(w * w) \ v5)) = a(x,y,a(z,u,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,12087,a(flip),b,13980,a),flip(a)].">
      <j1 rule="hyper" parents="325 12087 13980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      a(x,y,a(z,u * (w * w),v5)) = a(x,y,a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(10084(a,1),13982(a,1,3))].">
      <j1 rule="para" parents="10084 13982"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(221(a,1),13983(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="221 13983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      a(x,y,a(z,(u * u) * w,v5)) = a(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[para(9995(a,1),13983(a,1,3))].">
      <j1 rule="para" parents="9995 13983"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      a(x,a(y,y \ 1,z),a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12740,a(flip),b,13984,a),flip(a)].">
      <j1 rule="hyper" parents="65 12740 13984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12018,a(flip),b,13984,a),flip(a)].">
      <j1 rule="hyper" parents="65 12018 13984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      1 / ((x \ y) \ (y * (x \ 1))) = (x * (y \ (x \ y))) * 1
    ]]></literal>
    <justification jstring="[para(13987(a,1),13962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13987 13962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      a(x,y,a(z,z,u * z)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(10789,a,13988,a)].">
      <j1 rule="hyper" parents="10789 13988"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      a(x,y,a(z * u,z,z)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,13988,a)].">
      <j1 rule="hyper" parents="65 12836 13988"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (w * z))) = a(x,y,a(z,z,u * w))
    ]]></literal>
    <justification jstring="[para(12270(a,1),13990(a,1,3))].">
      <j1 rule="para" parents="12270 13990"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      x * a(x,y * z,a(y,y,z)) = L(x,y * z,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(13991(a,1),13403(a,1,2))].">
      <j1 rule="para" parents="13991 13403"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      a(x,y,a(z,((u * u) \ w) * v5,v6)) = a(x,y,a(z,w * v5,v6))
    ]]></literal>
    <justification jstring="[para(119(a,1),13985(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="119 13985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      1 / ((x \ y) \ (y * (x \ 1))) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,8,a(flip),b,13989,a),flip(a)].">
      <j1 rule="hyper" parents="325 8 13989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ 1 = (x \ y) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(195,a,13995,a)].">
      <j1 rule="hyper" parents="195 13995"/>
    </justification>
  </clause>

  <clause id="13998">
    <literal><![CDATA[
      (x \ y) \ (y * (x \ 1)) = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(65,a,12145,a(flip),b,13997,a),flip(a)].">
      <j1 rule="hyper" parents="65 12145 13997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u * w,v5)),a(z,((v6 * v6) \ u) * w,v5),y) = L(x,y,a(z,((v6 * v6) \ u) * w,v5))
    ]]></literal>
    <justification jstring="[para(13994(a,1),12111(a,1,1,2))].">
      <j1 rule="para" parents="13994 12111"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u * w,v5)),a(z,u * ((v6 * v6) \ w),v5),y) = L(x,y,a(z,((v6 * v6) \ u) * w,v5))
    ]]></literal>
    <justification jstring="[para(10302(a,1),13999(a,1,2))].">
      <j1 rule="para" parents="10302 13999"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u * w,v5)),a(z,u * w,v5),y) = L(x,y,a(z,((v6 * v6) \ u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,11298,a(flip),b,14000,a)].">
      <j1 rule="hyper" parents="65 11298 14000"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      L(x,y,a(z,((u * u) \ w) * v5,v6)) = L(x,y,a(z,w * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(65,a,12111,a(flip),b,14001,a),flip(a)].">
      <j1 rule="hyper" parents="65 12111 14001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      L(x,y,a(z,(u * u) * w,v5)) = L(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[para(176(a,1),14003(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="176 14003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      L(x,y,a(z,u * ((w * w) \ v5),v6)) = L(x,y,a(z,v5 * u,v6))
    ]]></literal>
    <justification jstring="[para(9995(a,1),14003(a,1,3))].">
      <j1 rule="para" parents="9995 14003"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      L(x,y,a(z,u * ((w * w) \ v5),v6)) = L(x,y,a(z,u * v5,v6))
    ]]></literal>
    <justification jstring="[para(10302(a,1),14003(a,1,3))].">
      <j1 rule="para" parents="10302 14003"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      L(x,y,a(z,(u \ 1) \ w,v5)) = L(x,y,a(z,u \ w,v5))
    ]]></literal>
    <justification jstring="[para(10265(a,1),14004(a,1,3))].">
      <j1 rule="para" parents="10265 14004"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      L(x,y,a(z,u \ 1,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(4386(a,1),14007(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4386 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      L(x,y,a(z,((a(u,u,w) / u) \ 1) \ w,v5)) = L(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(11612(a,1),14007(a,2,3,2))].">
      <j1 rule="para" parents="11612 14007"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      L(x,y,a(z,a(u,u,w) \ v5,v6)) = L(x,y,a(z,v5 * a(u,u,w),v6))
    ]]></literal>
    <justification jstring="[para(12719(a,1),14007(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12719 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      L(x,y,a(z,u * w,v5)) = L(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,14005,a(flip),b,14006,a)].">
      <j1 rule="hyper" parents="65 14005 14006"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      L(x,y,a(z,(a(u,u,w) \ u) \ w,v5)) = L(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(13414(a,1),14009(a,1,3,2,1))].">
      <j1 rule="para" parents="13414 14009"/>
    </justification>
  </clause>

  <clause id="14014">
    <literal><![CDATA[
      L(x,y,a(z,(u \ w) * a(u,u,w),v5)) = L(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(12739(a,1),14013(a,1,3,2))].">
      <j1 rule="para" parents="12739 14013"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      R(x,y,z) \ (a(R(x,y,z),L(x,y,z) \ 1,u) / (1 / R(x,y,z))) = L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(13789(a,1),11952(a,1,2,1))].">
      <j1 rule="para" parents="13789 11952"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      ((x \ y) \ (y * (x \ 1))) * a(x \ y,(x \ y) \ (y * (x \ 1)),(x \ y) \ (x * y)) = 1 / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(10683(a,1),12142(a,1,2))].">
      <j1 rule="para" parents="10683 12142"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      ((x \ y) \ (y * (x \ 1))) * a(x \ y,(x \ y) \ (y * (x \ 1)),a(x,x,y)) = 1 / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(12033(a,1),14016(a,1,2))].">
      <j1 rule="para" parents="12033 14016"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      ((x \ y) \ (y * (x \ 1))) * 1 = 1 / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(12017(a,1),14017(a,1,2))].">
      <j1 rule="para" parents="12017 14017"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      1 / (x * (y \ (x \ y))) = (x \ y) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(142,a,14018,a),flip(a)].">
      <j1 rule="hyper" parents="142 14018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      R(x,y,z) \ (a(L(x,y,z),L(x,y,z) \ 1,u) / (1 / R(x,y,z))) = L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(8679(a,1),14015(a,1,2,1))].">
      <j1 rule="para" parents="8679 14015"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      x * (R(R(x,y,z),u,x * L(x,y,z)) * (R(x,y,z) \ (u * (x \ R(x,y,z))))) = L(R(x,y,z) * u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(13031(a,1),13743(a,1,2,1))].">
      <j1 rule="para" parents="13031 13743"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      x * (R(x,y,z) * (R(x,y,z) \ (u * (x \ R(x,y,z))))) = L(R(x,y,z) * u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7713(a,1),14022(a,1,2,1))].">
      <j1 rule="para" parents="7713 14022"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      L(R(x,y,z) * u,x,x * L(x,y,z)) = x * (u * (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(331,a,14023,a),flip(a)].">
      <j1 rule="hyper" parents="331 14023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = (z * (K(x * y,z) * x)) \ (((x * (y * z)) / (x * y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(4578(a,1),11750(a,2,1))].">
      <j1 rule="para" parents="4578 11750"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = (z * (x * K(y * x,z))) \ (((x * (y * z)) / (x * y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(7373(a,1),14027(a,2,1,2))].">
      <j1 rule="para" parents="7373 14027"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = (z * (x * K(y * x,z))) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),14028(a,2,2))].">
      <j1 rule="para" parents="12 14028"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = K(z,y * x) * ((z * x) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,9611,a(flip),b,14029,a),flip(a)].">
      <j1 rule="hyper" parents="325 9611 14029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      L(a(x,y,z) \ y,x,z * K(x * y,z)) = K(z,y * x) * ((z * x) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(10052(a,1),14030(a,1,1,1))].">
      <j1 rule="para" parents="10052 14030"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      K(x,y * z) * ((x * z) \ (z * (y * x))) = L(a(z,y,x) \ y,z,x)
    ]]></literal>
    <justification jstring="[hyper(2334,a,14032,a),flip(a)].">
      <j1 rule="hyper" parents="2334 14032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      K(x,y * (z * z)) * (T(x,z * z) \ (y * x)) = L(a(z * z,y,x) \ y,z * z,x)
    ]]></literal>
    <justification jstring="[para(690(a,1),14033(a,1,2))].">
      <j1 rule="para" parents="690 14033"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      K(L(x,y,z),u * (w * w)) * (L(x * (w * w),y,z) \ ((w * w) * (u * L(x,y,z)))) = L(a(w * w,u,L(x,y,z)) \ u,w * w,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1069(a,2),14033(a,1,2,1))].">
      <j1 rule="para" parents="1069 14033"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      K(x,y * (z * z)) * T(K(z * z,x) * y,x) = L(a(z * z,y,x) \ y,z * z,x)
    ]]></literal>
    <justification jstring="[para(2705(a,2),14036(a,1,2))].">
      <j1 rule="para" parents="2705 14036"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      T(K(x,y * (z * z)) * (K(z * z,x) * y),x) = L(a(z * z,y,x) \ y,z * z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,4541,a,b,14038,a)].">
      <j1 rule="hyper" parents="65 4541 14038"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      T(K(x,y * (z * z)) * (K(z * z,x) * y),x) = L(1 \ y,z * z,x)
    ]]></literal>
    <justification jstring="[para(460(a,1),14039(a,2,1,1))].">
      <j1 rule="para" parents="460 14039"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      T(K(x,y * (z * z)) * (K(z * z,x) * y),x) = L(y,z * z,x)
    ]]></literal>
    <justification jstring="[para(67(a,1),14040(a,2,1))].">
      <j1 rule="para" parents="67 14040"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      R(x,y,y) \ (((y \ 1) \ L(y \ 1,z,u)) \ ((x * L(y,z,u)) * (y \ 1))) = a(y \ 1,(y \ 1) \ L(y \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(568(a,1),12123(a,1,1))].">
      <j1 rule="para" parents="568 12123"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      R(x,y,y) \ ((y \ (1 * L(1 \ y,z,u))) \ ((x * L(y,z,u)) * (y \ 1))) = a(y \ 1,(y \ 1) \ L(y \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(1410(a,1),14043(a,1,2,1))].">
      <j1 rule="para" parents="1410 14043"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      R(x,y,y) \ ((y \ (1 * L(y,z,u))) \ ((x * L(y,z,u)) * (y \ 1))) = a(y \ 1,(y \ 1) \ L(y \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(67(a,1),14044(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="67 14044"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      R(x,y,y) \ ((y \ L(y,z,u)) \ ((x * L(y,z,u)) * (y \ 1))) = a(y \ 1,(y \ 1) \ L(y \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),14045(a,1,2,1,2))].">
      <j1 rule="para" parents="7 14045"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      R(x,y,y) \ ((y \ L(y,z,u)) \ ((x * y) * L(y \ 1,z,u))) = a(y \ 1,(y \ 1) \ L(y \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9035(a,1),14046(a,1,2,2))].">
      <j1 rule="para" parents="9035 14046"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      a(x \ 1,(x \ 1) \ L(x \ 1,y,z),u * x) = R(u,x,x) \ R((u * x) / x,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9003(a,1),14047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9003 14047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      a(x \ 1,(x \ 1) \ L(x \ 1,y,z),u * x) = R(u,x,x) \ R(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),14048(a,2,2,1))].">
      <j1 rule="para" parents="11 14048"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      a(x \ 1,x \ (1 * L(1 \ x,y,z)),u * x) = R(u,x,x) \ R(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1410(a,1),14049(a,1,2))].">
      <j1 rule="para" parents="1410 14049"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      a(x \ 1,x \ (1 * L(x,y,z)),u * x) = R(u,x,x) \ R(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(67(a,1),14050(a,1,2,2,2,1))].">
      <j1 rule="para" parents="67 14050"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      a(x \ 1,x \ L(x,y,z),u * x) = R(u,x,x) \ R(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),14051(a,1,2,2))].">
      <j1 rule="para" parents="7 14051"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      R(x,y,y) \ R(x,y,L(y,z,u)) = a(y,y \ L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(1886,a,14052,a),flip(a)].">
      <j1 rule="hyper" parents="1886 14052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14054">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(y,y \ L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12989,a,b,14053,a)].">
      <j1 rule="hyper" parents="65 12989 14053"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      a(x,x \ L(x,y,y),z * x) = a(y,y,a(z,x,x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12988,a(flip),b,14053,a),flip(a)].">
      <j1 rule="hyper" parents="65 12988 14053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      a(x,y,y * L(y,z,z)) = a(z,z,a(x,y,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,13850,a(flip),b,14055,a)].">
      <j1 rule="hyper" parents="65 13850 14055"/>
    </justification>
  </clause>

  <clause id="14057">
    <literal><![CDATA[
      a(x,x,a(y,z,z) \ 1) \ 1 = a(y,z,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,7500,a(flip),b,14056,a),flip(a)].">
      <j1 rule="hyper" parents="65 7500 14056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      a(a(x,y,y),z,z) = a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(130,a,12742,a(flip),b,14057,a(flip))].">
      <j1 rule="hyper" parents="130 12742 14057"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13333,a(flip),b,14058,a),flip(a)].">
      <j1 rule="hyper" parents="65 13333 14058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      x * a(y * z,y,a(x,x,y)) = L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(14058(a,1),13204(a,1,2))].">
      <j1 rule="para" parents="14058 13204"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      a(x,x,a(y,x * z,x * z)) = a(y,x * z,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13988,a(flip),b,14059,a),flip(a)].">
      <j1 rule="hyper" parents="65 13988 14059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      x * a(y,z,a(z,x,x)) = L(x,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(12848(a,1),14060(a,1,2))].">
      <j1 rule="para" parents="12848 14060"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,13850,a(flip),b,14054,a),flip(a)].">
      <j1 rule="hyper" parents="325 13850 14054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13319,a(flip),b,14063,a),flip(a)].">
      <j1 rule="hyper" parents="65 13319 14063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      x \ L(x,x \ L(x,y,z),u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13670,a,b,14064,a)].">
      <j1 rule="hyper" parents="65 13670 14064"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),w,v5)) = a(a(L(x,w,v5),y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13852,a(flip),b,14064,a)].">
      <j1 rule="hyper" parents="65 13852 14064"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) = x * a(z,y,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,13333,a(flip),b,14065,a),flip(a)].">
      <j1 rule="hyper" parents="137 13333 14065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),y) = L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14062,a(flip),b,14067,a),flip(a)].">
      <j1 rule="hyper" parents="325 14062 14067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),w,v5)) = a(a(x,y,L(y,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(12660(a,1),14066(a,2,1))].">
      <j1 rule="para" parents="12660 14066"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      a(a(L(x,y,z),u,L(u,u,w)),w,v5) = a(x,u,L(a(v5,w,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13826,a(flip),b,14069,a),flip(a)].">
      <j1 rule="hyper" parents="65 13826 14069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      a(a(L(x,y,z),u,u),w,v5) = a(x,u,L(a(v5,w,u),y,z))
    ]]></literal>
    <justification jstring="[para(12865(a,1),14070(a,1,1))].">
      <j1 rule="para" parents="12865 14070"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),u,z)) = a(a(x,y,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12968,a(flip),b,14071,a),flip(a)].">
      <j1 rule="hyper" parents="65 12968 14071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      a(a(x,y,L(y,z,u)),w,v5) = a(x,y,L(a(v5,w,y),z,u))
    ]]></literal>
    <justification jstring="[para(12660(a,1),14071(a,1,1))].">
      <j1 rule="para" parents="12660 14071"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(11577(a,1),14072(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11577 14072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13345,a,b,14075,a)].">
      <j1 rule="hyper" parents="65 13345 14075"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13335,a(flip),b,14075,a),flip(a)].">
      <j1 rule="hyper" parents="65 13335 14075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14079">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13333,a(flip),b,14075,a)].">
      <j1 rule="hyper" parents="65 13333 14075"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,13723,a,b,14078,a)].">
      <j1 rule="hyper" parents="325 13723 14078"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14078,a(flip),b,14078,a),flip(a)].">
      <j1 rule="hyper" parents="325 14078 14078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,14059,a(flip),b,14078,a),flip(a)].">
      <j1 rule="hyper" parents="325 14059 14078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13347,a,b,14078,a)].">
      <j1 rule="hyper" parents="65 13347 14078"/>
    </justification>
  </clause>

  <clause id="14085">
    <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(12668(a,1),14079(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12668 14079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * z = L(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[para(14079(a,2),12910(a,1,1))].">
      <j1 rule="para" parents="14079 12910"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * u = u * a(z,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(14082(a,2),12841(a,2,2))].">
      <j1 rule="para" parents="14082 12841"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      (x * a(y,z,a(u,y,z))) / (a(u,y,z) \ a(z,z,a(u,y,y))) = L(x / (a(u,y,z) \ 1),a(u,y,z),a(y,z,a(u,y,z)))
    ]]></literal>
    <justification jstring="[para(14083(a,1),13431(a,1,2,2))].">
      <j1 rule="para" parents="14083 13431"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * u = L(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14084(a,1),13396(a,1,1))].">
      <j1 rule="para" parents="14084 13396"/>
    </justification>
  </clause>

  <clause id="14090">
    <literal><![CDATA[
      L(x * a(y,y,x),y,L(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13940,a,b,14089,a)].">
      <j1 rule="hyper" parents="65 13940 14089"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      (1 / x) \ L(y,x,L(x,z,u)) = x * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14089(a,1),13941(a,2,2))].">
      <j1 rule="para" parents="14089 13941"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13793,a(flip),b,14090,a)].">
      <j1 rule="hyper" parents="65 13793 14090"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      L(R(x,y,z) * u,x,a(x,y,z)) = x * (u * (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14024,a(flip),b,14092,a),flip(a)].">
      <j1 rule="hyper" parents="65 14024 14092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14095">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * u) = L(x \ u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1796,a(flip),b,14092,a)].">
      <j1 rule="hyper" parents="65 1796 14092"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y,y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(662,a,14091,a)].">
      <j1 rule="hyper" parents="662 14091"/>
    </justification>
  </clause>

  <clause id="14097">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,z) * ((((x \ L(x,y,z)) \ 1) * x) \ u)) = L(x \ (((L(x,y,z) / x) \ 1) \ u),x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(9943(a,1),14095(a,1,2))].">
      <j1 rule="para" parents="9943 14095"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,z) * (((L(x,y,z) \ x) * x) \ u)) = L(x \ (((L(x,y,z) / x) \ 1) \ u),x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2015(a,1),14097(a,1,2,2,1,1))].">
      <j1 rule="para" parents="2015 14097"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      L(x \ (((L(x,y,z) / x) \ 1) \ u),x,a(x,y,z)) = ((L(x,y,z) \ x) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(332,a,14098,a),flip(a)].">
      <j1 rule="hyper" parents="332 14098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      L(x \ (((x \ L(x,y,z)) \ 1) \ u),x,a(x,y,z)) = ((L(x,y,z) \ x) * x) \ u
    ]]></literal>
    <justification jstring="[para(1752(a,1),14099(a,1,1,2,1,1))].">
      <j1 rule="para" parents="1752 14099"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      L(x \ ((L(x,y,z) \ x) \ u),x,a(x,y,z)) = ((L(x,y,z) \ x) * x) \ u
    ]]></literal>
    <justification jstring="[para(2015(a,1),14101(a,1,1,2,1))].">
      <j1 rule="para" parents="2015 14101"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      a(T(x,y * z),T(x,y * z),L(u,z * T(x,y * z),y)) = (L(x,z,y) * (y * z)) \ (y * (z * R(T(x,y * z),x,u)))
    ]]></literal>
    <justification jstring="[para(9893(a,1),12275(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9893 12275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14104">
    <literal><![CDATA[
      a(T(x,y * z),T(x,y * z),L(u,z * T(x,y * z),y)) = (L(x,z,y) * (y * z)) \ (L(R(x,x,u),z,y) * (y * z))
    ]]></literal>
    <justification jstring="[para(832(a,1),14103(a,2,2))].">
      <j1 rule="para" parents="832 14103"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (L(R(x,x,u),y,z) * (z * y)) = a(T(x,z * y),T(x,z * y),L(u,y * x,z))
    ]]></literal>
    <justification jstring="[para(10811(a,1),14104(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10811 14104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14107">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (L(R(x,x,u),y,z) * (z * y)) = a(x,x,L(u,y * x,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10012,a(flip),b,14106,a),flip(a)].">
      <j1 rule="hyper" parents="325 10012 14106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      a(x,x,L(y,z * x,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13531,a(flip),b,14107,a),flip(a)].">
      <j1 rule="hyper" parents="65 13531 14107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      a(x,x,L(y,x * z,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11035,a,14110,a)].">
      <j1 rule="hyper" parents="11035 14110"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(y,x,a(u,z * x,x))
    ]]></literal>
    <justification jstring="[para(14110(a,1),14081(a,1,1))].">
      <j1 rule="para" parents="14110 14081"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      ((x * y) * z) \ (((1 / x) \ y) * z) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13323,a(flip),b,14111,a)].">
      <j1 rule="hyper" parents="65 13323 14111"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      a(x,y,a(z,u * y,y)) = a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13723,a(flip),b,14113,a),flip(a)].">
      <j1 rule="hyper" parents="65 13723 14113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      K(x,y * (z * z)) * (L(x * (z * z),u,w) \ ((z * z) * (y * L(x,u,w)))) = L(a(z * z,y,L(x,u,w)) \ y,z * z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7924(a,1),14037(a,1,1))].">
      <j1 rule="para" parents="7924 14037"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      K(x,y * (z * z)) * (L(T(x,z * z),u,w) \ (y * L(x,u,w))) = L(a(z * z,y,L(x,u,w)) \ y,z * z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(1348(a,1),14116(a,1,2))].">
      <j1 rule="para" parents="1348 14116"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      L(a(x * x,y,L(z,u,w)) \ y,x * x,L(z,u,w)) = K(z,y * (x * x)) * T(K(x * x,z) * y,z)
    ]]></literal>
    <justification jstring="[para(9814(a,1),14117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9814 14117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14120">
    <literal><![CDATA[
      T(K(x,y * (z * z)) * (K(z * z,x) * y),x) = L(a(z * z,y,L(x,u,w)) \ y,z * z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,4541,a,b,14119,a)].">
      <j1 rule="hyper" parents="325 4541 14119"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      L(a(x * x,y,L(z,u,w)) \ y,x * x,L(z,u,w)) = L(y,x * x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14041,a(flip),b,14120,a),flip(a)].">
      <j1 rule="hyper" parents="65 14041 14120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14123">
    <literal><![CDATA[
      L(1 \ x,y * y,L(z,u,w)) = L(x,y * y,z)
    ]]></literal>
    <justification jstring="[para(460(a,1),14122(a,1,1,1))].">
      <j1 rule="para" parents="460 14122"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      L(x,y * y,L(z,u,w)) = L(x,y * y,z)
    ]]></literal>
    <justification jstring="[para(67(a,1),14123(a,1,1))].">
      <j1 rule="para" parents="67 14123"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ (((L(1 / T(x,y),z,u) \ 1) \ T(x,y)) * w)) = L(w,T(L(1 / x,z,u) \ 1,y) \ x,L(1 / T(x,y),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(10780(a,2),13577(a,2,2,1))].">
      <j1 rule="para" parents="10780 13577"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ (((L(1 / T(x,y),z,u) \ 1) \ T(x,y)) * w)) = L(w,T(x,y) \ L(x,z,u),L(1 / T(x,y),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9347(a,1),14126(a,2,2))].">
      <j1 rule="para" parents="9347 14126"/>
    </justification>
  </clause>

  <clause id="14128">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ (((L(1 / T(x,y),z,u) \ 1) \ T(x,y)) * w)) = L(w,T(x,y) \ L(x,z,u),T(L(1 / x,z,u) \ 1,y))
    ]]></literal>
    <justification jstring="[para(10780(a,2),14127(a,2,3))].">
      <j1 rule="para" parents="10780 14127"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      L(x,T(y,z) \ L(y,u,w),L(1 / y,u,w) \ 1) = T(y,v5) * (L(T(y,v5),u,w) \ (((L(1 / T(y,v5),u,w) \ 1) \ T(y,v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(325,a,10938,a(flip),b,14128,a)].">
      <j1 rule="hyper" parents="325 10938 14128"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      L(x,T(y,z) \ L(y,u,w),L(1 / y,u,w)) = T(y,v5) * (L(T(y,v5),u,w) \ (((L(1 / T(y,v5),u,w) \ 1) \ T(y,v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(1625,a,14129,a)].">
      <j1 rule="hyper" parents="1625 14129"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      L(x,T(y,z) \ L(y,u,w),L(y,u,w)) = T(y,v5) * (L(T(y,v5),u,w) \ (((L(1 / T(y,v5),u,w) \ 1) \ T(y,v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,1512,a(flip),b,14130,a)].">
      <j1 rule="hyper" parents="65 1512 14130"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ (((L(1 / T(x,y),z,u) \ 1) \ T(x,y)) * w)) = L(w,x \ L(x,z,u),L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(10890,a,14132,a),flip(a)].">
      <j1 rule="hyper" parents="10890 14132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ ((T(L(1 / x,z,u) \ 1,y) \ T(x,y)) * w)) = L(w,x \ L(x,z,u),L(x,z,u))
    ]]></literal>
    <justification jstring="[para(10780(a,2),14133(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10780 14133"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ ((x \ L(x,z,u)) * w)) = L(w,x \ L(x,z,u),L(x,z,u))
    ]]></literal>
    <justification jstring="[para(10785(a,1),14134(a,1,2,2,1))].">
      <j1 rule="para" parents="10785 14134"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,y,z)) * u)) = L(u,x \ L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,9738,a(flip),b,14135,a)].">
      <j1 rule="hyper" parents="65 9738 14135"/>
    </justification>
  </clause>

  <clause id="14138">
    <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(65,a,8967,a(flip),b,14136,a),flip(a)].">
      <j1 rule="hyper" parents="65 8967 14136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      L(x,(y * z) \ L(y * z,z,y),L(y * z,z,y)) = L(x,y * z,y * (z * (y * z)))
    ]]></literal>
    <justification jstring="[para(100(a,1),14138(a,2,3))].">
      <j1 rule="para" parents="100 14138"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      L(x,a(y,z,y * z) \ 1,L(y * z,z,y)) = L(x,y * z,y * (z * (y * z)))
    ]]></literal>
    <justification jstring="[para(7438(a,1),14139(a,1,2))].">
      <j1 rule="para" parents="7438 14139"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      L(x,a(y,z,y * z) \ 1,z \ y) = L(x,y * z,y * (z * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,12373,a(flip),b,14140,a)].">
      <j1 rule="hyper" parents="65 12373 14140"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      L(L(x \ 1,x,y) \ z,((u * (y / u)) * x) \ (u * (y / u)),(u * (y / u)) * x) = T((((u * (y / u)) * x) * z) / (u * (y / u)),T(y,u))
    ]]></literal>
    <justification jstring="[para(2323(a,1),7406(a,1,1,1))].">
      <j1 rule="para" parents="2323 7406"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      T((((x * (y / x)) * z) * u) / (x * (y / x)),T(y,x)) = L(L(z \ 1,z,y) \ u,(y * z) \ y,(x * (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(11115(a,1),14142(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11115 14142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      L(L(x \ 1,x,y) \ z,(y * x) \ y,(u * (y / u)) * x) = (u * (y / u)) \ (((u * (y / u)) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,7390,a(flip),b,14144,a),flip(a)].">
      <j1 rule="hyper" parents="65 7390 14144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      L(L(x \ 1,x,y) \ z,(y * x) \ y,y * x) = (u * (y / u)) \ (((u * (y / u)) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,2915,a(flip),b,14145,a)].">
      <j1 rule="hyper" parents="65 2915 14145"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      (x * (y / x)) \ (((x * (y / x)) * z) * u) = y \ ((y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,736,a(flip),b,14147,a),flip(a)].">
      <j1 rule="hyper" parents="65 736 14147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (y * (a(z,u,w) * (x * a(a(z,u,w),x,y)))) = y * (a(z,u,w) * R(x * a(a(z,u,w),x,y),y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(12967(a,1),13372(a,1,1))].">
      <j1 rule="para" parents="12967 13372"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (y * (R(a(z,u,w),x,y) * x)) = y * (a(z,u,w) * R(x * a(a(z,u,w),x,y),y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(12886(a,1),14150(a,1,2,2))].">
      <j1 rule="para" parents="12886 14150"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (y * (L(a(z,u,w),x,y) * x)) = y * (a(z,u,w) * R(x * a(a(z,u,w),x,y),y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(13295(a,1),14151(a,1,2,2,1))].">
      <j1 rule="para" parents="13295 14151"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      x * (a(y,z,u) * R(w * a(a(y,z,u),w,x),x,a(y,z,u))) = a(w,x,a(y,z,u)) * ((x * w) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(12473(a,1),14152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12473 14152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14154">
    <literal><![CDATA[
      x * (a(y,z,u) * R(w * a(a(y,z,u),w,x),x,a(y,z,u))) = (x * R(w,x,a(y,z,u))) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,12959,a(flip),b,14153,a),flip(a)].">
      <j1 rule="hyper" parents="325 12959 14153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      x * (a(y,z,u) * R(w * a(a(y,z,u),w,x),x,a(y,z,u))) = (x * L(w,x,a(y,z,u))) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(13374(a,1),14154(a,2,1,2))].">
      <j1 rule="para" parents="13374 14154"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      x * (a(y,z,u) * R(w * a(a(y,z,u),w,x),x,a(y,z,u))) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(325,a,13370,a(flip),b,14155,a),flip(a)].">
      <j1 rule="hyper" parents="325 13370 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      x * (a(y,z,u) * L(w * a(a(y,z,u),w,x),x,a(y,z,u))) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(13374(a,1),14156(a,1,2,2))].">
      <j1 rule="para" parents="13374 14156"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      x * (a(y,z,u) * L(w,a(y,z,u),x)) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(13337(a,1),14157(a,1,2,2))].">
      <j1 rule="para" parents="13337 14157"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(906,a,14158,a(flip))].">
      <j1 rule="hyper" parents="906 14158"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      L(x \ 1,a(y,z,u),w) = L(x,a(y,z,u),w) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12347,a(flip),b,14159,a)].">
      <j1 rule="hyper" parents="65 12347 14159"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ L(x \ R(x,y,z),x,z * y)) * L(u,x \ R(x,y,z),a(x,y,z)) = (1 / (x \ R(x,y,z))) * (R(x \ R(x,y,z),x,z * y) * u)
    ]]></literal>
    <justification jstring="[para(13310(a,1),11136(a,1,1,2))].">
      <j1 rule="para" parents="13310 11136"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ a(x,y,z)) * L(u,x \ R(x,y,z),a(x,y,z)) = (1 / (x \ R(x,y,z))) * (R(x \ R(x,y,z),x,z * y) * u)
    ]]></literal>
    <justification jstring="[para(2326(a,2),14161(a,1,1,2))].">
      <j1 rule="para" parents="2326 14161"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      ((R(x,y,z) \ x) * a(x,y,z)) * L(u,x \ R(x,y,z),a(x,y,z)) = (1 / (x \ R(x,y,z))) * (R(x \ R(x,y,z),x,z * y) * u)
    ]]></literal>
    <justification jstring="[para(7265(a,1),14162(a,1,1))].">
      <j1 rule="para" parents="7265 14162"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * L(u,y \ R(y,x,z),a(y,x,z)) = (1 / (y \ R(y,x,z))) * (R(y \ R(y,x,z),y,z * x) * u)
    ]]></literal>
    <justification jstring="[para(12868(a,1),14163(a,1,1))].">
      <j1 rule="para" parents="12868 14163"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * L(u,y \ L(y,x,z),a(y,x,z)) = (1 / (y \ R(y,x,z))) * (R(y \ R(y,x,z),y,z * x) * u)
    ]]></literal>
    <justification jstring="[para(11436(a,1),14164(a,1,2))].">
      <j1 rule="para" parents="11436 14164"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * L(u,y * L(y,x,z),a(y,x,z)) = (1 / (y \ R(y,x,z))) * (R(y \ R(y,x,z),y,z * x) * u)
    ]]></literal>
    <justification jstring="[para(11009(a,1),14165(a,1,2))].">
      <j1 rule="para" parents="11009 14165"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y \ L(y,w,v5),y \ L(y,w,v5),L(y,z,u))) = a(L(L(y,z,u) * (x \ L(y,z,u)),z,u),y,L(y,w,v5) \ y) * x
    ]]></literal>
    <justification jstring="[para(12808(a,1),13757(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12808 13757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y \ L(y,w,v5),y \ L(y,w,v5),L(y,z,u))) = a(L(L(y,z,u) * (x \ L(y,z,u)),z,u),y,y * L(y,w,v5)) * x
    ]]></literal>
    <justification jstring="[para(7497(a,1),14167(a,2,1))].">
      <j1 rule="para" parents="7497 14167"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y \ L(y,w,v5),y \ L(y,w,v5),L(y,z,u))) = a(a(L(L(y,z,u) * (x \ L(y,z,u)),z,u),y,y),w,v5) * x
    ]]></literal>
    <justification jstring="[para(14064(a,1),14168(a,2,1))].">
      <j1 rule="para" parents="14064 14168"/>
    </justification>
  </clause>

  <clause id="14170">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y \ L(y,w,v5),y \ L(y,w,v5),L(y,z,u))) = a(a(L(y,z,u) * (x \ L(y,z,u)),y,L(y,z,u)),w,v5) * x
    ]]></literal>
    <justification jstring="[para(12660(a,1),14169(a,2,1,1))].">
      <j1 rule="para" parents="12660 14169"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y \ L(y,w,v5),y \ L(y,w,v5),L(y,z,u))) = a(a(x,y,L(y,z,u)),w,v5) * x
    ]]></literal>
    <justification jstring="[para(13234(a,1),14170(a,2,1,1))].">
      <j1 rule="para" parents="13234 14170"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      R(x,L(y,z,u),y \ L(y,w,v5)) = a(a(x,y,L(y,z,u)),w,v5) * x
    ]]></literal>
    <justification jstring="[para(7699(a,1),14171(a,1,3))].">
      <j1 rule="para" parents="7699 14171"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      L(x,L(y,z,u),y * L(y,w,v5)) = a(a(x,y,L(y,z,u)),w,v5) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,13763,a(flip),b,14172,a)].">
      <j1 rule="hyper" parents="65 13763 14172"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      L(x,L(y,z,u),y * L(y,w,v5)) = a(x,y,L(a(v5,w,y),z,u)) * x
    ]]></literal>
    <justification jstring="[para(14073(a,1),14173(a,2,1))].">
      <j1 rule="para" parents="14073 14173"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (((a(x,y,z) * u) / (a(x,y,z) \ 1)) * (w * (a(x,y,z) \ 1))) = L(w,a(x,y,z) \ 1,(a(x,y,z) * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(8479(a,1),7467(a,2,1))].">
      <j1 rule="para" parents="8479 7467"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (((a(x,y,z) * u) / (a(x,y,z) \ 1)) * (w * (a(x,y,z) \ 1))) = L(w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,1487,a(flip),b,14176,a),flip(a)].">
      <j1 rule="hyper" parents="325 1487 14176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (((a(x,y,z) \ 1) \ (a(x,y,z) * u)) * (w * (a(x,y,z) \ 1))) = L(w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(8490(a,1),14177(a,1,2,1))].">
      <j1 rule="para" parents="8490 14177"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (((a(x,y,z) * a(x,y,z)) * u) * (w * (a(x,y,z) \ 1))) = L(w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(7457(a,1),14179(a,1,2,1))].">
      <j1 rule="para" parents="7457 14179"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((a(x,y,z) * a(x,y,z)) * (u * (w * (a(x,y,z) \ 1)))) = L(w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14180(a,1,2))].">
      <j1 rule="para" parents="33 14180"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      (a(x,y,z) * u) \ T(u * (w * a(x,y,z)),a(x,y,z) \ (a(x,y,z) \ 1)) = L(w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(943(a,2),14181(a,1,2))].">
      <j1 rule="para" parents="943 14181"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(8665(a,1),14182(a,1,2))].">
      <j1 rule="para" parents="8665 14182"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,7473,a(flip),b,14183,a),flip(a)].">
      <j1 rule="hyper" parents="65 7473 14183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      L(x,y * z,y * (z * (y * z))) = L(x,a(y,z,y * z),z \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14141,a(flip),b,14184,a)].">
      <j1 rule="hyper" parents="65 14141 14184"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13069,a(flip),b,14184,a)].">
      <j1 rule="hyper" parents="65 13069 14184"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,a(x,y,z),w) = ((a(x,y,z) \ 1) * w) \ (w * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8511,a(flip),b,14184,a),flip(a)].">
      <j1 rule="hyper" parents="65 8511 14184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,z)),w) = L(x,(L(u,z,y) \ u) \ 1,w)
    ]]></literal>
    <justification jstring="[para(13747(a,1),14184(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13747 14184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,13324,a,b,14187,a)].">
      <j1 rule="hyper" parents="325 13324 14187"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(w,u,z),y) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,12111,a(flip),b,14187,a),flip(a)].">
      <j1 rule="hyper" parents="325 12111 14187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      L(x,a(y * z,u,w),v5) = L(x,a(w,u,z * y),v5)
    ]]></literal>
    <justification jstring="[para(2337(a,1),14187(a,1,2))].">
      <j1 rule="para" parents="2337 14187"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w) \ x,x,a(u,z,y)) = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(14187(a,1),12383(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14187 12383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      L(x,a(x,y,z),u) \ x = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14187(a,1),12960(a,1,1))].">
      <j1 rule="para" parents="14187 12960"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = L(x,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13044,a,b,14190,a)].">
      <j1 rule="hyper" parents="65 13044 14190"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      a(x,a(y,z,u),y) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12384,a(flip),b,14194,a)].">
      <j1 rule="hyper" parents="65 12384 14194"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      L(a(a(x,y,z) * (u \ a(x,y,z)),x,a(z,y,x)),w,v5) * u = R(u,a(x,y,z),R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(14194(a,1),13900(a,1,1,1))].">
      <j1 rule="para" parents="14194 13900"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      a(a(x,y,z) * (u \ a(x,y,z)),x,a(z,y,x)) = a(u,a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13128,a(flip),b,14196,a),flip(a)].">
      <j1 rule="hyper" parents="65 13128 14196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = L(x,a(x,z,y),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12396,a,b,14195,a)].">
      <j1 rule="hyper" parents="65 12396 14195"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      L(x,y,z) \ L(x * L(x,y,z),x,y) = L(x,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12392,a,b,14195,a)].">
      <j1 rule="hyper" parents="65 12392 14195"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * a(z,y,L(L(x,y,z),u,w)) = L(L(x,a(L(L(x,y,z),u,w),y,z),y),u,w)
    ]]></literal>
    <justification jstring="[hyper(43,a,930,a,b,14199,a),flip(a)].">
      <j1 rule="hyper" parents="43 930 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      L(x,a(y * z,y,z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,13436,a(flip),b,14192,a),flip(a)].">
      <j1 rule="hyper" parents="325 13436 14192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      L(x,a(y * z,z,z),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,12137,a(flip),b,14192,a),flip(a)].">
      <j1 rule="hyper" parents="325 12137 14192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      L(L(x,a(y,y,z),u) \ x,x,a(y,y,z)) = a(u,a(y * z,y,z),x)
    ]]></literal>
    <justification jstring="[para(14202(a,1),12388(a,1,1,1))].">
      <j1 rule="para" parents="14202 12388"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      a(x,y,L(z,u \ (w * (u * w)),v5)) = a(x,y,L(z,a(w,w,u),v5))
    ]]></literal>
    <justification jstring="[para(14203(a,1),13232(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14203 13232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14206">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,z)),w) = L(x,u \ L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(6998(a,1),14189(a,2,2))].">
      <j1 rule="para" parents="6998 14189"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      L(x,a(L(y,y,z),z,u),w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14187,a,b,14206,a)].">
      <j1 rule="hyper" parents="65 14187 14206"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13753,a(flip),b,14206,a)].">
      <j1 rule="hyper" parents="65 13753 14206"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(13747(a,1),14206(a,1,2))].">
      <j1 rule="para" parents="13747 14206"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x \ L(x,y,z),L(x,y,z)) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8992,a(flip),b,14208,a),flip(a)].">
      <j1 rule="hyper" parents="65 8992 14208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      L(x,L(y,z,u) \ L(L(y,z,u),w,v5),v6) = L(x,L(L(y,w,v5) \ y,z,u),v6)
    ]]></literal>
    <justification jstring="[para(12327(a,1),14209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12327 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(13009(a,1),14207(a,1,2))].">
      <j1 rule="para" parents="13009 14207"/>
    </justification>
  </clause>

  <clause id="14214">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y * R(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13096,a(flip),b,14212,a),flip(a)].">
      <j1 rule="hyper" parents="65 13096 14212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),y) = L(x,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13672,a(flip),b,14200,a)].">
      <j1 rule="hyper" parents="65 13672 14200"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      L(x,a(x,y,z),y) = L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14068,a(flip),b,14215,a),flip(a)].">
      <j1 rule="hyper" parents="65 14068 14215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12846,a(flip),b,14191,a)].">
      <j1 rule="hyper" parents="65 12846 14191"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w) \ x,x,a(u,z,y)) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(325,a,12383,a,b,14217,a),flip(a)].">
      <j1 rule="hyper" parents="325 12383 14217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(w,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,13366,a(flip),b,14217,a),flip(a)].">
      <j1 rule="hyper" parents="325 13366 14217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,v5,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,11782,a(flip),b,14217,a),flip(a)].">
      <j1 rule="hyper" parents="325 11782 14217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = (v5 / x) * L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,14217,a,b,8339,a),flip(a)].">
      <j1 rule="hyper" parents="137 14217 8339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      L(x,y,a(z * u,w,v5)) = L(x,y,a(v5,w,u * z))
    ]]></literal>
    <justification jstring="[para(2337(a,1),14217(a,1,3))].">
      <j1 rule="para" parents="2337 14217"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w * a(x,y,z))) = L(u,w,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(14217(a,1),13357(a,2,1))].">
      <j1 rule="para" parents="14217 13357"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      x * L(x \ y,x,a(x,z,u)) = L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14217(a,1),13404(a,1,2))].">
      <j1 rule="para" parents="14217 13404"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      L(x * y,x,a(x,z,u)) = x * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14217(a,1),13409(a,2,2))].">
      <j1 rule="para" parents="14217 13409"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      a(x,x,y * a(z,u,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12234,a(flip),b,14220,a)].">
      <j1 rule="hyper" parents="65 12234 14220"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      a(x,x,a(y,z,x) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(10136,a,14228,a)].">
      <j1 rule="hyper" parents="10136 14228"/>
    </justification>
  </clause>

  <clause id="14231">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) * y = (x \ y) * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14226(a,1),8381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14226 8381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ ((a(x,y,z) \ x) * u) = L(x * u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13393,a,b,14227,a)].">
      <j1 rule="hyper" parents="325 13393 14227"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      a(x,a(y,z,z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12386,a(flip),b,14193,a)].">
      <j1 rule="hyper" parents="65 12386 14193"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14193,a(flip),b,14218,a)].">
      <j1 rule="hyper" parents="65 14193 14218"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      a(x,a(y * z,u,w),v5) = a(x,a(w,u,z * y),v5)
    ]]></literal>
    <justification jstring="[para(2337(a,1),14234(a,1,2))].">
      <j1 rule="para" parents="2337 14234"/>
    </justification>
  </clause>

  <clause id="14236">
    <literal><![CDATA[
      (x / y) * L(y,z,a(u,w,v5)) = y * (L(y,z,a(v5,w,u)) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13598,a(flip),b,14221,a),flip(a)].">
      <j1 rule="hyper" parents="65 13598 14221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      a(x,y,z) \ ((u / w) * (w * a(x,y,z))) = u * a(w * u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13419,a(flip),b,14225,a),flip(a)].">
      <j1 rule="hyper" parents="325 13419 14225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      ((x \ (a(x,y,z) * x)) * a(x,y,z)) \ ((x \ (a(x,y,z) * x)) * L(a(x,y,z) * x,x,a(x,y,z))) = L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x))
    ]]></literal>
    <justification jstring="[para(14231(a,1),11706(a,1,2))].">
      <j1 rule="para" parents="14231 11706"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ (y * a(w,u,z))) = (a(w,u,z) * (T(y,a(w,u,z)) * x)) / x
    ]]></literal>
    <justification jstring="[hyper(65,a,5243,a(flip),b,14236,a),flip(a)].">
      <j1 rule="hyper" parents="65 5243 14236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      L(x,y * z,y * (z * (y * z))) = L(x,a(z,z,y),z \ y)
    ]]></literal>
    <justification jstring="[hyper(325,a,13436,a(flip),b,14186,a),flip(a)].">
      <j1 rule="hyper" parents="325 13436 14186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      L(x,y * z,y * (z * (y * z))) = L(x,z \ y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,12026,a(flip),b,14240,a),flip(a)].">
      <j1 rule="hyper" parents="325 12026 14240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      L(x,y * z,L(y,z,z) * y) = L(x,z \ y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,2400,a(flip),b,14241,a)].">
      <j1 rule="hyper" parents="65 2400 14241"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      L(x,y * z,y * L(y,z,z)) = L(x,z \ y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(2349,a,14242,a)].">
      <j1 rule="hyper" parents="2349 14242"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,1639,a(flip),b,14243,a),flip(a)].">
      <j1 rule="hyper" parents="65 1639 14243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      L(x,a(y,y,z),y \ z) = L(x,z * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12026,a,b,14244,a)].">
      <j1 rule="hyper" parents="65 12026 14244"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      a(x,y,L(z,(u \ w) * (w * u),v5)) = a(x,y,L(z,a(u,u,w),v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,13621,a(flip),b,14205,a)].">
      <j1 rule="hyper" parents="65 13621 14205"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      a(a(x,y,z) * (u \ a(x,y,z)),x,a(z,y,x)) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,14196,a(flip),b,14198,a),flip(a)].">
      <j1 rule="hyper" parents="325 14196 14198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      a(x,a(y * z,y,z),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12383,a,b,14204,a),flip(a)].">
      <j1 rule="hyper" parents="65 12383 14204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      a(x,a(y,z,y * z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14235,a(flip),b,14248,a)].">
      <j1 rule="hyper" parents="65 14235 14248"/>
    </justification>
  </clause>

  <clause id="14250">
    <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(65,a,13729,a(flip),b,14214,a)].">
      <j1 rule="hyper" parents="65 13729 14214"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      L(L(x,y,y \ L(y,z,u)),(y \ L(y,z,u)) * y,y \ L(y,z,u)) = y \ L(y * x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14250(a,1),9373(a,2,2))].">
      <j1 rule="para" parents="14250 9373"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x,x * L(x,y,z)) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14138,a(flip),b,14210,a)].">
      <j1 rule="hyper" parents="65 14138 14210"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x,a(x,y,z)) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14092,a(flip),b,14252,a)].">
      <j1 rule="hyper" parents="65 14092 14252"/>
    </justification>
  </clause>

  <clause id="14254">
    <literal><![CDATA[
      L(x,L(L(y,z,u) \ y,w,v5),v6) = L(x,L(y \ L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(4458(a,1),14211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4458 14211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),L(x \ L(x,y,z),u,w),v5),u,w) \ v5 = L(L(x,y,z) \ x,u,w) * v5
    ]]></literal>
    <justification jstring="[para(14254(a,1),13898(a,1,1,1))].">
      <j1 rule="para" parents="14254 13898"/>
    </justification>
  </clause>

  <clause id="14256">
    <literal><![CDATA[
      L(a(x,y,a(z,u,y)),w,v5) * x = R(x,a(y,u,z),R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(14247(a,1),14197(a,1,1,1))].">
      <j1 rule="para" parents="14247 14197"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),w,v5)) * x = R(x,a(y,u,z),R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(13823(a,2),14256(a,1,1))].">
      <j1 rule="para" parents="13823 14256"/>
    </justification>
  </clause>

  <clause id="14258">
    <literal><![CDATA[
      R(x,a(y,z,u),R(y,w,v5)) = R(x,y,L(a(u,z,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,13973,a(flip),b,14257,a),flip(a)].">
      <j1 rule="hyper" parents="65 13973 14257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      R(x,a(y,z,u),L(y,w,v5)) = R(x,y,L(a(u,z,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(9925,a,14258,a)].">
      <j1 rule="hyper" parents="9925 14258"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      R(x,y,L(a(z,u,y),w,v5)) = L(x,a(y,u,z),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,13324,a(flip),b,14259,a),flip(a)].">
      <j1 rule="hyper" parents="65 13324 14259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),w,v5)) * x = L(x,a(y,u,z),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,13973,a,b,14260,a)].">
      <j1 rule="hyper" parents="65 13973 14260"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      L(x,L(y,z,u),y * L(y,w,v5)) = L(x,a(y,w,v5),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14175,a,b,14261,a)].">
      <j1 rule="hyper" parents="65 14175 14261"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),x \ L(x,y,z),L(u,w,v5)),w,v5) \ u = L(L(x,y,z) \ x,w,v5) * u
    ]]></literal>
    <justification jstring="[para(12692(a,1),14255(a,1,1,1))].">
      <j1 rule="para" parents="12692 14255"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      L(L(x,a(L(L(x,y,z),y,z),y,z),y),y,z) = L(L(x,y,z),y,z) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(12044(a,1),14201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12044 14201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      L(L(x,a(L(L(x,y,z),y,z),y,z),y),y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(325,a,12550,a(flip),b,14265,a),flip(a)].">
      <j1 rule="hyper" parents="325 12550 14265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      L(L(x,a(x,y,z),y),y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(11872(a,1),14266(a,1,1,2))].">
      <j1 rule="para" parents="11872 14266"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      L(L(x,x,a(y,y,z)),y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(14216(a,1),14267(a,1,1))].">
      <j1 rule="para" parents="14216 14267"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      L(L(x,y,y \ L(y,z,u)),(y \ L(y,z,u)) * y,y \ L(y,z,u)) = L(y \ (y * x),a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,11843,a,b,14251,a),flip(a)].">
      <j1 rule="hyper" parents="325 11843 14251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      L(L(x,y,y \ L(y,z,u)),(y \ L(y,z,u)) * y,y \ L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),14270(a,2,1))].">
      <j1 rule="para" parents="9 14270"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      L(L(x,y,y * L(y,z,u)),(y \ L(y,z,u)) * y,y \ L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(1767(a,1),14271(a,1,1))].">
      <j1 rule="para" parents="1767 14271"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),(y \ L(y,z,u)) * y,y \ L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14092(a,1),14272(a,1,1))].">
      <j1 rule="para" parents="14092 14272"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),L(y,z,u),y \ L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10885,a,14273,a)].">
      <j1 rule="hyper" parents="10885 14273"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),L(y,z,u),y * L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(2366,a,14274,a)].">
      <j1 rule="hyper" parents="2366 14274"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),a(y,z,u),L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14262,a(flip),b,14275,a)].">
      <j1 rule="hyper" parents="65 14262 14275"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y,a(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13832,a(flip),b,14277,a)].">
      <j1 rule="hyper" parents="65 13832 14277"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,13366,a(flip),b,14278,a),flip(a)].">
      <j1 rule="hyper" parents="65 13366 14278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(10955,a,14279,a),flip(a)].">
      <j1 rule="hyper" parents="10955 14279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14283">
    <literal><![CDATA[
      L(x,a(y,z,u),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,14217,a,b,14279,a)].">
      <j1 rule="hyper" parents="65 14217 14279"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,12631,a(flip),b,14279,a),flip(a)].">
      <j1 rule="hyper" parents="65 12631 14279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,12629,a(flip),b,14279,a),flip(a)].">
      <j1 rule="hyper" parents="65 12629 14279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      x \ (a(y,z,u) \ x) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,12631,a(flip),b,14279,a(flip))].">
      <j1 rule="hyper" parents="132 12631 14279"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,v5 * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14279(a,1),11990(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14279 11990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(14279(a,1),11997(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14279 11997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ v5) * v6) = a(x,y,(v5 * a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(14279(a,1),12027(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14279 12027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(u * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(14279(a,1),12490(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14279 12490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,a(v5,v6,v7)) = L(x,w * a(y,z,u),a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(14279(a,1),12534(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14279 12534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14295">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(14279(a,1),13601(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14279 13601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14279(a,1),13947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14279 13947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,8490,a,b,14280,a)].">
      <j1 rule="hyper" parents="65 8490 14280"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ x) * u) = L(x * u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14232,a(flip),b,14280,a),flip(a)].">
      <j1 rule="hyper" parents="65 14232 14280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      a(x,y,(z \ (a(u,u \ 1,w) * w)) * v5) = a(x,y,(z \ L(w,u \ 1,u)) * v5)
    ]]></literal>
    <justification jstring="[para(14280(a,1),10659(a,1,3,1,2))].">
      <j1 rule="para" parents="14280 10659"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = a(x,y,a(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(12554(a,1),14280(a,1,1))].">
      <j1 rule="para" parents="12554 14280"/>
    </justification>
  </clause>

  <clause id="14303">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = a(w,u,a(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[para(13339(a,1),14280(a,1,1))].">
      <j1 rule="para" parents="13339 14280"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      a(x,y,y * (L(a(z,u,w) \ 1,v5,v6) \ y)) = L(a(x,y,y * (a(z,u,w) * y)),v5,v6)
    ]]></literal>
    <justification jstring="[para(14280(a,1),13719(a,2,1,3,2))].">
      <j1 rule="para" parents="14280 13719"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) = ((a(x,y,z) \ 1) * w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(14280(a,1),14188(a,1,1))].">
      <j1 rule="para" parents="14280 14188"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(132,a,7193,a(flip),b,14284,a)].">
      <j1 rule="hyper" parents="132 7193 14284"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,v5) \ v6)) = L(x,y,z * (v6 * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(14284(a,1),1547(a,1,3,2))].">
      <j1 rule="para" parents="14284 1547"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * (a(x,y,z) \ w)) = a(x,y,z) \ (u * (w * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(14284(a,1),9143(a,1,2,2))].">
      <j1 rule="para" parents="14284 9143"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ v6)) = a(x,y,z * (v6 * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(14284(a,1),10643(a,1,3,2))].">
      <j1 rule="para" parents="14284 10643"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      (R(x,y,z) \ x) * ((R(x,y,z) \ x) * ((a(x,y,z) \ 1) \ u)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,13967,a,b,14286,a)].">
      <j1 rule="hyper" parents="65 13967 14286"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(9015,a,14286,a(flip))].">
      <j1 rule="hyper" parents="9015 14286"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,u,a(x,y,z)) = (a(x,y,z) \ 1) * (u * w)
    ]]></literal>
    <justification jstring="[para(14286(a,1),1502(a,1,1))].">
      <j1 rule="para" parents="14286 1502"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      T((a(x,y,z) \ (u * w)) / ((a(x,y,z) \ 1) * u),u) = ((a(x,y,z) \ 1) * (w * u)) / ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(14286(a,1),1652(a,1,1,1))].">
      <j1 rule="para" parents="14286 1652"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / T((a(x,y,z) \ 1) * u,w) = L(w,u,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(14286(a,1),7413(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14286 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      a(L(L(a(x,y,z),u,w),a(x,y,z),L(v5,u,w)),v5,v6) = L((a(x,y,z) \ 1) * R(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(14286(a,2),13036(a,2,1))].">
      <j1 rule="para" parents="14286 13036"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * (v5 * a(x,y,z)) = v5 * (a(x,y,z) \ L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14288(a,1),9262(a,1,1,1))].">
      <j1 rule="para" parents="14288 9262"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) \ 1 = u \ ((L(z,y,x) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(13747(a,1),14288(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13747 14288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),a(x,y,z),v5) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14319(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14319 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      a(x,y,z) \ R(a(x,y,z),u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14319(a,1),13009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14319 13009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14319(a,1),13747(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14319 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ R((x \ ((x * y) * z)) / z,y,u) = a(y * a(x,y,z),y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13630,a,b,14293,a)].">
      <j1 rule="hyper" parents="65 13630 14293"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      a(x \ (y \ (L(y,z,x) * (x * z))),u,w) = a(z * a(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11942,a,b,14293,a)].">
      <j1 rule="hyper" parents="65 11942 14293"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      (a(a(x,y,a(z,u,w)),v5,v6) \ a(x,y,a(z,u,w))) \ 1 = a(x,y,a(z,u,w)) * a(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,13413,a,b,14302,a)].">
      <j1 rule="hyper" parents="65 13413 14302"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / a(z,u,w) = a(x * y,y,a(z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,13146,a(flip),b,14302,a)].">
      <j1 rule="hyper" parents="65 13146 14302"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      x \ ((L(y,z,u) \ y) \ x) = (L(y,z,u) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(13747(a,1),14331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13747 14331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      x \ ((L(y,z,u) \ y) \ x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,6998,a(flip),b,14348,a),flip(a)].">
      <j1 rule="hyper" parents="325 6998 14348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(137,a,6998,a(flip),b,14348,a),flip(a)].">
      <j1 rule="hyper" parents="137 6998 14348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = x * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(201,a,14349,a(flip),b,9340,a)].">
      <j1 rule="hyper" parents="201 14349 9340"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      L(x \ L(x,y,z),x \ L(x,y,z),u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14349(a,1),12335(a,1,1))].">
      <j1 rule="para" parents="14349 12335"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) = x * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,7819,a,b,14351,a)].">
      <j1 rule="hyper" parents="65 7819 14351"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      L(x \ (y * (x \ L(x,z,u))),x,a(x,z,u)) = ((L(x,z,u) \ x) * x) \ y
    ]]></literal>
    <justification jstring="[para(14351(a,1),14102(a,1,1,2))].">
      <j1 rule="para" parents="14351 14102"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      L(x * (y \ L(y,z,u)),y,a(y,z,u)) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(14351(a,1),14253(a,1,1))].">
      <j1 rule="para" parents="14351 14253"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      (x / y) * (y / (L(y \ x,z,u) \ (y \ x))) = x * ((y \ x) \ L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10597,a,b,14358,a)].">
      <j1 rule="hyper" parents="65 10597 14358"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(x,y,z) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(7208,a,14337,a)].">
      <j1 rule="hyper" parents="7208 14337"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12457,a(flip),b,14341,a)].">
      <j1 rule="hyper" parents="65 12457 14341"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(x,y,z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,13295,a(flip),b,14364,a),flip(a)].">
      <j1 rule="hyper" parents="325 13295 14364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(7208,a,14368,a)].">
      <j1 rule="hyper" parents="7208 14368"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      a(x,y,z) * a(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,13333,a,b,14368,a)].">
      <j1 rule="hyper" parents="137 13333 14368"/>
    </justification>
  </clause>

  <clause id="14375">
    <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(132,a,14368,a(flip),b,1310,a)].">
      <j1 rule="hyper" parents="132 14368 1310"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * a(x,x,y) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12056,a,b,14371,a),flip(a)].">
      <j1 rule="hyper" parents="325 12056 14371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = L(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(13335(a,1),14371(a,1,1))].">
      <j1 rule="para" parents="13335 14371"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(y,y,x) = a(y,y,L(x,u,z))
    ]]></literal>
    <justification jstring="[para(14077(a,1),14376(a,1,1))].">
      <j1 rule="para" parents="14077 14376"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      L(a(x,y,z),u,u * w) \ w = ((a(x,y,z) \ 1) * u) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13439,a(flip),b,14295,a),flip(a)].">
      <j1 rule="hyper" parents="65 13439 14295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * L(a(x,y,z),w,v5)) = a(x,y,z) * (R(a(x,y,z),w,v5) \ u)
    ]]></literal>
    <justification jstring="[para(14296(a,1),13300(a,1,2))].">
      <j1 rule="para" parents="14296 13300"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ v5 = L(L(x,y,z) \ x,u,w) * v5
    ]]></literal>
    <justification jstring="[para(14356(a,1),14264(a,1,1,1))].">
      <j1 rule="para" parents="14356 14264"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(u,w,a(z,y,L(x,x,y))) = L(a(z,y,L(x,x,y)) \ 1,w,u)
    ]]></literal>
    <justification jstring="[para(13747(a,1),14375(a,1,1))].">
      <j1 rule="para" parents="13747 14375"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      a(x,x,L(y * z,y,a(y,u,x))) = a(x,x,(a(y,u,x) \ y) * z)
    ]]></literal>
    <justification jstring="[para(14300(a,1),14229(a,1,3))].">
      <j1 rule="para" parents="14300 14229"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      x / a(y,y,L(z,u,u * (x * a(y,y,z)))) = (x / (u * a(y,y,z))) * u
    ]]></literal>
    <justification jstring="[para(14310(a,1),13713(a,1,2,3))].">
      <j1 rule="para" parents="14310 13713"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      a(x,y,y * (y * a(z,u,(w \ u) * u))) = w \ (L(L(w,u,z) / w,y,x) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13813,a(flip),b,14312,a),flip(a)].">
      <j1 rule="hyper" parents="65 13813 14312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      L(a(x,y,z),u,u * w) \ w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(14286(a,1),14380(a,2,1))].">
      <j1 rule="para" parents="14286 14380"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      a(x,x,(a(y,z,x) \ y) * u) = a(x,x,y * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13520,a(flip),b,14387,a),flip(a)].">
      <j1 rule="hyper" parents="65 13520 14387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      a(x,x,(y * a(y,z,x)) * u) = a(x,x,y * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14292,a(flip),b,14392,a)].">
      <j1 rule="hyper" parents="65 14292 14392"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) = (a(x,y,z) \ w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(14286(a,1),14305(a,2,1))].">
      <j1 rule="para" parents="14286 14305"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (a(x,y,z) \ w)) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),14396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 14396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      (a(x,y,z) \ a(z,y,x)) * u = a(z,y,x) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(137,a,14283,a(flip),b,14397,a)].">
      <j1 rule="hyper" parents="137 14283 14397"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      (a(x,y,z) \ u) * K(w,v5) = u * (a(x,y,z) \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(137,a,7892,a(flip),b,14397,a)].">
      <j1 rule="hyper" parents="137 7892 14397"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,v5)) = x * (a(y,z,u) \ K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,9744,a,b,14399,a)].">
      <j1 rule="hyper" parents="65 9744 14399"/>
    </justification>
  </clause>

  <clause id="14401">
    <literal><![CDATA[
      1 / (1 * (a(x,y,z) \ K(u,w))) = a(x,y,z) * K(w,u)
    ]]></literal>
    <justification jstring="[para(14400(a,1),13316(a,1,2))].">
      <j1 rule="para" parents="14400 13316"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,u,a(x,y,z)) = a(x,y,z) \ (u * w)
    ]]></literal>
    <justification jstring="[hyper(325,a,14286,a(flip),b,14320,a),flip(a)].">
      <j1 rule="hyper" parents="325 14286 14320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(x,y,z) \ (u * w)) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,14286,a(flip),b,14320,a)].">
      <j1 rule="hyper" parents="132 14286 14320"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      (a(x,x,y) \ (y * x)) * L(z,y * x,a(x,x,y)) = (y * x) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,13287,a(flip),b,14402,a),flip(a)].">
      <j1 rule="hyper" parents="325 13287 14402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      a(x \ (L(y,z,x) * (y \ (x * z))),u,w) = a(z * a(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(1246(a,1),14344(a,1,1,2))].">
      <j1 rule="para" parents="1246 14344"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      a(x \ ((x * (y * z)) / z),u,w) = a(y * a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8374(a,1),14405(a,1,1,2))].">
      <j1 rule="para" parents="8374 14405"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      a(x \ (y \ (x * (z * y))),u,w) = a(z * a(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,5118,a(flip),b,14406,a)].">
      <j1 rule="hyper" parents="65 5118 14406"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      a(L(L(x,y,z),z,y),u,w) = a(x * a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11884,a(flip),b,14407,a)].">
      <j1 rule="hyper" parents="65 11884 14407"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      L((x \ y) * (x \ L(x,z,u)),x,a(x,z,u)) = ((L(x,z,u) \ x) * x) \ y
    ]]></literal>
    <justification jstring="[para(7709(a,1),14359(a,1,1))].">
      <j1 rule="para" parents="7709 14359"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      a(x,x,L(y,z,z * (u * a(x,x,y)))) \ u = (u / (z * a(x,x,y))) * z
    ]]></literal>
    <justification jstring="[hyper(7210,a,14388,a)].">
      <j1 rule="hyper" parents="7210 14388"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * x) \ u = L(x,y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14360,a(flip),b,14409,a),flip(a)].">
      <j1 rule="hyper" parents="65 14360 14409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      a(x,x,L(y,z,z * (u * a(x,x,y)))) \ u = z * ((a(x,x,y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,13311,a(flip),b,14410,a),flip(a)].">
      <j1 rule="hyper" parents="325 13311 14410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ 1) \ (u \ w))) * v5) = a(x,y,(z \ L(w,u \ 1,u)) * v5)
    ]]></literal>
    <justification jstring="[para(12380(a,1),14301(a,1,3,1,2))].">
      <j1 rule="para" parents="12380 14301"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w \ 1,w)) * v5) = a(x,y,(z \ (w \ (w \ u))) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10656,a(flip),b,14413,a),flip(a)].">
      <j1 rule="hyper" parents="65 10656 14413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14415">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w \ 1,w)) * v5) = a(x,y,(z \ L(u,w,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,13788,a(flip),b,14414,a),flip(a)].">
      <j1 rule="hyper" parents="325 13788 14414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      a(x,y,(z \ L(u * w,u,u)) * v5) = a(x,y,v5 * (z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13504,a(flip),b,14415,a),flip(a)].">
      <j1 rule="hyper" parents="65 13504 14415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w * v5,v5,v5))) = a(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10755,a(flip),b,14416,a)].">
      <j1 rule="hyper" parents="65 10755 14416"/>
    </justification>
  </clause>

  <clause id="14418">
    <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(65,a,14280,a(flip),b,14311,a),flip(a)].">
      <j1 rule="hyper" parents="65 14280 14311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14419">
    <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(65,a,7303,a,b,14418,a)].">
      <j1 rule="hyper" parents="65 7303 14418"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = u * a(w * u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14237,a(flip),b,14418,a),flip(a)].">
      <j1 rule="hyper" parents="65 14237 14418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * y = a(z,u,w) * (x * (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13357,a(flip),b,14418,a)].">
      <j1 rule="hyper" parents="65 13357 14418"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      (R(x,y,z) \ x) * ((R(x,y,z) \ x) * (a(x,y,z) * u)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(14280(a,1),14317(a,1,2,2))].">
      <j1 rule="para" parents="14280 14317"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / T(a(x,y,z) \ u,w) = L(w,u,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(14286(a,1),14323(a,1,2,1))].">
      <j1 rule="para" parents="14286 14323"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      L(1 / x,a(y,z,u) \ w,a(y,z,u)) \ 1 = L(x,w,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,12568,a(flip),b,14423,a)].">
      <j1 rule="hyper" parents="65 12568 14423"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      L(1 / x,y * a(z,u,w),a(z,u,w)) \ 1 = L(x,y,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(14294(a,1),14424(a,1,1))].">
      <j1 rule="para" parents="14294 14424"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      L(x,y * a(z,u,w),a(z,u,w)) = L(x,y,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(65,a,13365,a(flip),b,14425,a)].">
      <j1 rule="hyper" parents="65 13365 14425"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      L(x,y * a(z,u,w),a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,1499,a(flip),b,14426,a),flip(a)].">
      <j1 rule="hyper" parents="325 1499 14426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(y,z,u)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10884,a,14427,a)].">
      <j1 rule="hyper" parents="10884 14427"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      (x / y) * (y / (L(y \ x,z,u) \ (y \ x))) = x * (y \ (x * L(x \ y,z,u)))
    ]]></literal>
    <justification jstring="[para(1410(a,1),14362(a,2,2))].">
      <j1 rule="para" parents="1410 14362"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      (L(x,y,y) * y) * L(z,x * y,a(y,y,x)) = (x * y) * (a(y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(12956(a,1),14404(a,1,1))].">
      <j1 rule="para" parents="12956 14404"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      (x / y) * (y * ((y \ x) \ L(y \ x,z,u))) = x * (y \ (x * L(x \ y,z,u)))
    ]]></literal>
    <justification jstring="[para(14358(a,1),14429(a,1,2))].">
      <j1 rule="para" parents="14358 14429"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      (x / y) * (x * L(x \ y,z,u)) = x * (y \ (x * L(x \ y,z,u)))
    ]]></literal>
    <justification jstring="[para(1411(a,1),14431(a,1,2))].">
      <j1 rule="para" parents="1411 14431"/>
    </justification>
  </clause>

  <clause id="14433">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(u,w,L(x,y,z) \ x) = L(a(z,y,L(x,x,y)) \ 1,w,u)
    ]]></literal>
    <justification jstring="[para(13747(a,1),14386(a,1,2,3))].">
      <j1 rule="para" parents="13747 14386"/>
    </justification>
  </clause>

  <clause id="14434">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(u,w,x * L(x,y,z)) = L(a(z,y,L(x,x,y)) \ 1,w,u)
    ]]></literal>
    <justification jstring="[para(7497(a,1),14433(a,1,2))].">
      <j1 rule="para" parents="7497 14433"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * (z \ L(z,u,w)) = L(a(w,u,L(z,z,u)) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14351,a(flip),b,14434,a)].">
      <j1 rule="hyper" parents="65 14351 14434"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * (z \ L(z,u,w)) = L((L(z,u,w) \ z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(13747(a,1),14435(a,2,1,1))].">
      <j1 rule="para" parents="13747 14435"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * (z \ L(z,u,w)) = L(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(6998(a,1),14436(a,2,1))].">
      <j1 rule="para" parents="6998 14436"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      a(x,y,y * (L(a(z,u,w) \ 1,v5,v6) \ y)) = L(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(13181(a,1),14304(a,2,1))].">
      <j1 rule="para" parents="13181 14304"/>
    </justification>
  </clause>

  <clause id="14439">
    <literal><![CDATA[
      a(x,y,y * (L(a(z,u,w) \ 1,x,v5) \ y)) = a(L(x,x,v5),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,13908,a,b,14438,a),flip(a)].">
      <j1 rule="hyper" parents="325 13908 14438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      a(x,y,y * (y * L(a(z,u,w),x,v5))) = a(L(x,x,v5),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14296(a,1),14439(a,1,3,2))].">
      <j1 rule="para" parents="14296 14439"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w),y,y),x,v5)) = a(L(x,x,v5),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10119,a,14440,a)].">
      <j1 rule="hyper" parents="10119 14440"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      a(L(x,x,y),z,a(u,w,v5)) = a(x,z,L(a(u,w,v5),x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13180,a(flip),b,14441,a),flip(a)].">
      <j1 rule="hyper" parents="65 13180 14441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      a(x,y * x,L(a(z,u,w),x,y)) = x \ R(x,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13035,a(flip),b,14442,a),flip(a)].">
      <j1 rule="hyper" parents="65 13035 14442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      a(x,x \ y,L(a(z,u,w),x,y)) = x \ R(x,x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13011,a(flip),b,14442,a),flip(a)].">
      <j1 rule="hyper" parents="65 13011 14442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      a(x,y * x,L(a(z,u,w),x,y)) = x \ L(x,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(13374(a,1),14443(a,2,2))].">
      <j1 rule="para" parents="13374 14443"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      a(x,x \ y,L(a(z,u,w),x,y)) = x \ L(x,x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(13374(a,1),14444(a,2,2))].">
      <j1 rule="para" parents="13374 14444"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * L(a(x,y,z),w,v5)) = u * (a(x,y,z) \ L(a(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,8342,a(flip),b,14330,a)].">
      <j1 rule="hyper" parents="65 8342 14330"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(a(x,y,z),w,v5)) = a(x,y,z) * (R(a(x,y,z),w,v5) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14286,a(flip),b,14381,a)].">
      <j1 rule="hyper" parents="65 14286 14381"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      a(x,y,z) * (R(a(x,y,z),u,w) \ v5) = v5 * (a(x,y,z) \ L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14381,a(flip),b,14447,a)].">
      <j1 rule="hyper" parents="65 14381 14447"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      a(x,y,z) * (R(a(x,y,z),u,w) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14368(a,1),14450(a,2,2))].">
      <j1 rule="para" parents="14368 14450"/>
    </justification>
  </clause>

  <clause id="14452">
    <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(65,a,14449,a,b,14451,a)].">
      <j1 rule="hyper" parents="65 14449 14451"/>
    </justification>
  </clause>

  <clause id="14453">
    <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="[para(13295(a,1),14451(a,1,2,1))].">
      <j1 rule="para" parents="13295 14451"/>
    </justification>
  </clause>

  <clause id="14455">
    <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(40,a,10580,a,b,14452,a),flip(a)].">
      <j1 rule="hyper" parents="40 10580 14452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14456">
    <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(1253,a,14453,a),flip(a)].">
      <j1 rule="hyper" parents="1253 14453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14457">
    <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="[para(14453(a,1),13575(a,1,2))].">
      <j1 rule="para" parents="14453 13575"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (L(z,y,x) \ z) = u * a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12418(a,1),14455(a,1,2))].">
      <j1 rule="para" parents="12418 14455"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      (x * a(y,z,a(u,y,z))) * (z \ L(z,y,u)) = a(u,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(136,a,14458,a(flip),b,14355,a)].">
      <j1 rule="hyper" parents="136 14458 14355"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      (x * a(y,R(z,u,w),a(w,y,R(z,u,w)))) * (R(z,u,w) \ (L(z,y,w) * (z \ R(z,u,w)))) = a(w,y,R(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(12468(a,2),14460(a,1,2,2))].">
      <j1 rule="para" parents="12468 14460"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ L(x,y,z)) = a(z,y,x) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12869(a,1),14460(a,1,1))].">
      <j1 rule="para" parents="12869 14460"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      (x * a(y,z,a(z,u,u))) * (u \ L(u,z,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(14079(a,2),14460(a,1,1,2))].">
      <j1 rule="para" parents="14079 14460"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      R(x,y,z) * L(x \ 1,y,z) = a(z,y,x) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,5065,a(flip),b,14462,a)].">
      <j1 rule="hyper" parents="65 5065 14462"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      a(x,y,z) \ a(z,y,x) = z \ L(R(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,12614,a(flip),b,14464,a),flip(a)].">
      <j1 rule="hyper" parents="65 12614 14464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      (x \ L(R(x,y,z),y,z)) * u = a(x,y,z) * (a(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(14465(a,1),14398(a,1,1))].">
      <j1 rule="para" parents="14465 14398"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      (a(x,y,a(y,z,z)) * u) * (z \ L(z,y,x)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(7228,a,14463,a)].">
      <j1 rule="hyper" parents="7228 14463"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * (a(w,u,z) \ v5)) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(14466(a,1),12477(a,1,3))].">
      <j1 rule="para" parents="14466 12477"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * (a(w,u,z) \ v5)) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(14466(a,1),13812(a,1,3))].">
      <j1 rule="para" parents="14466 13812"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) = a(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(7193(a,1),14468(a,1,3,2))].">
      <j1 rule="para" parents="7193 14468"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * (v5 * a(w,u,z))) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,14310,a(flip),b,14469,a)].">
      <j1 rule="hyper" parents="65 14310 14469"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) * a(v5,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2349,a,14471,a)].">
      <j1 rule="hyper" parents="2349 14471"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (a(y,z,x) \ u) = L(a(y,z,x),x,z) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,14087,a,b,14456,a)].">
      <j1 rule="hyper" parents="65 14087 14456"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,a(z,y,x)) = L(a(x,y,z),v5,w) * u
    ]]></literal>
    <justification jstring="[hyper(65,a,12844,a,b,14457,a)].">
      <j1 rule="hyper" parents="65 12844 14457"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (a(y,z,x) \ u) = (L(x,z,y) \ x) \ u
    ]]></literal>
    <justification jstring="[para(12418(a,1),14474(a,2,1))].">
      <j1 rule="para" parents="12418 14474"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      a(x,y,z) \ a(z,z,a(x,y,y)) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,14351,a(flip),b,14477,a),flip(a)].">
      <j1 rule="hyper" parents="36 14351 14477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      L(x / (a(y,z,u) \ 1),a(y,z,u),a(z,u,a(y,z,u))) = (x * a(z,u,a(y,z,u))) / (u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(14478(a,1),14088(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14478 14088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      x \ ((y \ ((y * z) * x)) * R((y \ ((y * z) * x)) \ x,z,u)) = a(z * a(y,z,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(4243,a,14343,a)].">
      <j1 rule="hyper" parents="4243 14343"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      a(x,y,L(a(z,u,(w \ u) * u),y,y)) = w \ (L(L(w,u,z) / w,y,x) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(10117,a,14389,a)].">
      <j1 rule="hyper" parents="10117 14389"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      a(x,y,a(z,u,(L(w,y,y) \ u) * u)) = w \ (L(L(w,u,z) / w,y,x) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[para(13718(a,2),14481(a,1,3))].">
      <j1 rule="para" parents="13718 14481"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      a(x,y,a(z,u,(L(w,y,y) \ u) * u)) = w \ (L(w \ L(w,u,z),y,x) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[para(1752(a,1),14482(a,2,2,1,1))].">
      <j1 rule="para" parents="1752 14482"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      a(x,y,a(z,u,(L(w,y,y) \ u) * u)) = w \ (L(L(w,u,z) \ w,y,x) * L(w,u,z))
    ]]></literal>
    <justification jstring="[para(14384(a,1),14483(a,2,2))].">
      <j1 rule="para" parents="14384 14483"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      x \ (y \ (((y * z) * R((y * z) \ y,z,u)) * x)) = a(z * a(y,z,x),z,u)
    ]]></literal>
    <justification jstring="[para(1814(a,1),14480(a,1,2))].">
      <j1 rule="para" parents="1814 14480"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      x \ (y \ ((y * (z \ R(z,z,u))) * x)) = a(z * a(y,z,x),z,u)
    ]]></literal>
    <justification jstring="[para(1084(a,1),14485(a,1,2,2,1))].">
      <j1 rule="para" parents="1084 14485"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      a(x * a(y,x,z),x,u) = z \ (y \ ((y * a(x,x,u)) * z))
    ]]></literal>
    <justification jstring="[para(11590(a,1),14486(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11590 14486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      x \ (x * (a(y,y,z) * a(u,a(y,y,z),x))) = a(y * a(u,y,x),y,z)
    ]]></literal>
    <justification jstring="[para(11635(a,1),14487(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11635 14487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      a(x,x,y) * a(z,a(x,x,y),u) = a(x * a(z,x,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(332,a,14488,a)].">
      <j1 rule="hyper" parents="332 14488"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      a(x,x,y) * a(z,a(y,x,x),u) = a(x * a(z,x,u),x,y)
    ]]></literal>
    <justification jstring="[para(14233(a,2),14489(a,1,2))].">
      <j1 rule="para" parents="14233 14489"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * R(a(x,y,z),u,w),v5,v6) = a(L(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(14336(a,1),14326(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14336 14326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * L(a(x,y,z),u,w),v5,v6) = a(L(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(13295(a,1),14492(a,1,1,2))].">
      <j1 rule="para" parents="13295 14492"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      L(1 * a(x,y,a(z,u,w)),v5,v6) = a(L(a(z,u,w),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(14455(a,1),14493(a,1,1))].">
      <j1 rule="para" parents="14455 14493"/>
    </justification>
  </clause>

  <clause id="14496">
    <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(7(a,1),14495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 14495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      a(x,y,y * (L(a(z,u,w) \ 1,v5,v6) \ y)) = a(L(a(z,u,w),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,14438,a,b,14496,a)].">
      <j1 rule="hyper" parents="325 14438 14496"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      a(x,y,y * (y * L(a(z,u,w),v5,v6))) = a(L(a(z,u,w),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(14296(a,1),14497(a,1,3,2))].">
      <j1 rule="para" parents="14296 14497"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w),y,y),v5,v6)) = a(L(a(z,u,w),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[hyper(10119,a,14498,a)].">
      <j1 rule="hyper" parents="10119 14498"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = a(v6,v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13180,a(flip),b,14499,a),flip(a)].">
      <j1 rule="hyper" parents="65 13180 14499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      L(a(L(a(x,y,z),u,w),v5,v6) \ 1,v6,v5 * L(a(x,y,z),u,w)) = R(v6,v5,L(a(x,y,z),u,w)) \ v6
    ]]></literal>
    <justification jstring="[para(14500(a,2),13483(a,1,1,1))].">
      <j1 rule="para" parents="14500 13483"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      L(x / (a(y,z,u) \ 1),a(y,z,u),a(z,u,a(y,z,u))) = (x * a(z,u,a(y,z,u))) * (L(u,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,14355,a(flip),b,14479,a),flip(a)].">
      <j1 rule="hyper" parents="325 14355 14479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(y,z,a(x,y,z))) = (u * a(y,z,a(x,y,z))) * (L(z,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(14299(a,1),14503(a,1,1))].">
      <j1 rule="para" parents="14299 14503"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      T((a(x,y,z) \ (u * w)) / (a(x,y,z) \ u),u) = ((a(x,y,z) \ 1) * (w * u)) / ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(14286(a,1),14321(a,1,1,2))].">
      <j1 rule="para" parents="14286 14321"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / ((a(x,y,z) \ 1) * w) = (a(x,y,z) \ w) \ (a(x,y,z) \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13266,a(flip),b,14505,a),flip(a)].">
      <j1 rule="hyper" parents="65 13266 14505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / ((a(x,y,z) \ 1) * w) = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14403,a(flip),b,14506,a),flip(a)].">
      <j1 rule="hyper" parents="325 14403 14506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / ((a(x,y,z) \ 1) * w) = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14286(a,1),14507(a,1,1))].">
      <j1 rule="para" parents="14286 14507"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / (a(x,y,z) \ w) = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14286(a,1),14508(a,1,2))].">
      <j1 rule="para" parents="14286 14508"/>
    </justification>
  </clause>

  <clause id="14510">
    <literal><![CDATA[
      ((x * L(y,a(z,u,w),x)) * a(a(z,u,w),x,L(y,a(z,u,w),x))) / (a(z,u,w) \ (T(a(z,u,w),x) * y)) = L(x,T(a(z,u,w),x) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(11641(a,2),14509(a,1,1))].">
      <j1 rule="para" parents="11641 14509"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      (a(x,y,a(z,u,a(w,v5,v6))) * a(z,u,a(w,v5,v6))) \ 1 = a(z,u,a(w,v5,v6)) * a(a(z,u,a(w,v5,v6)),y,x)
    ]]></literal>
    <justification jstring="[para(14303(a,1),14345(a,1,1))].">
      <j1 rule="para" parents="14303 14345"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(a(x,y,a(z,u,w)),v5,v6) = L(a(x,y,a(z,u,w)),v5,v6) \ 1
    ]]></literal>
    <justification jstring="[para(14372(a,1),14511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14372 14511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(a(x,y,a(z,u,w)),v5,v6) = a(L(a(z,u,w),v5,v6),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(14496(a,2),14512(a,2,1))].">
      <j1 rule="para" parents="14496 14512"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) \ 1 = L(a(v6,v5,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14373,a(flip),b,14513,a),flip(a)].">
      <j1 rule="hyper" parents="65 14373 14513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) \ 1 = a(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,14496,a,b,14514,a),flip(a)].">
      <j1 rule="hyper" parents="325 14496 14514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      L(a(L(a(x,y,z),u,w),v5,v6),v6,v5 * L(a(x,y,z),u,w)) = R(v6,v5,L(a(x,y,z),u,w)) \ v6
    ]]></literal>
    <justification jstring="[para(14515(a,1),14502(a,1,1))].">
      <j1 rule="para" parents="14515 14502"/>
    </justification>
  </clause>

  <clause id="14517">
    <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="[hyper(41,a,12854,a(flip),b,14516,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 12854 14516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      L(R(x,y,y),y * y,L(a(z,u,x),y,y)) = R(x,y,y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13965,a(flip),b,14517,a),flip(a)].">
      <j1 rule="hyper" parents="65 13965 14517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      L(R(x,y,y),y * y,a(z,u,x)) = R(x,y,y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14124,a(flip),b,14518,a)].">
      <j1 rule="hyper" parents="65 14124 14518"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      R(x,y,y * a(z,u,x)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(13384,a,14519,a),flip(a)].">
      <j1 rule="hyper" parents="13384 14519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      a(x,y,y * a(z,u,x)) = x \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(14520(a,1),13237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14520 13237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      a(x,y,y * a(z,u,x)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1896,a(flip),b,14523,a),flip(a)].">
      <j1 rule="hyper" parents="325 1896 14523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      a(x,y,L(L(y,x,z),z,x)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,13081,a,b,14524,a)].">
      <j1 rule="hyper" parents="65 13081 14524"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      (x * a(y,R(z,u,w),a(w,y,L(z,u,w)))) * (R(z,u,w) \ (L(z,y,w) * (z \ R(z,u,w)))) = a(w,y,R(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(10407(a,1),14461(a,1,1,2,3))].">
      <j1 rule="para" parents="10407 14461"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      (x * a(y,L(z,u,w),a(w,y,L(z,u,w)))) * (R(z,u,w) \ (L(z,y,w) * (z \ R(z,u,w)))) = a(w,y,R(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(10526(a,1),14527(a,1,1,2))].">
      <j1 rule="para" parents="10526 14527"/>
    </justification>
  </clause>

  <clause id="14529">
    <literal><![CDATA[
      (x * a(y,z,a(z,u,u))) * (R(u,w,y) \ (L(u,z,y) * (u \ R(u,w,y)))) = a(y,z,R(u,w,y)) \ x
    ]]></literal>
    <justification jstring="[para(14085(a,1),14528(a,1,1,2))].">
      <j1 rule="para" parents="14085 14528"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      (x * a(y,z,a(z,u,u))) * (R(u,w,y) \ L(R(u,w,y),z,y)) = a(y,z,R(u,w,y)) \ x
    ]]></literal>
    <justification jstring="[para(12468(a,1),14529(a,1,2,2))].">
      <j1 rule="para" parents="12468 14529"/>
    </justification>
  </clause>

  <clause id="14532">
    <literal><![CDATA[
      (x * a(y,z,a(z,u,u))) * L(u \ L(u,z,y),w,y) = a(y,z,R(u,w,y)) \ x
    ]]></literal>
    <justification jstring="[para(12571(a,1),14530(a,1,2))].">
      <j1 rule="para" parents="12571 14530"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      a(x,y,R(z,u,x)) \ w = (w * a(x,y,a(y,z,z))) * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[para(11859(a,1),14532(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11859 14532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) \ w = (w * a(x,y,a(y,z,z))) * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[para(10407(a,1),14533(a,1,1))].">
      <j1 rule="para" parents="10407 14533"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,14467,a(flip),b,14534,a),flip(a)].">
      <j1 rule="hyper" parents="41 14467 14534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10508,a,14537,a)].">
      <j1 rule="hyper" parents="10508 14537"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      a(x,y,L(y,x,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14526,a(flip),b,14537,a),flip(a)].">
      <j1 rule="hyper" parents="65 14526 14537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      a(x,y,(z * x) \ u) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12050,a(flip),b,14537,a),flip(a)].">
      <j1 rule="hyper" parents="65 12050 14537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      a(x,y,x \ z) = a(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11997,a(flip),b,14537,a)].">
      <j1 rule="hyper" parents="65 11997 14537"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      a(x,y,z * a(x,z,u)) = a(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11797,a(flip),b,14537,a),flip(a)].">
      <j1 rule="hyper" parents="65 11797 14537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      a(x,y,z \ x) = a(x,y,z * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11700,a(flip),b,14537,a)].">
      <j1 rule="hyper" parents="65 11700 14537"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      a(x,y,(x \ z) \ u) = a(x,y,z \ (x * u))
    ]]></literal>
    <justification jstring="[para(469(a,1),14537(a,1,3)),flip(a)].">
      <j1 rule="para" parents="469 14537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      a(x,y,L((x * z) \ u,w,v5)) = a(x,y,L(z \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(525(a,1),14537(a,1,3))].">
      <j1 rule="para" parents="525 14537"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      R(x,y,y) * (x \ z) = a(x,y,y) * z
    ]]></literal>
    <justification jstring="[para(14541(a,1),12702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14541 12702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      a(x * y,z,(y * x) \ u) = a(x * y,z,(x * y) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10059,a,b,14546,a)].">
      <j1 rule="hyper" parents="65 10059 14546"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      a(x,y,y) * (R(x,y,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,957,a(flip),b,14557,a),flip(a)].">
      <j1 rule="hyper" parents="65 957 14557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14561">
    <literal><![CDATA[
      x * (a(x,y,y) * z) = R(x,y,y) * z
    ]]></literal>
    <justification jstring="[hyper(137,a,14557,a(flip),b,958,a)].">
      <j1 rule="hyper" parents="137 14557 958"/>
    </justification>
  </clause>

  <clause id="14562">
    <literal><![CDATA[
      a(x,y,((z \ u) * L(z,w,w)) * v5) = a(x,y,v5 * (a(z,w,w) * u))
    ]]></literal>
    <justification jstring="[para(14557(a,1),11372(a,2,3,2))].">
      <j1 rule="para" parents="14557 11372"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      R(x,y,y) * (a(x,y,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(137,a,77,a(flip),b,14560,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 77 14560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      a(x,a(y,z,z) * (L(y,z,z) \ u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(14560(a,1),13876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14560 13876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      R(x,y,y) * (L(y,y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(12675(a,1),14561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12675 14561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(65,a,12773,a,b,14566,a)].">
      <j1 rule="hyper" parents="65 12773 14566"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      x * (L(x,y,y) \ z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(331,a,14569,a),flip(a)].">
      <j1 rule="hyper" parents="331 14569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,13583,a,b,14569,a)].">
      <j1 rule="hyper" parents="37 13583 14569"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      ((x * y) * z) \ (((1 / x) \ y) * z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14114,a,b,14572,a)].">
      <j1 rule="hyper" parents="65 14114 14572"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      a(x,x,(y * (z * u)) \ (y * z)) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10756,a(flip),b,14572,a)].">
      <j1 rule="hyper" parents="65 10756 14572"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,14572,a(flip),b,14378,a),flip(a)].">
      <j1 rule="hyper" parents="133 14572 14378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      (x / y) * L(y,z,z) = a(z,z,y) \ x
    ]]></literal>
    <justification jstring="[para(14572(a,1),12750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14572 12750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      a(x,y,a(y,x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,14576,a)].">
      <j1 rule="hyper" parents="65 12836 14576"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,14083,a(flip),b,14576,a)].">
      <j1 rule="hyper" parents="65 14083 14576"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,14082,a(flip),b,14576,a)].">
      <j1 rule="hyper" parents="65 14082 14576"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,14078,a(flip),b,14576,a)].">
      <j1 rule="hyper" parents="65 14078 14576"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,z,u))) = x
    ]]></literal>
    <justification jstring="[para(14576(a,2),217(a,1,3))].">
      <j1 rule="para" parents="14576 217"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      x * a(y,z,a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,14578,a,b,69,a)].">
      <j1 rule="hyper" parents="137 14578 69"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(u,u,a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,14576,a,b,14579,a)].">
      <j1 rule="hyper" parents="325 14576 14579"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * u = u
    ]]></literal>
    <justification jstring="[hyper(136,a,14579,a,b,79,a)].">
      <j1 rule="hyper" parents="136 14579 79"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,w))) = x
    ]]></literal>
    <justification jstring="[para(14579(a,2),217(a,1,3))].">
      <j1 rule="para" parents="14579 217"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      L(a(x,x,y),z,z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,14580,a)].">
      <j1 rule="hyper" parents="54 14580"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      a(x,a(y,z,y * z) * u,a(w,w,a(z,z,y) * u)) = 1
    ]]></literal>
    <justification jstring="[para(10754(a,1),14581(a,1,3))].">
      <j1 rule="para" parents="10754 14581"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13798,a(flip),b,14584,a),flip(a)].">
      <j1 rule="hyper" parents="65 13798 14584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(65,a,13065,a(flip),b,14584,a),flip(a)].">
      <j1 rule="hyper" parents="65 13065 14584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(137,a,14584,a(flip),b,13065,a(flip))].">
      <j1 rule="hyper" parents="137 14584 13065"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,14584,a(flip),b,13798,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 14584 13798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,14086,a(flip),b,14586,a)].">
      <j1 rule="hyper" parents="65 14086 14586"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(41,a,14477,a(flip),b,14586,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 14477 14586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      x \ (x * L(y,y,L(z,u,u))) = L(y,y,z)
    ]]></literal>
    <justification jstring="[para(14586(a,1),13604(a,1,1))].">
      <j1 rule="para" parents="14586 13604"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(14597(a,1),52(a,2))].">
      <j1 rule="para" parents="14597 52"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      a(x,x,y) * (z * y) = z * (y * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(14597(a,1),13382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14597 13382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,7190,a,b,14593,a),flip(a)].">
      <j1 rule="hyper" parents="325 7190 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13374,a(flip),b,14593,a),flip(a)].">
      <j1 rule="hyper" parents="65 13374 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,u)) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,1404,a,b,14593,a(flip))].">
      <j1 rule="hyper" parents="36 1404 14593"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      a(x * (y \ x),x,z) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,13121,a(flip),b,14593,a(flip))].">
      <j1 rule="hyper" parents="36 13121 14593"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      a((x \ y) * y,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,13118,a(flip),b,14593,a(flip))].">
      <j1 rule="hyper" parents="36 13118 14593"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      R(x,y,z) \ x = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(14593(a,2),14308(a,1,1))].">
      <j1 rule="para" parents="14593 14308"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      a(x,x,R(y,z,x) * u) = a(x,x,y * u)
    ]]></literal>
    <justification jstring="[para(14593(a,2),14394(a,1,3,1))].">
      <j1 rule="para" parents="14593 14394"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,14269,a,b,14594,a)].">
      <j1 rule="hyper" parents="43 14269 14594"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      a(x,y,z \ y) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(41,a,13693,a,b,14594,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 13693 14594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ w) * v5,v6) \ v6 = L(v6,(R(y,z,u) \ w) * v5,x)
    ]]></literal>
    <justification jstring="[para(13873(a,1),14594(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13873 14594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      (1 / (x * (y * x))) * y = (x * (y * x)) \ y
    ]]></literal>
    <justification jstring="[para(14632(a,1),12280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14632 12280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(37,a,11862,a,b,14595,a),flip(a)].">
      <j1 rule="hyper" parents="37 11862 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      a(x,y,z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(14595(a,1),300(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14595 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      a(x \ y,y,z) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,13136,a(flip),b,14596,a),flip(a)].">
      <j1 rule="hyper" parents="325 13136 14596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,11554,a(flip),b,14596,a)].">
      <j1 rule="hyper" parents="325 11554 14596"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ R(z * u,w,v5)) = a(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(14596(a,2),10384(a,2,3))].">
      <j1 rule="para" parents="14596 10384"/>
    </justification>
  </clause>

  <clause id="14662">
    <literal><![CDATA[
      L(R(x,y,z) * u,x,a(x,y,z)) = x * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14596(a,2),14093(a,2,2,2))].">
      <j1 rule="para" parents="14596 14093"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      a(x,y,(z \ y) * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,13682,a,b,14598,a)].">
      <j1 rule="hyper" parents="325 13682 14598"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(325,a,13364,a(flip),b,14598,a)].">
      <j1 rule="hyper" parents="325 13364 14598"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,12327,a(flip),b,14598,a)].">
      <j1 rule="hyper" parents="325 12327 14598"/>
    </justification>
  </clause>

  <clause id="14670">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = x * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(137,a,14598,a,b,4169,a),flip(a)].">
      <j1 rule="hyper" parents="137 14598 4169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      (x \ 1) * a(y,z,x) = L(x,z,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(137,a,14598,a,b,1527,a)].">
      <j1 rule="hyper" parents="137 14598 1527"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      a(L(L(x,y,z),z,y),u,w) = L(w,u,x * a(y,x,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(65,a,14408,a,b,14598,a)].">
      <j1 rule="hyper" parents="65 14408 14598"/>
    </justification>
  </clause>

  <clause id="14677">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(14598(a,2),1570(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14598 1570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(14598(a,2),7491(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14598 7491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(14598(a,2),7497(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14598 7497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x,u,w)) = L(x,u,w) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(14598(a,2),9028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14598 9028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      a(x,y * a(z,u,y),a(w,v5,v6)) = a(x,L(y,u,z),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(14598(a,2),12219(a,1,2,2))].">
      <j1 rule="para" parents="14598 12219"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      x \ (y * (x * a(z,x,y))) = T(a(z,x,y) * y,x)
    ]]></literal>
    <justification jstring="[para(14598(a,2),12427(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14598 12427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x,u,z)) = L(x * a(z,y,x),u,z)
    ]]></literal>
    <justification jstring="[para(14598(a,2),13894(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14598 13894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      x * (y \ L(y,z,u)) = a(u,z,y) \ x
    ]]></literal>
    <justification jstring="[para(14598(a,2),14351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14598 14351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x \ u)) = (a(z,y,x) * x) \ u
    ]]></literal>
    <justification jstring="[para(14598(a,2),14411(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14598 14411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      (x * a(y,z,a(u,y,z))) * (L(z,y,u) \ z) = a(u,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,14504,a(flip),b,14582,a)].">
      <j1 rule="hyper" parents="65 14504 14582"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12056,a,b,14590,a)].">
      <j1 rule="hyper" parents="65 12056 14590"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      a(x,x,y) * (z \ 1) = z \ a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,14590,a(flip),b,12455,a)].">
      <j1 rule="hyper" parents="136 14590 12455"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      a(x,x,L(L(y,z,z),u,w)) = a(x,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(10508,a,14697,a)].">
      <j1 rule="hyper" parents="10508 14697"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      a(x,x,L(y \ z,u,w)) = a(x,x,L(z * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12063,a(flip),b,14697,a)].">
      <j1 rule="hyper" parents="65 12063 14697"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      a(x,x,y \ z) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11997,a(flip),b,14697,a)].">
      <j1 rule="hyper" parents="65 11997 14697"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      a(x,x,y \ z) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11996,a(flip),b,14697,a)].">
      <j1 rule="hyper" parents="65 11996 14697"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      (x \ y) * a(y,y,z) = x \ R(y,y,z)
    ]]></literal>
    <justification jstring="[para(14697(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="14697 13552"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,y * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,14598,a(flip),b,14618,a),flip(a)].">
      <j1 rule="hyper" parents="65 14598 14618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(R(x,y,z),u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(14618(a,1),13166(a,1,1,1))].">
      <j1 rule="para" parents="14618 13166"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      x * (R(y,z,u) \ y) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(137,a,14627,a,b,14288,a)].">
      <j1 rule="hyper" parents="137 14627 14288"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(14627(a,2),14286(a,1,1))].">
      <j1 rule="para" parents="14627 14286"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      a(x,y,((z * u) \ (z * w)) * (u \ w)) = a(x,y,a(z,u,u * w))
    ]]></literal>
    <justification jstring="[para(14633(a,1),13639(a,2,3))].">
      <j1 rule="para" parents="14633 13639"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      a(x * y,y,z) \ z = L(z,y,x \ y)
    ]]></literal>
    <justification jstring="[para(14649(a,1),14594(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14649 14594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      a(x,x,(y * (z * u)) * ((y * z) * u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14(a,2),14704(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14 14704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      a(x,x,((y * z) * u) * (y * u)) = a(x,x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10289,a(flip),b,14705,a),flip(a)].">
      <j1 rule="hyper" parents="65 10289 14705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      (x * a(y,y,x)) * z = x * (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(137,a,14570,a(flip),b,13587,a),flip(a)].">
      <j1 rule="hyper" parents="137 14570 13587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      (a(x,x,y) \ z) * y = z * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,14577,a(flip),b,1712,a)].">
      <j1 rule="hyper" parents="136 14577 1712"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      x * (a(y,y,x) \ z) = L(x,y,y) * z
    ]]></literal>
    <justification jstring="[para(14577(a,1),8380(a,1,2))].">
      <j1 rule="para" parents="14577 8380"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      a(x,y,((z \ u) * L(z,w,w)) * v5) = a(x,y,(a(w,w,z) \ u) * v5)
    ]]></literal>
    <justification jstring="[para(14577(a,1),10053(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14577 10053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      a(x,y * z,a(y,y,z)) = a(u,w,a(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14061,a(flip),b,14585,a)].">
      <j1 rule="hyper" parents="325 14061 14585"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      (x * (y \ 1)) * a(z,u,x * (y \ 1)) = L(R(y / x,x,y),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(1009(a,2),14670(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1009 14670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      R(x,y,z * (u * L(1 / w,v5,v6))) = R(x,y,z * (u * (w * a(v6,v5,w))))
    ]]></literal>
    <justification jstring="[para(14670(a,1),8632(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="14670 8632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (L(x,u,z) \ x) = L(L(x,y,z),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(14645(a,1),14671(a,1,2))].">
      <j1 rule="para" parents="14645 14671"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),w,v5) = a(u,z,L(y,w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(4458(a,1),14692(a,1,2))].">
      <j1 rule="para" parents="4458 14692"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      (a(x,x,y) / z) \ 1 = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(132,a,85,a(flip),b,14698,a),flip(a)].">
      <j1 rule="hyper" parents="132 85 14698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) = R(y,y,z) / (x \ R(y,y,z))
    ]]></literal>
    <justification jstring="[para(14707(a,1),13380(a,2,2))].">
      <j1 rule="para" parents="14707 13380"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      L(x,y,y * (z \ y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,14598,a(flip),b,14708,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 14598 14708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      L(x,y,L(z,z,y * x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13912,a,b,14747,a)].">
      <j1 rule="hyper" parents="65 13912 14747"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      a(x,y,L(z * a(u * (w \ u),z,u),u,w)) = a(x,y,L(z,u * (w \ u),u))
    ]]></literal>
    <justification jstring="[para(14747(a,1),11797(a,1,3))].">
      <j1 rule="para" parents="14747 11797"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      a(x,y,(L(z,z,u * w) * u) \ (z \ (u * w))) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(14748(a,1),11483(a,2,3))].">
      <j1 rule="para" parents="14748 11483"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      a(x,y,y) \ K(x * y,y) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13421,a(flip),b,14714,a),flip(a)].">
      <j1 rule="hyper" parents="65 13421 14714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      L(x,y,z \ y) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(14646,a,14717,a),flip(a)].">
      <j1 rule="hyper" parents="14646 14717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      L(x,y,L(z * a(u \ w,z,w),w,u * w)) = L(x,y,L(z,u \ w,w))
    ]]></literal>
    <justification jstring="[para(14756(a,1),11793(a,1,3))].">
      <j1 rule="para" parents="14756 11793"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      a(x,y,L(z * a(u \ w,z,w),w,u * w)) = a(x,y,L(z,u \ w,w))
    ]]></literal>
    <justification jstring="[para(14756(a,1),11797(a,1,3))].">
      <j1 rule="para" parents="14756 11797"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w \ u),u,w * u)) = L(x,y,L(z,w \ u,u))
    ]]></literal>
    <justification jstring="[para(14756(a,1),13477(a,1,3))].">
      <j1 rule="para" parents="14756 13477"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) \ w) * (u * L(v5,u,a(z,z,u) \ w))) = a(x,y,(w * L(u,z,z)) * v5)
    ]]></literal>
    <justification jstring="[para(14722(a,1),12637(a,2,3,1))].">
      <j1 rule="para" parents="14722 12637"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      a(x,x,y) * (z * L(y,x,x)) = z * y
    ]]></literal>
    <justification jstring="[para(14722(a,1),12922(a,1,2))].">
      <j1 rule="para" parents="14722 12922"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      x * (y * (a(y,y,x) \ z)) = L(x,y,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(11659(a,1),14723(a,1,2))].">
      <j1 rule="para" parents="11659 14723"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      L(x,x,L(y,z,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(332,a,14599,a)].">
      <j1 rule="hyper" parents="332 14599"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      L(x,x,y \ z) = L(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,11990,a(flip),b,14763,a)].">
      <j1 rule="hyper" parents="65 11990 14763"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      L(x,x,y * (z \ y)) = L(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(1576,a,14765,a),flip(a)].">
      <j1 rule="hyper" parents="1576 14765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      (x \ y) * L(z,z,y * x) = (x \ y) / (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,14765,a(flip),b,1721,a(flip))].">
      <j1 rule="hyper" parents="137 14765 1721"/>
    </justification>
  </clause>

  <clause id="14770">
    <literal><![CDATA[
      (x * (y * L(z,z,u * w))) / T(x * y,z) = L(L(z,y,x),z,w \ u)
    ]]></literal>
    <justification jstring="[para(14765(a,1),8634(a,1,1,2,2))].">
      <j1 rule="para" parents="14765 8634"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      a(x,x,L(y,z,x) * u) = a(x,x,y * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11359,a(flip),b,14628,a)].">
      <j1 rule="hyper" parents="65 11359 14628"/>
    </justification>
  </clause>

  <clause id="14772">
    <literal><![CDATA[
      a(x,x,(y \ z) / ((y * L(u,w,x)) \ z)) = a(x,x,u * a(y,L(u,w,x),L(u,w,x) * (y \ z)))
    ]]></literal>
    <justification jstring="[para(13195(a,2),14771(a,1,3))].">
      <j1 rule="para" parents="13195 14771"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      ((x * (y * z)) / z) \ (x * y) = a(x,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(14568(a,1),13569(a,1,1,1))].">
      <j1 rule="para" parents="14568 13569"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      R(x,y,L(z * u,a(w,w,u),v5) * (v5 * a(w,w,u))) = R(x,y,v5 * (z * (u * a(w,w,u))))
    ]]></literal>
    <justification jstring="[para(14601(a,1),8692(a,2,3,2))].">
      <j1 rule="para" parents="14601 8692"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      a(x,x,y * (z * R(z \ y,u,w))) = a(x,x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(14616(a,1),14704(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14616 14704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      (1 / (x * (y * x))) * y = x \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(325,a,13664,a(flip),b,14642,a),flip(a)].">
      <j1 rule="hyper" parents="325 13664 14642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = L(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(14596(a,2),14650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14596 14650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      a(L(x,y,z),u,z) = a(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10561,a(flip),b,14782,a),flip(a)].">
      <j1 rule="hyper" parents="325 10561 14782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      a(x \ y,z,y) = a(y * x,z,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12267,a(flip),b,14784,a)].">
      <j1 rule="hyper" parents="65 12267 14784"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      a(x \ y,z,x) = a(x * y,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,1848,a(flip),b,14784,a),flip(a)].">
      <j1 rule="hyper" parents="65 1848 14784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      a((x \ y) \ z,u,x) = a(y \ (x * z),u,x)
    ]]></literal>
    <justification jstring="[para(469(a,1),14784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="469 14784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      a(x * (y \ x),z,x) = a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(1879,a,14791,a),flip(a)].">
      <j1 rule="hyper" parents="1879 14791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,z * x) = a((z * x) * (z * y),u,z * x)
    ]]></literal>
    <justification jstring="[para(102(a,2),14793(a,1,1))].">
      <j1 rule="para" parents="102 14793"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      L(x * a(y * z,x,y),y,z * y) = z \ (((z / y) * x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(14793(a,1),13700(a,1,1,2))].">
      <j1 rule="para" parents="14793 13700"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      a(x * y,y,L(z,z,x)) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13712,a(flip),b,14668,a),flip(a)].">
      <j1 rule="hyper" parents="65 13712 14668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14598(a,2),14668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14598 14668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14782,a,b,14816,a)].">
      <j1 rule="hyper" parents="325 14782 14816"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = a(w,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,14377,a,b,14816,a)].">
      <j1 rule="hyper" parents="325 14377 14816"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) * u) / (y * u) = a(x,y,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,13296,a,b,14816,a)].">
      <j1 rule="hyper" parents="325 13296 14816"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,11782,a(flip),b,14816,a),flip(a)].">
      <j1 rule="hyper" parents="325 11782 14816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * (w * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,14816,a,b,7235,a)].">
      <j1 rule="hyper" parents="136 14816 7235"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12044,a(flip),b,14816,a),flip(a)].">
      <j1 rule="hyper" parents="65 12044 14816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      x * (y * a(z,u,L(w,y,x))) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(14816(a,2),12462(a,1,2,2))].">
      <j1 rule="para" parents="14816 12462"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * a(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[para(14816(a,2),12463(a,2,2))].">
      <j1 rule="para" parents="14816 12463"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,y,y))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14816(a,2),13179(a,1,3))].">
      <j1 rule="para" parents="14816 13179"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      x * a(y,z,L(u,w,w * x)) = (a(y,z,u) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(14816(a,2),13307(a,1,2))].">
      <j1 rule="para" parents="14816 13307"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14816(a,2),14341(a,1,1))].">
      <j1 rule="para" parents="14816 14341"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      a(x,y,L(z,u,u * w)) \ w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(14816(a,2),14391(a,1,1))].">
      <j1 rule="para" parents="14816 14391"/>
    </justification>
  </clause>

  <clause id="14843">
    <literal><![CDATA[
      a(x,y * x,a(z,u,L(w,x,y))) = x \ L(x,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14816(a,2),14445(a,1,3))].">
      <j1 rule="para" parents="14816 14445"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      a(x,x \ y,a(z,u,L(w,x,y))) = x \ L(x,x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14816(a,2),14446(a,1,3))].">
      <j1 rule="para" parents="14816 14446"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,L(z,u,w)) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14816(a,2),14453(a,1,2,1))].">
      <j1 rule="para" parents="14816 14453"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,a(z,y,x)) = a(x,y,L(z,v5,w)) * u
    ]]></literal>
    <justification jstring="[para(14816(a,2),14475(a,2,1))].">
      <j1 rule="para" parents="14816 14475"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14816(a,2),14537(a,1,3))].">
      <j1 rule="para" parents="14816 14537"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      a(x * (y * x),z,u) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(3520,a,14817,a)].">
      <j1 rule="hyper" parents="3520 14817"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(x,z,L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(3519,a,14817,a)].">
      <j1 rule="hyper" parents="3519 14817"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      a((x * y) * x,z,u) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(2364,a,14817,a)].">
      <j1 rule="hyper" parents="2364 14817"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,L(x,y,z) \ 1,L(u,y,z)) = a(x,x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13545,a,b,14817,a)].">
      <j1 rule="hyper" parents="65 13545 14817"/>
    </justification>
  </clause>

  <clause id="14857">
    <literal><![CDATA[
      a(L(x,y,y * z),u,L(w,z,z)) = a(z * ((x * y) * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13225,a(flip),b,14817,a),flip(a)].">
      <j1 rule="hyper" parents="65 13225 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      a(x * y,z,L(u,y,x)) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,12267,a(flip),b,14817,a),flip(a)].">
      <j1 rule="hyper" parents="65 12267 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,x,y)) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11931,a(flip),b,14817,a),flip(a)].">
      <j1 rule="hyper" parents="65 11931 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      a((x * y) \ (y * z),u,w) = a(x \ z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,8573,a(flip),b,14817,a)].">
      <j1 rule="hyper" parents="65 8573 14817"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      a(L(x,y * x,z),u,L(w,x,y)) = a((z * (y * x)) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,1910,a(flip),b,14817,a),flip(a)].">
      <j1 rule="hyper" parents="65 1910 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      a(x \ y,z,L(u,x,x)) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1848,a(flip),b,14817,a),flip(a)].">
      <j1 rule="hyper" parents="65 1848 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ z = L(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(14817(a,1),14594(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14817 14594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      a((x * y) * z,z,L(x,x,y)) = a((x * y) * z,z,x)
    ]]></literal>
    <justification jstring="[hyper(11271,a,14809,a)].">
      <j1 rule="hyper" parents="11271 14809"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      a(x * y,z,L(u,x,y)) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2363,a,14860,a)].">
      <j1 rule="hyper" parents="2363 14860"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      a(x \ y,z,x \ u) = a(x * y,z,x * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11997,a(flip),b,14864,a)].">
      <j1 rule="hyper" parents="65 11997 14864"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      a(x \ y,z,a(u,u,w)) = a(x * y,z,a(u,u,w))
    ]]></literal>
    <justification jstring="[para(14590(a,1),14864(a,1,3))].">
      <j1 rule="para" parents="14590 14864"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      a(x \ y,z,x \ (y \ u)) = a(x * y,z,(y * x) \ u)
    ]]></literal>
    <justification jstring="[para(308(a,1),14869(a,1,3)),flip(a)].">
      <j1 rule="para" parents="308 14869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      L(x,a(y,z,u),y * L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,14283,a(flip),b,14677,a),flip(a)].">
      <j1 rule="hyper" parents="325 14283 14677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13763,a,b,14677,a)].">
      <j1 rule="hyper" parents="65 13763 14677"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      L(x,y * L(y,z,u),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,13731,a,b,14874,a)].">
      <j1 rule="hyper" parents="65 13731 14874"/>
    </justification>
  </clause>

  <clause id="14879">
    <literal><![CDATA[
      (1 / (x \ R(x,y,z))) * (R(x \ R(x,y,z),x,z * y) * u) = a(y,x,a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(14877(a,1),14166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14877 14166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      L(x,y * z,a(y,y,z)) = x * a(u,w,a(v5,u,w))
    ]]></literal>
    <justification jstring="[para(14726(a,1),13993(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14726 13993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      (1 / (x * y)) * (y \ x) = y \ (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13219,a(flip),b,14779,a)].">
      <j1 rule="hyper" parents="65 13219 14779"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      a((x \ y) * y,z,(x \ y) * u) = a(x,z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(1879,a,14870,a),flip(a)].">
      <j1 rule="hyper" parents="1879 14870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      a((x \ y) \ z,u,(x \ y) \ x) = a((x \ y) * z,u,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,10047,a(flip),b,14870,a),flip(a)].">
      <j1 rule="hyper" parents="325 10047 14870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      a(x * y,y,x \ z) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14649,a(flip),b,14870,a)].">
      <j1 rule="hyper" parents="65 14649 14870"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      (x * y) \ (y \ x) = y \ (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13428,a(flip),b,14885,a)].">
      <j1 rule="hyper" parents="65 13428 14885"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      a((x * T(y,z)) * y,y,(x * T(y,z)) * u) = a((x * y) * T(y,z),y,(x * T(y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(1131(a,1),14888(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1131 14888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      a(x * y,y,x \ (L(x,z,u) * (x \ w))) = a(x * y,y,L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(1245(a,1),14888(a,2,3))].">
      <j1 rule="para" parents="1245 14888"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      a(x,x,L(y * (y * z),u,w)) = a(x,x,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10244,a,b,14701,a)].">
      <j1 rule="hyper" parents="65 10244 14701"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      1 / (1 * (x * (y \ (x \ y)))) = a(y,x,x) * K(x,y * x)
    ]]></literal>
    <justification jstring="[para(14753(a,1),14401(a,1,2,2))].">
      <j1 rule="para" parents="14753 14401"/>
    </justification>
  </clause>

  <clause id="14897">
    <literal><![CDATA[
      L(x,y,y) \ ((y * x) * L(z,z,x * (1 / y))) = x \ (((1 / y) \ x) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(14769(a,1),13771(a,2,2))].">
      <j1 rule="para" parents="14769 13771"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,y,y))) = a(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14681,a,b,14834,a),flip(a)].">
      <j1 rule="hyper" parents="325 14681 14834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      a(x,y,a(z,u,y \ w)) = a(x,y,a(z,u,y * w))
    ]]></literal>
    <justification jstring="[para(11997(a,1),14834(a,1,3))].">
      <j1 rule="para" parents="11997 14834"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      a(x,y,a(z,u,(x * w) \ v5)) = a(x,y,a(z,u,w \ (x \ v5)))
    ]]></literal>
    <justification jstring="[para(308(a,1),14847(a,1,3,3))].">
      <j1 rule="para" parents="308 14847"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      a(x,y,a(z,u,(x \ w) \ v5)) = a(x,y,a(z,u,w \ (x * v5)))
    ]]></literal>
    <justification jstring="[para(469(a,1),14847(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="469 14847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      a(x,y,T(a(z,u,w) * w,u) \ v5) = a(x,y,L(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(14689(a,1),12591(a,1,3,1))].">
      <j1 rule="para" parents="14689 12591"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      a(x,L(y,y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11710,a,b,14773,a),flip(a)].">
      <j1 rule="hyper" parents="65 11710 14773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      a(x * (y \ x),L((y \ x) \ 1,(y \ x) \ 1,x * (y \ x)),z) = a(y,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,13174,a(flip),b,14903,a),flip(a)].">
      <j1 rule="hyper" parents="325 13174 14903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      R(x,L(y,y,x),z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,14903,a(flip),b,14596,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 14903 14596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      R(x,L(y,y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,14593,a,b,14905,a),flip(a)].">
      <j1 rule="hyper" parents="325 14593 14905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      R(x,y,L(y,y,x) * z) * z = (x * L(y,y,x)) * (L(y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(14906(a,1),13212(a,1,1))].">
      <j1 rule="para" parents="14906 13212"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      a(x,x,L((y * y) * (z * (z * u)),w,v5)) = a(x,x,L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10100,a,b,14894,a)].">
      <j1 rule="hyper" parents="65 10100 14894"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      a(x,x,L(L(y,y,z),y * z,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11036,a,14575,a)].">
      <j1 rule="hyper" parents="11036 14575"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ L(R(x,y,z),u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(14816(a,2),14709(a,1,1))].">
      <j1 rule="para" parents="14816 14709"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      x \ ((x * y) * a(y,z,u)) = R(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,14593,a,b,14833,a),flip(a)].">
      <j1 rule="hyper" parents="325 14593 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      (x / y) \ (x * a(y,z,u)) = R(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,12519,a,b,14914,a)].">
      <j1 rule="hyper" parents="65 12519 14914"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      a((x * y) * z,z,L(u,x,y)) = a(x \ (y \ z),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14649,a(flip),b,14861,a)].">
      <j1 rule="hyper" parents="65 14649 14861"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      a((x * y) \ z,u,x * y) = a(x \ (y \ z),u,x \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10285,a(flip),b,14861,a)].">
      <j1 rule="hyper" parents="65 10285 14861"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      a((x \ y) \ z,u,(x * ((x \ y) * y)) / y) = a(((x \ y) * x) \ (x * z),u,y)
    ]]></literal>
    <justification jstring="[para(727(a,2),14862(a,2,3)),flip(a)].">
      <j1 rule="para" parents="727 14862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14919">
    <literal><![CDATA[
      a(x,y,a(z,u,(L(w,y,y) \ u) * u)) = a(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[para(14665(a,2),14898(a,1,3))].">
      <j1 rule="para" parents="14665 14898"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,L(w,y,z)) = L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(7208,a,14912,a)].">
      <j1 rule="hyper" parents="7208 14912"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      a(x \ (y \ z),z,x) = a((x * y) * z,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14868,a(flip),b,14916,a),flip(a)].">
      <j1 rule="hyper" parents="65 14868 14916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      a((x * y) * z,z,x) = a(x * (y \ z),z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14793,a(flip),b,14921,a),flip(a)].">
      <j1 rule="hyper" parents="65 14793 14921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      a(x * (y \ z),z,x) = a(z * (x * y),z,x)
    ]]></literal>
    <justification jstring="[hyper(2363,a,14922,a),flip(a)].">
      <j1 rule="hyper" parents="2363 14922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),z,u)) = L(x,y,a(u,z,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(14923(a,1),14217(a,1,3))].">
      <j1 rule="para" parents="14923 14217"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,w \ L(w,v5,z)) = L(R(x,u,w \ L(w,v5,z)),y,z)
    ]]></literal>
    <justification jstring="[para(11859(a,1),14920(a,1,2,3))].">
      <j1 rule="para" parents="11859 14920"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      L(x * a(y,z,x),u,y) = L(x,u,y) * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14684,a(flip),b,14691,a),flip(a)].">
      <j1 rule="hyper" parents="65 14684 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14928">
    <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(14927(a,2),450(a,1,2,2))].">
      <j1 rule="para" parents="14927 450"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      x * L(x \ L(x,y,z),u,w) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14865,a(flip),b,14738,a),flip(a)].">
      <j1 rule="hyper" parents="325 14865 14738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,82,a(flip),b,14745,a),flip(a)].">
      <j1 rule="hyper" parents="325 82 14745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      a(x,y,y) \ (z \ y) = z \ L(y,y,x)
    ]]></literal>
    <justification jstring="[para(14933(a,1),13385(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14933 13385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      a((a(x,y,y) \ 1) \ (z \ y),u,w) = a(z \ L(y,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(14934(a,1),5172(a,2,1))].">
      <j1 rule="para" parents="14934 5172"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      a(x \ y,z,x \ (y \ u)) = a(x * y,z,(x * y) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,14559,a(flip),b,14872,a),flip(a)].">
      <j1 rule="hyper" parents="325 14559 14872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      a((x \ y) * y,z,(x \ y) * u) = a(x,z,y \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14550,a(flip),b,14886,a),flip(a)].">
      <j1 rule="hyper" parents="325 14550 14886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      a((x \ y) \ z,u,x * (y \ x)) = a((x \ y) * z,u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12104,a(flip),b,14887,a)].">
      <j1 rule="hyper" parents="65 12104 14887"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      a(x \ (y \ z),u,x \ y) = a((x * y) * z,u,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14793,a(flip),b,14917,a),flip(a)].">
      <j1 rule="hyper" parents="65 14793 14917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      a(x * y,z,(x * y) * u) = a(x * y,z,x * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14870,a(flip),b,14936,a),flip(a)].">
      <j1 rule="hyper" parents="65 14870 14936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      a((x \ y) * y,y,(x \ y) * z) = a(x,y,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13183,a(flip),b,14937,a),flip(a)].">
      <j1 rule="hyper" parents="325 13183 14937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      a((x * y) * z,u,x * y) = a(x * (y \ z),u,x * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14870,a(flip),b,14939,a),flip(a)].">
      <j1 rule="hyper" parents="65 14870 14939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      a(x,y,(x \ y) * z) = a(x,y,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14619,a(flip),b,14941,a)].">
      <j1 rule="hyper" parents="65 14619 14941"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      a(L(x,y,z),u,L(w,z,y)) = L(w,u,x * a(y,x,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(65,a,14817,a(flip),b,14674,a)].">
      <j1 rule="hyper" parents="65 14817 14674"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      a(x,x,((y / (z / (u * u))) * (z * w)) * ((y * (u * u)) * w)) = a(x,x,a(y / (z / (u * u)),z,w))
    ]]></literal>
    <justification jstring="[para(563(a,1),14718(a,1,3,2,1))].">
      <j1 rule="para" parents="563 14718"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      a(x,x,((y \ T(z,u)) * (y * w)) * (T((y \ z) * y,u) * w)) = a(x,x,a(y \ T(z,u),y,w))
    ]]></literal>
    <justification jstring="[para(5147(a,2),14718(a,1,3,2,1))].">
      <j1 rule="para" parents="5147 14718"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      a(x,x,(y * (z * (z * (y * u)))) * ((y * z) * (z * (y * u)))) = a(x,x,a(y,z,(y \ z) * u))
    ]]></literal>
    <justification jstring="[para(14943(a,2),14718(a,2,3))].">
      <j1 rule="para" parents="14943 14718"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      a(x,y,y) * K(y,x * y) = 1 / (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(7(a,1),14895(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 14895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      a(x,y,y) * K(y,x * y) = (y \ x) \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(325,a,14019,a(flip),b,14948,a),flip(a)].">
      <j1 rule="hyper" parents="325 14019 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      a(x,y,y) * K(y,x * y) = x \ (y * (x * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(325,a,13998,a(flip),b,14949,a),flip(a)].">
      <j1 rule="hyper" parents="325 13998 14949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = L(z,y,x * a(w,x,u)) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,14817,a(flip),b,14944,a)].">
      <j1 rule="hyper" parents="65 14817 14944"/>
    </justification>
  </clause>

  <clause id="14952">
    <literal><![CDATA[
      a(x * a(y,x,z),u,w) = a(x,u,L(L(w,z,y),y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14598,a,b,14951,a)].">
      <j1 rule="hyper" parents="325 14598 14951"/>
    </justification>
  </clause>

  <clause id="14953">
    <literal><![CDATA[
      a(x,y,L((z * x) \ u,w,v5)) = a(x,y,L(z \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(10396,a,14551,a)].">
      <j1 rule="hyper" parents="10396 14551"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x,z)) = a(x,y,x \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12050,a(flip),b,14551,a),flip(a)].">
      <j1 rule="hyper" parents="65 12050 14551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x,z)) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14546,a(flip),b,14954,a),flip(a)].">
      <j1 rule="hyper" parents="325 14546 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      a(x,(y * a(z,u,a(w,z,u))) * (R(u,z,w) \ u),v5) = a(x,a(w,z,u) * y,v5)
    ]]></literal>
    <justification jstring="[para(14696(a,1),13876(a,2,2))].">
      <j1 rule="para" parents="14696 13876"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z) \ 1,L(x,y,z) \ 1,u) = (1 / x) \ R(1 / x,1 / L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14732(a,1),13975(a,1,1))].">
      <j1 rule="para" parents="14732 13975"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      a(x,x,y * (z * L(z \ y,u,w))) = a(x,x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(11370,a,14778,a)].">
      <j1 rule="hyper" parents="11370 14778"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      a(x,y,L(z,y,a(x,u,z))) = a(x,y * a(x,u,z),z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13084,a(flip),b,14820,a),flip(a)].">
      <j1 rule="hyper" parents="65 13084 14820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      a(x,y * a(x,z,u),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14822,a(flip),b,14960,a),flip(a)].">
      <j1 rule="hyper" parents="65 14822 14960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      a(x,a(x,y,z) \ u,z) = a(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(10161,a,14961,a),flip(a)].">
      <j1 rule="hyper" parents="10161 14961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      a(x,(x * y) * z,z) = a(x,x * (y * z),z)
    ]]></literal>
    <justification jstring="[para(89(a,1),14961(a,1,2))].">
      <j1 rule="para" parents="89 14961"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      a(x,x \ (y * z),z) = a(x,(x \ y) * z,z)
    ]]></literal>
    <justification jstring="[para(11640(a,1),14961(a,1,2))].">
      <j1 rule="para" parents="11640 14961"/>
    </justification>
  </clause>

  <clause id="14968">
    <literal><![CDATA[
      a(x,y * (x * z),y) = a(x,x * (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(10160,a,14964,a)].">
      <j1 rule="hyper" parents="10160 14964"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      L(x,a(y,z * (u * y),z),w) = L(x,a(z,y * (z * u),y),w)
    ]]></literal>
    <justification jstring="[para(14968(a,2),14187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14968 14187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14970">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * w) \ v5) = a(x,y,L(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(10144,a,14902,a)].">
      <j1 rule="hyper" parents="10144 14902"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      a(x,x,L(((y * y) * z) * (z * u),w,v5)) = a(x,x,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(33(a,2),14910(a,1,3,1))].">
      <j1 rule="para" parents="33 14910"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),z,w)) = L(x,y,a(w,z,w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(3512(a,1),14924(a,1,3))].">
      <j1 rule="para" parents="3512 14924"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ y),u,w) = a(z \ L(y,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(12715(a,1),14935(a,1,1))].">
      <j1 rule="para" parents="12715 14935"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      a(x,x,L((y * z) \ ((u * u) * y),w,v5)) = a(x,x,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,14703,a,b,14972,a)].">
      <j1 rule="hyper" parents="65 14703 14972"/>
    </justification>
  </clause>

  <clause id="14976">
    <literal><![CDATA[
      L(x,y,a(z,u,u * (w * z))) = L(x,y,a(z,u,z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14217,a,b,14973,a)].">
      <j1 rule="hyper" parents="65 14217 14973"/>
    </justification>
  </clause>

  <clause id="14977">
    <literal><![CDATA[
      a(x,x,(y * z) \ ((z * L(z,u,w)) * y)) = a(x,x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(13960(a,1),14975(a,1,3))].">
      <j1 rule="para" parents="13960 14975"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),y,w)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10397,a,14977,a)].">
      <j1 rule="hyper" parents="10397 14977"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      a(x,x,L(L(y,y,z),u,w)) = a(x,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(10508,a,14978,a)].">
      <j1 rule="hyper" parents="10508 14978"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      a(x,x,L(y,y * z,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14911,a(flip),b,14979,a),flip(a)].">
      <j1 rule="hyper" parents="65 14911 14979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(u,y * z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(14980(a,1),13723(a,1,1))].">
      <j1 rule="para" parents="14980 13723"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      a(x,y * z,a(u,u,y)) = a(x,z,a(u,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,14839,a(flip),b,14982,a),flip(a)].">
      <j1 rule="hyper" parents="65 14839 14982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14984">
    <literal><![CDATA[
      a(x \ y,z,L(u * x,x,u)) = a((u * x) * (u * y),z,u * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14817,a(flip),b,14804,a)].">
      <j1 rule="hyper" parents="65 14817 14804"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      a(x,y,a(z,u,(L(w,y,y) \ u) * u)) = v5 \ (a(x,y,w * L(w,u,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,7207,a,b,14919,a),flip(a)].">
      <j1 rule="hyper" parents="325 7207 14919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      a((x * y) * (x * z),u,x * y) = a(y \ z,u,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,11699,a(flip),b,14984,a),flip(a)].">
      <j1 rule="hyper" parents="65 11699 14984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      a(x * (y \ (x * z)),u,x * y) = a(y \ z,u,y \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14942,a(flip),b,14987,a)].">
      <j1 rule="hyper" parents="65 14942 14987"/>
    </justification>
  </clause>

  <clause id="14989">
    <literal><![CDATA[
      a(x * (y \ (x * z)),u,x * y) = a(y * z,u,y * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,14870,a(flip),b,14988,a),flip(a)].">
      <j1 rule="hyper" parents="325 14870 14988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14990">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * v5,v6) = L(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(14646,a,14638,a),flip(a)].">
      <j1 rule="hyper" parents="14646 14638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      L(x,(L(y \ 1,z,u) \ (y \ 1)) * w,v5) = L(x,(R(y,z,u) \ y) * w,v5)
    ]]></literal>
    <justification jstring="[para(1518(a,2),14990(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1518 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ L(z * u,w,v5)) = a(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,11384,a(flip),b,14658,a)].">
      <j1 rule="hyper" parents="65 11384 14658"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      a(x,y,((z \ u) * L(z,w,w)) * v5) = a(x,y,(u * a(w,w,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,14292,a(flip),b,14724,a),flip(a)].">
      <j1 rule="hyper" parents="325 14292 14724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      a(x * ((y * z) * (z \ x)),u,w) = a(y,u,L(L(w,x,x),z,z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14817,a(flip),b,14857,a),flip(a)].">
      <j1 rule="hyper" parents="65 14817 14857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * y),u,w) = a(z,u,L(L(w,z,y),y * z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14817,a(flip),b,14863,a),flip(a)].">
      <j1 rule="hyper" parents="65 14817 14863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      R(x,y,L(y,y,x) * z) * z = (x / (y \ 1)) * (L(y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(1720(a,1),14907(a,2,1))].">
      <j1 rule="para" parents="1720 14907"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      a(x,y,z * (u * L(u \ z,w,v5))) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(8822(a,1),14992(a,1,3))].">
      <j1 rule="para" parents="8822 14992"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      a(x,x,a(y \ z,u,w)) = a(x,x,a(z * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14959,a(flip),b,14997,a)].">
      <j1 rule="hyper" parents="65 14959 14997"/>
    </justification>
  </clause>

  <clause id="14999">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,w)) * v5) = a(x,y,v5 * (a(w,u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14562,a(flip),b,14993,a),flip(a)].">
      <j1 rule="hyper" parents="65 14562 14993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      a((x * (y * z)) * (x * y),u,x * (y * z)) = a(z,u,L(L(x * (y * z),z,y),y * z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14793,a(flip),b,14995,a)].">
      <j1 rule="hyper" parents="65 14793 14995"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      (x * (y \ 1)) * a(z,u,x * y) = L(R(y / x,x,y),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(7496(a,1),14729(a,1,2))].">
      <j1 rule="para" parents="7496 14729"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      L(x,y,L(z * a(u * w,z,u),u,w * u)) = L(x,y,L(z,w \ u,u))
    ]]></literal>
    <justification jstring="[para(14791(a,1),14757(a,1,3,1,2))].">
      <j1 rule="para" parents="14791 14757"/>
    </justification>
  </clause>

  <clause id="15003">
    <literal><![CDATA[
      a(x,y,L(z * a(u * w,z,u),u,w * u)) = a(x,y,L(z,w \ u,u))
    ]]></literal>
    <justification jstring="[para(14791(a,1),14758(a,1,3,1,2))].">
      <j1 rule="para" parents="14791 14758"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w * u),u,w * u)) = L(x,y,L(z,w \ u,u))
    ]]></literal>
    <justification jstring="[para(14549(a,1),14759(a,1,3,1,2))].">
      <j1 rule="para" parents="14549 14759"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      L(L(x,y,z),x,u \ w) = L(L(x,y,z),x,w * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,8634,a(flip),b,14770,a),flip(a)].">
      <j1 rule="hyper" parents="65 8634 14770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,w * u)) = a(x,y,(w * (u * z)) \ (w * u))
    ]]></literal>
    <justification jstring="[para(15005(a,1),12778(a,1,3))].">
      <j1 rule="para" parents="15005 12778"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((w * L(w,u,z)) * (z * u))) = a(x,y,(z * (u * w)) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(10283,a,15006,a)].">
      <j1 rule="hyper" parents="10283 15006"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      L(x,y,z \ (((z / u) * w) * T(u,w))) = L(x,y,L(w,z \ u,u))
    ]]></literal>
    <justification jstring="[para(14805(a,1),15002(a,1,3))].">
      <j1 rule="para" parents="14805 15002"/>
    </justification>
  </clause>

  <clause id="15009">
    <literal><![CDATA[
      L(x,y,z \ (((z / u) * w) * u)) = L(x,y,L(w,z \ u,u))
    ]]></literal>
    <justification jstring="[hyper(8371,a,15008,a)].">
      <j1 rule="hyper" parents="8371 15008"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      L(x,y,z \ (((u \ z) * w) * u)) = L(x,y,L(w,z \ u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,8394,a(flip),b,15009,a)].">
      <j1 rule="hyper" parents="65 8394 15009"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      L(x,y,L(z,u \ w,w)) = L(x,y,L(z,w \ u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,8569,a(flip),b,15011,a),flip(a)].">
      <j1 rule="hyper" parents="65 8569 15011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      a(x,y,z \ (((z / u) * w) * T(u,w))) = a(x,y,L(w,z \ u,u))
    ]]></literal>
    <justification jstring="[para(14805(a,1),15003(a,1,3))].">
      <j1 rule="para" parents="14805 15003"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      a(x,y,z \ (((z / u) * w) * u)) = a(x,y,L(w,z \ u,u))
    ]]></literal>
    <justification jstring="[hyper(10156,a,15013,a)].">
      <j1 rule="hyper" parents="10156 15013"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      a(x,y,z \ (((u \ z) * w) * u)) = a(x,y,L(w,z \ u,u))
    ]]></literal>
    <justification jstring="[hyper(10281,a,15014,a)].">
      <j1 rule="hyper" parents="10281 15014"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,w)) = a(x,y,L(z,w \ u,w))
    ]]></literal>
    <justification jstring="[hyper(10435,a,15015,a),flip(a)].">
      <j1 rule="hyper" parents="10435 15015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15018">
    <literal><![CDATA[
      L(x,y,L(z,u \ w,w)) = L(x,y,L(z,u * w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13477,a(flip),b,15004,a),flip(a)].">
      <j1 rule="hyper" parents="65 13477 15004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      L(x,y,L(z,u \ w,u)) = L(x,y,L(z,w * u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15012,a(flip),b,15018,a)].">
      <j1 rule="hyper" parents="65 15012 15018"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      R(x,y,z * (u * (w * a(v5,v6,w)))) = R(x,y,z * (u * L(w,v6,v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,12173,a(flip),b,14730,a),flip(a)].">
      <j1 rule="hyper" parents="65 12173 14730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ 1,L(u,y,z)) = a(x,x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(1886,a,14854,a)].">
      <j1 rule="hyper" parents="1886 14854"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      a(x * y,y,L(x,z,u) * (x \ (x \ w))) = a(x * y,y,L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(1246(a,1),14892(a,1,3))].">
      <j1 rule="para" parents="1246 14892"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      L(R(x,y,z \ L(z,u,w)),v5,w) = L(x,v5,w) * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(14680(a,1),14926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14680 14926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,a(z,w,v5)) = L(L(x,u,a(z,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(14875(a,1),15023(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14875 15023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      L(x,(L(y \ 1,z,u) \ (y \ 1)) * w,v5) = L(x,a(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(14714(a,1),14991(a,2,2))].">
      <j1 rule="para" parents="14714 14991"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      L(x,a(y,z,u \ 1) * w,v5) = L(x,a(u,z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(14598(a,2),15025(a,1,2,1))].">
      <j1 rule="para" parents="14598 15025"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,v5) = L(x,a(u,z,y) * w,v5)
    ]]></literal>
    <justification jstring="[para(7484(a,1),15026(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7484 15026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      L(x,a(y,z,u) * (a(u,z,y) * w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(10899,a,15027,a),flip(a)].">
      <j1 rule="hyper" parents="10899 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      L(x,a(y,y,z) * (L(y,y,z) \ u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(12677(a,1),15027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12677 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      a(x * y,y,(a(z,u,x) * x) \ w) = a(x * y,y,L(x,u,z) * w)
    ]]></literal>
    <justification jstring="[para(14694(a,1),15022(a,1,3))].">
      <j1 rule="para" parents="14694 15022"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      a(x * y,y,L(x,z,u) \ w) = a(x * y,y,L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14970,a(flip),b,15030,a)].">
      <j1 rule="hyper" parents="65 14970 15030"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,w),w,u)) = a(x,y,L(z,w * (u \ w),w))
    ]]></literal>
    <justification jstring="[para(14803(a,1),14749(a,1,3,1,2))].">
      <j1 rule="para" parents="14803 14749"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      a(x,y,L(z,u * (w \ u),u)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11797,a(flip),b,15032,a),flip(a)].">
      <j1 rule="hyper" parents="65 11797 15032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      a(x,y,L(z,u / w,u)) = a(x,y,L(z,u * w,u))
    ]]></literal>
    <justification jstring="[para(85(a,1),15033(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="85 15033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      a(x,x,L(y,(z * u) * (u \ (z * u)),z * u)) \ u = (z / u) \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(15033(a,2),13447(a,1,1))].">
      <j1 rule="para" parents="15033 13447"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,w)) = a(x,y,L(z,w * u,w))
    ]]></literal>
    <justification jstring="[para(10814(a,1),15034(a,1,3))].">
      <j1 rule="para" parents="10814 15034"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,u)) = a(x,y,L(z,u * w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15017,a(flip),b,15036,a)].">
      <j1 rule="hyper" parents="65 15017 15036"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,L(z,u * w,u)) \ v5) = v5 * a(u,w \ u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(15036(a,1),14845(a,1,2,1))].">
      <j1 rule="para" parents="15036 14845"/>
    </justification>
  </clause>

  <clause id="15039">
    <literal><![CDATA[
      a(x,y,L(z \ u,w * z,w)) = a(x,y,(w \ z) \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12051,a(flip),b,15037,a),flip(a)].">
      <j1 rule="hyper" parents="65 12051 15037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      (x * K(x \ y,x)) \ (a(z,z,u) \ y) = a(z,z,L(u,x * y,x)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(15037(a,1),13708(a,2,1))].">
      <j1 rule="para" parents="15037 13708"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,(z / (u \ 1)) * (z * u),z / (u \ 1))) = a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[para(11733(a,1),15039(a,2,3,1))].">
      <j1 rule="para" parents="11733 15039"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * L(x,y,z) = a(w,u,x * L(x,y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(40,a,14484,a(flip),b,14986,a(flip))].">
      <j1 rule="hyper" parents="40 14484 14986"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = a(w,u,x * L(x,y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,8343,a(flip),b,15042,a)].">
      <j1 rule="hyper" parents="65 8343 15042"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = x * a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7190,a(flip),b,15043,a),flip(a)].">
      <j1 rule="hyper" parents="325 7190 15043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      T(x * a(y,z,x * L(x,u,w)),L(x,u,w)) = L(x,z,y) * (L(L(x,z,y),u,w) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(15044(a,1),12333(a,1,1))].">
      <j1 rule="para" parents="15044 12333"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w))) = (L(x,y,z) / x) * (x * a(w,u,x * L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(15044(a,1),14432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15044 14432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      x * a(y,z \ y,a(u,w,v5)) = x * a(y,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,14845,a(flip),b,15038,a),flip(a)].">
      <j1 rule="hyper" parents="65 14845 15038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      L(x,y,y) \ ((y * x) * L(z,z,y * x)) = x \ (((1 / y) \ x) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2331(a,1),14897(a,1,2,2))].">
      <j1 rule="para" parents="2331 14897"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      L(x,y,y) \ ((y * x) / (z \ 1)) = x \ (((1 / y) \ x) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1720(a,1),15048(a,1,2))].">
      <j1 rule="para" parents="1720 15048"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      a(L(x,y,y) \ (z \ (y * x)),u,w) = a(x \ (((1 / y) \ x) / (z \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(15049(a,1),11081(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15049 11081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      a(L(x,y,y) \ (z \ (y * x)),u,w) = a(x \ ((z \ 1) \ ((1 / y) \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,5118,a(flip),b,15050,a),flip(a)].">
      <j1 rule="hyper" parents="325 5118 15050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      a(L(x,y,y) \ (z \ (y * x)),u,w) = a(x \ ((z \ 1) \ ((y \ 1) \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11457,a(flip),b,15051,a),flip(a)].">
      <j1 rule="hyper" parents="325 11457 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      a(L(x,y,y) \ (z \ (y * x)),u,w) = a(x \ ((z \ 1) \ (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11236,a(flip),b,15052,a),flip(a)].">
      <j1 rule="hyper" parents="325 11236 15052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      a(L(x,y,y) \ (z \ (y * x)),u,w) = a(x \ (z \ (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11080,a(flip),b,15053,a),flip(a)].">
      <j1 rule="hyper" parents="325 11080 15053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      a((x \ y) \ z,u,(x * ((x \ y) * y)) / y) = a(y \ (x * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,6256,a(flip),b,14918,a),flip(a)].">
      <j1 rule="hyper" parents="325 6256 14918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      a((x \ y) \ z,u,(x * ((x \ y) * y)) / y) = a(y * (x * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,14793,a(flip),b,15055,a),flip(a)].">
      <j1 rule="hyper" parents="325 14793 15055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(y,x \ y,x)) = a(y * (x * z),u,y)
    ]]></literal>
    <justification jstring="[para(727(a,1),15057(a,1,3))].">
      <j1 rule="para" parents="727 15057"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      a((x \ y) \ z,u,x * (y \ x)) = a(y * (x * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12103,a(flip),b,15058,a)].">
      <j1 rule="hyper" parents="65 12103 15058"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      a((x \ y) \ z,u,(y \ x) * x) = a(y * (x * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(10136,a,15059,a)].">
      <j1 rule="hyper" parents="10136 15059"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      a((x \ y) * z,u,y) = a(y * (x * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14938,a(flip),b,15059,a)].">
      <j1 rule="hyper" parents="65 14938 15059"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      a(x * (y * (a(z,u,z) * w)),v5,x) = a(w * (y \ x),v5,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,6895,a(flip),b,15061,a),flip(a)].">
      <j1 rule="hyper" parents="65 6895 15061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      a((K(x * y,y) \ a(x,y,y)) \ z,u,(y * (x \ (y \ x))) * K(x * y,y)) = a(a(x,y,y) * (K(x * y,y) * z),u,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(14753(a,1),15060(a,1,3,1))].">
      <j1 rule="para" parents="14753 15060"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      a((x * y) * z,u,z) = a(x * (y \ z),u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6901,a(flip),b,15062,a)].">
      <j1 rule="hyper" parents="65 6901 15062"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      a(x * (a(y,z,y) * (u * w)),v5,x) = a(w * (u \ x),v5,x)
    ]]></literal>
    <justification jstring="[para(7599(a,2),15062(a,1,1,2))].">
      <j1 rule="para" parents="7599 15062"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      a((x * y) * z,u,z) = a(y * (x \ z),u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,6895,a(flip),b,15065,a)].">
      <j1 rule="hyper" parents="65 6895 15065"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      a(x * (y \ z),u,z) = a(y * (x \ z),u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15064,a(flip),b,15066,a)].">
      <j1 rule="hyper" parents="65 15064 15066"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      L(x,y,a(z * (u \ w),v5,w)) = L(x,y,a(w,v5,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(15067(a,1),14217(a,1,3))].">
      <j1 rule="para" parents="15067 14217"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      a(x,x,L(y,(z * u) * T(z,u),z * u)) \ u = (z / u) \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(22(a,2),15035(a,1,1,3,2,2))].">
      <j1 rule="para" parents="22 15035"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      a(x,x,L(y,(z * u) * z,z * u)) \ u = (z / u) \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(10811(a,1),15069(a,1,1,3))].">
      <j1 rule="para" parents="10811 15069"/>
    </justification>
  </clause>

  <clause id="15072">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (R(x \ R(x,y,z),x,z * y) * u) = a(y,x,a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(5796(a,1),14879(a,1,1))].">
      <j1 rule="para" parents="5796 14879"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (L(x \ R(x,y,z),x,z * y) * u) = a(y,x,a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(13310(a,1),15072(a,1,2,1))].">
      <j1 rule="para" parents="13310 15072"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (a(x,y,z) * u) = a(y,x,a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(2326(a,2),15073(a,1,2,1))].">
      <j1 rule="para" parents="2326 15073"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (a(y,x,a(z,y,x)) * u) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(15074(a,1),14422(a,1,2))].">
      <j1 rule="para" parents="15074 14422"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      (a(x,y,a(z,x,y)) * u) * (R(y,x,z) \ y) = a(y,x,z) \ u
    ]]></literal>
    <justification jstring="[hyper(10767,a,15075,a)].">
      <j1 rule="hyper" parents="10767 15075"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      (x * a(y,z,a(u,y,z))) * (R(z,y,u) \ z) = a(z,y,u) \ x
    ]]></literal>
    <justification jstring="[hyper(7212,a,15076,a)].">
      <j1 rule="hyper" parents="7212 15076"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,v5) = a(x,a(u,z,y) * w,v5)
    ]]></literal>
    <justification jstring="[para(15077(a,1),14957(a,1,2))].">
      <j1 rule="para" parents="15077 14957"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      a(x,a(y,z,x) * u,y) = a(x,u,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14962,a(flip),b,15078,a),flip(a)].">
      <j1 rule="hyper" parents="65 14962 15078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      a(x * (y \ x),L((y \ x) \ 1,(y \ x) \ 1,y),z) = a(y,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(14768(a,1),14904(a,1,2))].">
      <j1 rule="para" parents="14768 14904"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      a(x * (y \ x),L((y \ x) \ 1,y \ x,y),z) = a(y,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12556,a(flip),b,15080,a)].">
      <j1 rule="hyper" parents="65 12556 15080"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      a(x * (y \ x),x \ y,z) = a(y,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(359(a,1),15081(a,1,2))].">
      <j1 rule="para" parents="359 15081"/>
    </justification>
  </clause>

  <clause id="15084">
    <literal><![CDATA[
      a(x,(x \ y) \ 1,z) = a(x,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13157,a(flip),b,15083,a),flip(a)].">
      <j1 rule="hyper" parents="65 13157 15083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      a(x,(x \ (x * y)) \ 1,z) = a(x,x \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(325,a,10260,a(flip),b,15084,a),flip(a)].">
      <j1 rule="hyper" parents="325 10260 15084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      a(x,y \ x,a(z,u,w)) = a(x,x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12215,a(flip),b,15084,a),flip(a)].">
      <j1 rule="hyper" parents="65 12215 15084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      a(x,x \ (y \ x),z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),15085(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 15085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      L(x,y \ (z \ y),y) = a(y,z \ 1,x) \ x
    ]]></literal>
    <justification jstring="[para(15087(a,1),14594(a,2,1))].">
      <j1 rule="para" parents="15087 14594"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      L(x,y \ (z \ y),y) = L(x,z \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,14594,a,b,15088,a),flip(a)].">
      <j1 rule="hyper" parents="325 14594 15088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      L(x,(y \ z) \ 1,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(10945,a,15089,a),flip(a)].">
      <j1 rule="hyper" parents="10945 15089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      L(x,L((y \ z) \ 1,z \ y,z) \ u,w) = L(x,L((y \ z) \ 1,y \ z,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(15090(a,1),13819(a,1,2,1))].">
      <j1 rule="para" parents="15090 13819"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      L(x,L((y \ z) \ 1,y \ z,z) \ u,w) = L(x,(((z \ y) \ (z \ z)) \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(12367(a,1),15092(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12367 15092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      L(x,L((y \ z) \ 1,y \ z,z) \ u,w) = L(x,(((z \ y) \ 1) \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(69(a,1),15093(a,2,2,1,1,2))].">
      <j1 rule="para" parents="69 15093"/>
    </justification>
  </clause>

  <clause id="15095">
    <literal><![CDATA[
      L(x,L((y \ z) \ 1,y \ z,z) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10823,a(flip),b,15094,a),flip(a)].">
      <j1 rule="hyper" parents="325 10823 15094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15098">
    <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),14928(a,1,2))].">
      <j1 rule="para" parents="100 14928"/>
    </justification>
  </clause>

  <clause id="15099">
    <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(774,a,15098,a)].">
      <j1 rule="hyper" parents="774 15098"/>
    </justification>
  </clause>

  <clause id="15100">
    <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(14816(a,2),15099(a,1,1))].">
      <j1 rule="para" parents="14816 15099"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      L(a(x,y,z),L(z,u,x),x * u) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(11619,a,15100,a),flip(a)].">
      <j1 rule="hyper" parents="11619 15100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      a(x,y,L(z,L(z,u,x),x * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14816,a,b,15101,a)].">
      <j1 rule="hyper" parents="65 14816 15101"/>
    </justification>
  </clause>

  <clause id="15104">
    <literal><![CDATA[
      a(x,y,L(z,z,L(x * u,u,x))) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12760,a(flip),b,15103,a)].">
      <j1 rule="hyper" parents="65 12760 15103"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      a(x,y,L(((z * u) * w) \ ((w * w) * (z * u)),u,z)) = a(x,y,(z * (u * w)) \ (z * u))
    ]]></literal>
    <justification jstring="[para(13960(a,2),15007(a,1,3))].">
      <j1 rule="para" parents="13960 15007"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      a(x,y,L(((z * u) * w) \ (z * u),u,z)) = a(x,y,(z * (u * w)) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(10550,a,15105,a)].">
      <j1 rule="hyper" parents="10550 15105"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      a(x,y,L((z * u) \ (w \ (z * u)),u,z)) = a(x,y,(z * (u * w)) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11334,a(flip),b,15106,a)].">
      <j1 rule="hyper" parents="65 11334 15106"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ (z * u)) = a(x,y,u \ (z \ (w \ (z * u))))
    ]]></literal>
    <justification jstring="[hyper(65,a,12047,a(flip),b,15108,a),flip(a)].">
      <j1 rule="hyper" parents="65 12047 15108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),z * u,w)) = a(x,y,u \ (w \ (z \ (w * u))))
    ]]></literal>
    <justification jstring="[hyper(11036,a,15109,a)].">
      <j1 rule="hyper" parents="11036 15109"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ (w * z)) = a(x,y,z \ (w \ (u \ (w * z))))
    ]]></literal>
    <justification jstring="[hyper(65,a,10059,a,b,15109,a)].">
      <j1 rule="hyper" parents="65 10059 15109"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) \ w) * (u * L(v5,u,w * a(z,z,u)))) = a(x,y,(w * L(u,z,z)) * v5)
    ]]></literal>
    <justification jstring="[para(14290(a,1),14760(a,1,3,2,2))].">
      <j1 rule="para" parents="14290 14760"/>
    </justification>
  </clause>

  <clause id="15113">
    <literal><![CDATA[
      R(x,y,(a(z,z,u) * (w * u)) * v5) = R(x,y,v5 * (w * (u * a(z,z,u))))
    ]]></literal>
    <justification jstring="[para(13423(a,1),14774(a,1,3))].">
      <j1 rule="para" parents="13423 14774"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      R(x,y,(a(z,z,u) * (w * u)) * v5) = R(x,y,v5 * (w * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,15020,a(flip),b,15113,a),flip(a)].">
      <j1 rule="hyper" parents="325 15020 15113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      a((x * T(y,z)) * y,y,(x * T(y,z)) * u) = a((x * y) * T(y,z),y,(y * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10256,a(flip),b,14891,a),flip(a)].">
      <j1 rule="hyper" parents="325 10256 14891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      a((x * T(y,z)) * y,y,(x * T(y,z)) * u) = a((x * y) * y,y,(y * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,2319,a(flip),b,15115,a),flip(a)].">
      <j1 rule="hyper" parents="325 2319 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      a((x * T(y,z)) * y,y,(x * T(y,z)) * u) = a(x,y,L((y * x) \ u,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,14850,a(flip),b,15117,a),flip(a)].">
      <j1 rule="hyper" parents="325 14850 15117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      a((x * T(y,z)) * y,y,(x * T(y,z)) * u) = a(x,y,(y * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,13179,a(flip),b,15119,a),flip(a)].">
      <j1 rule="hyper" parents="325 13179 15119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      a((x * T(y,z)) * y,y,(x * T(y,z)) * u) = a(x,y,y \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14544,a(flip),b,15120,a),flip(a)].">
      <j1 rule="hyper" parents="325 14544 15120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      a((x * T(y,z)) * y,y,(x * T(y,z)) * u) = a(x,y,y * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(325,a,13183,a(flip),b,15121,a),flip(a)].">
      <j1 rule="hyper" parents="325 13183 15121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      a((x * y) * T(y,z),y,(x * T(y,z)) * u) = a(x,y,y * (x \ u))
    ]]></literal>
    <justification jstring="[para(1131(a,1),15122(a,1,1))].">
      <j1 rule="para" parents="1131 15122"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      a((x * y) * T(y,z),y,(x * y) * u) = a(x,y,y * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(10274,a,15123,a)].">
      <j1 rule="hyper" parents="10274 15123"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      a((x * y) * y,y,(x * y) * z) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(2320,a,15124,a)].">
      <j1 rule="hyper" parents="2320 15124"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      a(x,y,L((x * y) * z,y,y)) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14850,a(flip),b,15125,a)].">
      <j1 rule="hyper" parents="65 14850 15125"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),L(x,y,z) \ 1,u) = (1 / x) \ R(1 / x,1 / L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(1886,a,14958,a)].">
      <j1 rule="hyper" parents="1886 14958"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ 1,L(u,y,z)) = (1 / x) \ R(1 / x,1 / L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14817,a(flip),b,15127,a)].">
      <j1 rule="hyper" parents="65 14817 15127"/>
    </justification>
  </clause>

  <clause id="15129">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,1 / L(x,y,z),u) = a(x,x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15021,a(flip),b,15128,a),flip(a)].">
      <j1 rule="hyper" parents="65 15021 15128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,L(x,y,z) \ 1,u) = a(x,x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(4320(a,1),15129(a,1,2))].">
      <j1 rule="para" parents="4320 15129"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      x \ (1 * R(1 \ x,L(x,y,z) \ 1,u)) = a(x,x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(4243,a,15130,a)].">
      <j1 rule="hyper" parents="4243 15130"/>
    </justification>
  </clause>

  <clause id="15132">
    <literal><![CDATA[
      x \ (1 * R(x,L(x,y,z) \ 1,u)) = a(x,x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(67(a,1),15131(a,1,2,2,1))].">
      <j1 rule="para" parents="67 15131"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      x \ R(x,L(x,y,z) \ 1,u) = a(x,x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(305,a,15132,a)].">
      <j1 rule="hyper" parents="305 15132"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w) \ 1,v5) = L(a(x,x \ 1,L(v5,u,w)),y,z)
    ]]></literal>
    <justification jstring="[para(15133(a,1),14650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15133 14650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w) \ 1,v5) = a(x,x \ 1,L(L(v5,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14816,a,b,15134,a),flip(a)].">
      <j1 rule="hyper" parents="325 14816 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      R(x,y,z) \ (a(x,x \ 1,L(L(u,y,z),y,z)) / (1 / R(x,y,z))) = L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(15135(a,1),14021(a,1,2,1))].">
      <j1 rule="para" parents="15135 14021"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      a(x * ((y * z) \ (x * y)),u,x * (y * z)) = a(z,u,L(L(x * (y * z),z,y),y * z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14942,a(flip),b,15000,a)].">
      <j1 rule="hyper" parents="65 14942 15000"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,w)) * (w * L(v5,w,z * a(u,u,w)))) = a(x,y,(z * L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,14292,a(flip),b,15112,a)].">
      <j1 rule="hyper" parents="65 14292 15112"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      a(x,y,L(L(z * (u * x),x,u),u * x,z)) = a((u * x) * u,y,(u * x) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14989,a(flip),b,15139,a),flip(a)].">
      <j1 rule="hyper" parents="65 14989 15139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      a(x,y,L(L(z * (u * x),x,u),u * x,z)) = a(x,y,L((u * x) * z,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14851,a(flip),b,15141,a),flip(a)].">
      <j1 rule="hyper" parents="325 14851 15141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      a(x,y,L((z * x) \ u,x,z)) = a(x,y,L((z * x) * u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,12446,a(flip),b,15142,a)].">
      <j1 rule="hyper" parents="65 12446 15142"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x,z)) = a(x,y,L((z * x) * u,z,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14953,a(flip),b,15143,a)].">
      <j1 rule="hyper" parents="65 14953 15143"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      a(x,y,L((z * x) * u,z,z)) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14955,a(flip),b,15144,a),flip(a)].">
      <j1 rule="hyper" parents="65 14955 15144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      a(x,y,(y * x) * z) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13179,a(flip),b,15145,a)].">
      <j1 rule="hyper" parents="65 13179 15145"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      a(x * y,y,(x * y) * (y \ z)) = a(x * y,y,L(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(10419,a,15146,a),flip(a)].">
      <j1 rule="hyper" parents="10419 15146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      a(x * y,y,x * (y \ (y \ z))) = a(x * y,y,L(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14940,a(flip),b,15147,a)].">
      <j1 rule="hyper" parents="65 14940 15147"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      a(x * y,y,L(z,y,y) * x) = a(x * y,y,L(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12020,a(flip),b,15148,a)].">
      <j1 rule="hyper" parents="65 12020 15148"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      a(x,y,((z * a(u,u,w)) * w) * v5) = a(x,y,(z * L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,12637,a(flip),b,15140,a)].">
      <j1 rule="hyper" parents="65 12637 15140"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * (w * u)) * v5) = a(x,y,(w * L(u,z,z)) * v5)
    ]]></literal>
    <justification jstring="[para(12926(a,1),15150(a,1,3,1))].">
      <j1 rule="para" parents="12926 15150"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      T(x * a(y,z,x * L(x,u,w)),x) = L(x,z,y) * (L(L(x,z,y),u,w) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(8047,a,15045,a)].">
      <j1 rule="hyper" parents="8047 15045"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),u,w) \ L(x,u,w)) = a(z,y,x * L(x,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,7678,a(flip),b,15152,a),flip(a)].">
      <j1 rule="hyper" parents="65 7678 15152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = a(z,y,x * L(x,u,w)) * x
    ]]></literal>
    <justification jstring="[para(12328(a,1),15154(a,1,2))].">
      <j1 rule="para" parents="12328 15154"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(w,u,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,15043,a(flip),b,15155,a(flip))].">
      <j1 rule="hyper" parents="37 15043 15155"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14681,a(flip),b,15156,a),flip(a)].">
      <j1 rule="hyper" parents="325 14681 15156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14681,a(flip),b,15157,a)].">
      <j1 rule="hyper" parents="65 14681 15157"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,13335,a,b,15159,a)].">
      <j1 rule="hyper" parents="325 13335 15159"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13333,a,b,15159,a)].">
      <j1 rule="hyper" parents="325 13333 15159"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,12836,a,b,15159,a)].">
      <j1 rule="hyper" parents="325 12836 15159"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      a(x,x,a(y,z,u * (w * x))) = a(y,z,a(x,x,u * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,13992,a(flip),b,15159,a),flip(a)].">
      <j1 rule="hyper" parents="325 13992 15159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(w,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,15159,a,b,14839,a)].">
      <j1 rule="hyper" parents="137 15159 14839"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,15159,a,b,7207,a),flip(a)].">
      <j1 rule="hyper" parents="137 15159 7207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(15159(a,1),14606(a,1,2))].">
      <j1 rule="para" parents="15159 14606"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = a(v5,w,a(x,z * y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13338,a(flip),b,15161,a)].">
      <j1 rule="hyper" parents="65 13338 15161"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      L(x,y,a(a(z,u,x),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(15161(a,2),13379(a,1,3))].">
      <j1 rule="para" parents="15161 13379"/>
    </justification>
  </clause>

  <clause id="15172">
    <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(15161(a,1),13373(a,2,2))].">
      <j1 rule="para" parents="15161 13373"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      x * L(y,z,a(a(u,w,y),v5,v6)) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,15171,a,b,9,a)].">
      <j1 rule="hyper" parents="137 15171 9"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14667,a,b,15162,a)].">
      <j1 rule="hyper" parents="65 14667 15162"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      a(x,y \ ((z * z) \ u),a(w,v5,v6)) = a(v6,v5,a(x,y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13659,a,b,15162,a)].">
      <j1 rule="hyper" parents="65 13659 15162"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      a(x,y * ((z * z) \ u),a(w,v5,v6)) = a(v6,v5,a(x,u * y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13354,a,b,15162,a)].">
      <j1 rule="hyper" parents="65 13354 15162"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15161,a(flip),b,15162,a)].">
      <j1 rule="hyper" parents="65 15161 15162"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),u,a(y,z,w)) = L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[para(15162(a,1),13337(a,1,1,2))].">
      <j1 rule="para" parents="15162 13337"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(z,u,a(y * x,x,w))
    ]]></literal>
    <justification jstring="[para(15162(a,1),13416(a,2,2))].">
      <j1 rule="para" parents="15162 13416"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      a(a(x \ (y * z),u,y),w,v5) = a((y \ x) \ z,u,a(v5,w,y))
    ]]></literal>
    <justification jstring="[para(14794(a,1),15162(a,1,1))].">
      <j1 rule="para" parents="14794 15162"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      a(a(x * (y \ z),u,z),w,v5) = a((y * x) * z,u,a(v5,w,z))
    ]]></literal>
    <justification jstring="[para(15066(a,1),15162(a,1,1))].">
      <j1 rule="para" parents="15066 15162"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,12836,a,b,15163,a)].">
      <j1 rule="hyper" parents="325 12836 15163"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,v6)) = a(w,v5,a(v6,u,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(325,a,3512,a,b,15163,a)].">
      <j1 rule="hyper" parents="325 3512 15163"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15163,a(flip),b,15163,a)].">
      <j1 rule="hyper" parents="325 15163 15163"/>
    </justification>
  </clause>

  <clause id="15190">
    <literal><![CDATA[
      a(x * y,y,a(z,u,y)) = a(z,u,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12840,a,b,15163,a)].">
      <j1 rule="hyper" parents="65 12840 15163"/>
    </justification>
  </clause>

  <clause id="15192">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(w,u,a(z,x,x * y))
    ]]></literal>
    <justification jstring="[para(15163(a,2),13417(a,2,2))].">
      <j1 rule="para" parents="15163 13417"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(15163(a,2),14606(a,1,2))].">
      <j1 rule="para" parents="15163 14606"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(v5,z,a(u,w,y * x))
    ]]></literal>
    <justification jstring="[hyper(10789,a,15178,a),flip(a)].">
      <j1 rule="hyper" parents="10789 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,v5,v6)) = a(v6,u,a(w,v5,z * (y * x)))
    ]]></literal>
    <justification jstring="[hyper(3517,a,15178,a)].">
      <j1 rule="hyper" parents="3517 15178"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(v5,z,a(y * x,w,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12837,a,b,15178,a),flip(a)].">
      <j1 rule="hyper" parents="325 12837 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15197">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,y,a(u,u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,10693,a,b,15178,a)].">
      <j1 rule="hyper" parents="325 10693 15178"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15163,a(flip),b,15178,a)].">
      <j1 rule="hyper" parents="325 15163 15178"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      a(x,x,a(y,z * x,u)) = a(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14115,a(flip),b,15178,a),flip(a)].">
      <j1 rule="hyper" parents="325 14115 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * y,w,a(z,u,x)) = L(y,a(z,u,x),w)
    ]]></literal>
    <justification jstring="[para(15178(a,1),12966(a,1,1,1))].">
      <j1 rule="para" parents="15178 12966"/>
    </justification>
  </clause>

  <clause id="15204">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[para(15178(a,1),14606(a,1,2))].">
      <j1 rule="para" parents="15178 14606"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15178,a,b,15186,a)].">
      <j1 rule="hyper" parents="325 15178 15186"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15163,a,b,15186,a)].">
      <j1 rule="hyper" parents="325 15163 15186"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = a(v5,z * y,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(10160,a,15188,a)].">
      <j1 rule="hyper" parents="10160 15188"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15161,a,b,15188,a)].">
      <j1 rule="hyper" parents="325 15161 15188"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      a(x * y,z,a(u,x,x)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13988,a(flip),b,15188,a),flip(a)].">
      <j1 rule="hyper" parents="65 13988 15188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,w,v5))) = a(z,y,a(u,u,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(13515(a,1),15188(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13515 15188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,x) = a(z,u,L(x,y,w))
    ]]></literal>
    <justification jstring="[para(15188(a,2),14818(a,1,1))].">
      <j1 rule="para" parents="15188 14818"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      a(x \ y,z,a(u,u,w)) = a(x * y,u,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14871,a,b,15198,a)].">
      <j1 rule="hyper" parents="325 14871 15198"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      a(x,y * (z * u),a(u,w,y)) = a(x,w,a(y,u * (y * z),u))
    ]]></literal>
    <justification jstring="[para(14968(a,2),15198(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14968 15198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,x) = a(w,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(15206(a,1),14818(a,1,1))].">
      <j1 rule="para" parents="15206 14818"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * z = L(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(7226,a,15168,a)].">
      <j1 rule="hyper" parents="7226 15168"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w * (v5 \ z))) = a(v5 * (w \ z),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,15068,a(flip),b,15168,a)].">
      <j1 rule="hyper" parents="132 15068 15168"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      L(x,y * z,a(y,y,z)) = L(x,u,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14884,a,b,15168,a)].">
      <j1 rule="hyper" parents="65 14884 15168"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      L(x,y,a(z,(z \ u) \ 1,w)) = x * a(z,u \ z,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(15084(a,1),15168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15084 15168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      a(x,x \ y,a(z,u,L(w,x,y))) = a(z,u,a(x,x \ y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14844,a,b,15175,a)].">
      <j1 rule="hyper" parents="65 14844 15175"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      a(x,y * x,a(z,u,L(w,x,y))) = a(z,u,a(x,y * x,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14843,a,b,15175,a)].">
      <j1 rule="hyper" parents="65 14843 15175"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      a(x,x,a(y,z,u * x)) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15178,a,b,15190,a)].">
      <j1 rule="hyper" parents="65 15178 15190"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15193,a(flip),b,15204,a)].">
      <j1 rule="hyper" parents="65 15193 15204"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14217,a,b,15226,a)].">
      <j1 rule="hyper" parents="325 14217 15226"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,a(z,y,w)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,14219,a(flip),b,15226,a),flip(a)].">
      <j1 rule="hyper" parents="325 14219 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15229">
    <literal><![CDATA[
      L(x,y,a(y * z,u,y)) = L(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13202,a(flip),b,15226,a),flip(a)].">
      <j1 rule="hyper" parents="325 13202 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      L(x,y * (z * u),a(y,w,z)) = L(x,w,a(z,z * (u * y),y))
    ]]></literal>
    <justification jstring="[para(14968(a,1),15226(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14968 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(y,v5,u)) = L(x,v5,a(u,w,y))
    ]]></literal>
    <justification jstring="[para(15079(a,1),15226(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15079 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      L(x,y,a(y,z,a(u,w,w))) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,14587,a(flip),b,15227,a),flip(a)].">
      <j1 rule="hyper" parents="325 14587 15227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      L(x,y,a(z,z,a(y,u,w))) = x
    ]]></literal>
    <justification jstring="[para(15163(a,1),15232(a,1,3))].">
      <j1 rule="para" parents="15163 15232"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      (x * y) * a(z,z,a(y,u,w)) = x * (a(z,z,a(y,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(15233(a,1),13272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15233 13272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      R(L(x,y,a(z,u,w)),u,a(z,y,w)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,13374,a,b,15228,a)].">
      <j1 rule="hyper" parents="65 13374 15228"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      L(x,y * z,a(z,z,y)) = L(x,u,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(10884,a,15221,a)].">
      <j1 rule="hyper" parents="10884 15221"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,u,a(u,w,w)) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(15221(a,1),12117(a,1,2))].">
      <j1 rule="para" parents="15221 12117"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      L(x,a(y,y,z),y \ z) = L(x,u,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14245,a,b,15237,a)].">
      <j1 rule="hyper" parents="65 14245 15237"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      (L(x,y,y) * y) * L(z,u,a(u,w,w)) = (x * y) * (a(y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(15237(a,1),14430(a,1,2))].">
      <j1 rule="para" parents="15237 14430"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      L(x,a(y,y,z),y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,15232,a(flip),b,15239,a),flip(a)].">
      <j1 rule="hyper" parents="325 15232 15239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) * u = a(x,y,w) * ((u / z) * (a(x,y,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14420,a,b,15167,a),flip(a)].">
      <j1 rule="hyper" parents="325 14420 15167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      a(x \ y,z,a(y,y,u)) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,15190,a(flip),b,15215,a),flip(a)].">
      <j1 rule="hyper" parents="325 15190 15215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      a(x,y,L(z,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14584,a(flip),b,15166,a)].">
      <j1 rule="hyper" parents="65 14584 15166"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(u,w,a(w,z,u) \ z)) = a(x,y,a(w,z,u) \ z)
    ]]></literal>
    <justification jstring="[para(12158(a,1),15166(a,1,1))].">
      <j1 rule="para" parents="12158 15166"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      a(x,y,(x * y) \ (z * y)) = a(x,y,x \ z)
    ]]></literal>
    <justification jstring="[hyper(10286,a,15245,a)].">
      <j1 rule="hyper" parents="10286 15245"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      a(x,y,y * (x \ (z * y))) = a(x,y,x \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13186,a(flip),b,15247,a)].">
      <j1 rule="hyper" parents="65 13186 15247"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      a(x,y,y * (x \ (z * y))) = a(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,14546,a(flip),b,15248,a),flip(a)].">
      <j1 rule="hyper" parents="325 14546 15248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      a(x,y,y * (x \ (y * z))) = a(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(10340,a,15249,a)].">
      <j1 rule="hyper" parents="10340 15249"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      a(x,y,(x \ z) * y) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10328,a,15249,a)].">
      <j1 rule="hyper" parents="10328 15249"/>
    </justification>
  </clause>

  <clause id="15252">
    <literal><![CDATA[
      a(x,R(y,z,u),R(y,z,u) * (x \ ((y * z) * u))) = a(x,R(y,z,u),x * (z * u))
    ]]></literal>
    <justification jstring="[para(109(a,1),15250(a,1,3,2,2))].">
      <j1 rule="para" parents="109 15250"/>
    </justification>
  </clause>

  <clause id="15253">
    <literal><![CDATA[
      L(x,y,a(z * (u \ w),z,u)) = L(x,y,a(u,z,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(15251(a,1),14223(a,2,3))].">
      <j1 rule="para" parents="15251 14223"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      a(x,y,z) * a(z,u,a(w,y,x)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12841,a(flip),b,15214,a)].">
      <j1 rule="hyper" parents="65 12841 15214"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      a(x,x,L(y,z,a(x,u,w) * v5)) = a(y,z,a(x,x,v5)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(12238(a,1),15214(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="12238 15214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      a(x,y,z) * a(z,z * u,a(w,y,x)) = a(x,y,L(z,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15047,a(flip),b,15254,a)].">
      <j1 rule="hyper" parents="65 15047 15254"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14584,a(flip),b,15254,a),flip(a)].">
      <j1 rule="hyper" parents="65 14584 15254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15259">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,x,w))) = a(u,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(14541(a,1),15212(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14541 15212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),a(w,z,y) * u,a(w,z,y)) = L(u,a(w,z,y),a(w,z,y)) \ L(u * L(x,a(w,z,y),u),a(w,z,y),a(w,z,y))
    ]]></literal>
    <justification jstring="[para(15172(a,1),9234(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15172 9234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      a((x \ y) \ z,u,a(w,v5,x)) = a(y \ (x * z),u,a(w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15162,a(flip),b,15183,a),flip(a)].">
      <j1 rule="hyper" parents="65 15162 15183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,v5,z)) = a(y * (x \ z),u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15162,a(flip),b,15184,a),flip(a)].">
      <j1 rule="hyper" parents="65 15162 15184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      a(x * (y * z),y,a(u,w,y)) = a(u,w,a(y,y,x * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13992,a(flip),b,15187,a),flip(a)].">
      <j1 rule="hyper" parents="325 13992 15187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15264">
    <literal><![CDATA[
      L(x,y * (z * u),a(u,w,y)) = L(x,u * (y * z),a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,15226,a,b,15230,a)].">
      <j1 rule="hyper" parents="325 15226 15230"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      (x * y) * a(z,z,a(y,u,w)) = x * L(y,u,a(z,z,w))
    ]]></literal>
    <justification jstring="[para(15218(a,1),15234(a,2,2))].">
      <j1 rule="para" parents="15218 15234"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,a(y,u,w))) = L(y,u,a(z,z,w))
    ]]></literal>
    <justification jstring="[hyper(532,a,15265,a)].">
      <j1 rule="hyper" parents="532 15265"/>
    </justification>
  </clause>

  <clause id="15267">
    <literal><![CDATA[
      (a(x,x,y) * (z / u)) * a(x,x,a(u,u \ z,y)) = (a(x,x,y) * z) / u
    ]]></literal>
    <justification jstring="[hyper(6860,a,15266,a),flip(a)].">
      <j1 rule="hyper" parents="6860 15266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      ((x / y) \ (x * a(z,z,a(y,y \ u,w)))) \ (u * a(z,z,w)) = T(a(z,z,w) * (T(u,a(z,z,w)) / y),y)
    ]]></literal>
    <justification jstring="[para(15266(a,2),10876(a,1,1))].">
      <j1 rule="para" parents="15266 10876"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      L(x,y,a(z,u,u * (z \ w))) = L(x,y,a(z,u,z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14217,a,b,15253,a)].">
      <j1 rule="hyper" parents="65 14217 15253"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      a((x \ y) \ z,u,a(w,v5,x)) = a(x,v5,a(y \ (x * z),u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15163,a(flip),b,15261,a),flip(a)].">
      <j1 rule="hyper" parents="325 15163 15261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      (x * y) * (a(x,x,y) * z) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,15173,a(flip),b,15238,a),flip(a)].">
      <j1 rule="hyper" parents="65 15173 15238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15273">
    <literal><![CDATA[
      x * (a(y,y,y \ x) * z) = ((1 / y) \ (y \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(528,a,15271,a)].">
      <j1 rule="hyper" parents="528 15271"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      L(x,L(y,(1 / z) \ u,w) * (w * ((1 / z) \ u)),v5) = L(x,w * ((z * u) * (a(z,z,u) * y)),v5)
    ]]></literal>
    <justification jstring="[para(15271(a,2),10819(a,2,2,2))].">
      <j1 rule="para" parents="15271 10819"/>
    </justification>
  </clause>

  <clause id="15275">
    <literal><![CDATA[
      x * (a(y,y,y * x) * z) = ((1 / y) \ (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(13183(a,1),15273(a,1,2,1))].">
      <j1 rule="para" parents="13183 15273"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      (((x \ y) / y) * x) * (y * z) = ((1 / x) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,13224,a,b,15275,a)].">
      <j1 rule="hyper" parents="65 13224 15275"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ (z * y))) * u,w) = L(x,u * (((1 / y) \ (y \ z)) * y),w)
    ]]></literal>
    <justification jstring="[para(15276(a,1),12038(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15276 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      a(x,y,L(z,u \ z,w)) = a(x,y,L(z,z * u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15254,a(flip),b,15257,a),flip(a)].">
      <j1 rule="hyper" parents="65 15254 15257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      a(x * (y \ z),u,a(w,v5,z)) = a(z,u,a(w,v5,y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15175,a(flip),b,15220,a),flip(a)].">
      <j1 rule="hyper" parents="65 15175 15220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,v5,z)) = a(z,u,a(w,v5,x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15262,a,b,15279,a)].">
      <j1 rule="hyper" parents="65 15262 15279"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      a((x * y) * z,u,a(z,w,v5)) = a(z,w,a(v5,u,x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15198,a,b,15280,a)].">
      <j1 rule="hyper" parents="65 15198 15280"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ x))) = a(z,u,a(x,y,x * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15195,a(flip),b,15281,a),flip(a)].">
      <j1 rule="hyper" parents="65 15195 15281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      (x * y) * (a(y,y,x) \ z) = (L(x,y,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(65,a,15173,a(flip),b,15240,a),flip(a)].">
      <j1 rule="hyper" parents="65 15173 15240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      (x * (y * (a(y,y,x) \ z))) \ ((L(x,y,y) * y) * z) = a(x,y,a(y,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,15283,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="132 15283 89"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      a(x,x,L(y,z,a(x,u,w) * v5)) = a(x,x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,15214,a(flip),b,15255,a),flip(a)].">
      <j1 rule="hyper" parents="325 15214 15255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      a(x,x,L(y,z,u * (w * a(x,v5,v6)))) = a(x,x,L(y,z,u * w))
    ]]></literal>
    <justification jstring="[para(14823(a,1),15286(a,1,3,3))].">
      <j1 rule="para" parents="14823 15286"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      a(x,x,L(y,z,z * u)) \ u = z * ((a(x,x,y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(15287(a,1),14412(a,1,1))].">
      <j1 rule="para" parents="15287 14412"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      (a(x,x,y) \ z) * (z \ u) = z * ((a(x,x,y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14842,a(flip),b,15288,a)].">
      <j1 rule="hyper" parents="65 14842 15288"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      (x / y) * (a(z,z,u) \ y) = y * ((a(z,z,u) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(65,a,13288,a(flip),b,15289,a)].">
      <j1 rule="hyper" parents="65 13288 15289"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      L((a(x,x,y) \ K(z,u)) \ ((w / K(z,u)) \ v5),a(x,x,y) \ 1,w / K(z,u)) = (K(z,u) * ((a(x,x,y) * K(z,u)) \ w)) \ v5
    ]]></literal>
    <justification jstring="[para(15291(a,1),10878(a,2,1))].">
      <j1 rule="para" parents="15291 10878"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      (L(x,y,y) * (y * z)) \ ((L(x,y,y) * y) * z) = a(x,y,a(y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(14762(a,1),15285(a,1,1))].">
      <j1 rule="para" parents="14762 15285"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      a(x,y,a(y,y,x) \ z) = a(L(x,y,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(709,a,15293,a),flip(a)].">
      <j1 rule="hyper" parents="709 15293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      a(x,y,a(y,y,x) \ z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,13161,a(flip),b,15294,a),flip(a)].">
      <j1 rule="hyper" parents="325 13161 15294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      a(x,y,z * a(y,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10101,a,15295,a),flip(a)].">
      <j1 rule="hyper" parents="10101 15295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      a(x,y,a(y,y,x) * z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14291,a(flip),b,15295,a)].">
      <j1 rule="hyper" parents="65 14291 15295"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      R(x,y,z * a(y,y,x)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,15296,a(flip),b,14596,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 15296 14596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      a(x * y,y,a(y,y,x * y) * (x \ z)) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,14888,a(flip),b,15297,a),flip(a)].">
      <j1 rule="hyper" parents="325 14888 15297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      R(x,y,z * a(y,y,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,14593,a,b,15298,a),flip(a)].">
      <j1 rule="hyper" parents="325 14593 15298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      R(x,y,(y * z) * a(y,y,x)) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,13208,a,b,15300,a),flip(a)].">
      <j1 rule="hyper" parents="325 13208 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      R(x,y,y * (z * a(y,y,x))) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(11582(a,1),15301(a,1,3))].">
      <j1 rule="para" parents="11582 15301"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      R(x,y,R(y,y,x) * z) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(12252(a,1),15302(a,1,3))].">
      <j1 rule="para" parents="12252 15302"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      R(x,y,L(y,y,x) * z) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13168,a(flip),b,15303,a)].">
      <j1 rule="hyper" parents="65 13168 15303"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      R(x,y,L(y,y,x) * z) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,13208,a(flip),b,15304,a),flip(a)].">
      <j1 rule="hyper" parents="325 13208 15304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      R(x,y,y * z) * z = (x / (y \ 1)) * (L(y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(15305(a,1),14996(a,1,1))].">
      <j1 rule="para" parents="15305 14996"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      (x / (y \ 1)) * (L(y,y,x) \ z) = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13212,a(flip),b,15306,a),flip(a)].">
      <j1 rule="hyper" parents="65 13212 15306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      a(x,y,(z * u) * (u \ L(w,L(u,u,z),L(u,u,z)))) = a(x,y,(L(u,u,z) * w) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(15307(a,1),10482(a,1,3))].">
      <j1 rule="para" parents="15307 10482"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(u,w,a(w,z,u) * z)) = a(x,y,a(w,z,u) \ z)
    ]]></literal>
    <justification jstring="[para(14291(a,1),15246(a,1,2,3))].">
      <j1 rule="para" parents="14291 15246"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      a(x,R(y,z,y),(x \ L(z,y,y)) * R(y,z,y)) = a(x,R(y,z,y),x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10490,a(flip),b,15252,a)].">
      <j1 rule="hyper" parents="65 10490 15252"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      a(x,R(y,z,y),(x \ L(z,y,y)) * L(y,z,y)) = a(x,R(y,z,y),x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,11354,a(flip),b,15310,a)].">
      <j1 rule="hyper" parents="65 11354 15310"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      a(x,R(y,z,y),y * (x \ L(z,y,y))) = a(x,R(y,z,y),x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,11364,a(flip),b,15311,a)].">
      <j1 rule="hyper" parents="65 11364 15311"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      a(x,R(y,z,y),x * (z * y)) = a(x,y,y * (x \ L(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(10220,a,15312,a),flip(a)].">
      <j1 rule="hyper" parents="10220 15312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(u,w,z * a(u,z,w))) = a(x,y,a(w,z,u) \ z)
    ]]></literal>
    <justification jstring="[para(14470(a,1),15309(a,1,2,3))].">
      <j1 rule="para" parents="14470 15309"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(u,w,L(z,u,w))) = a(x,y,a(w,z,u) \ z)
    ]]></literal>
    <justification jstring="[para(14548(a,1),15316(a,1,2,3))].">
      <j1 rule="para" parents="14548 15316"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(u,w,z)) = a(x,y,a(w,z,u) \ z)
    ]]></literal>
    <justification jstring="[para(15245(a,1),15317(a,1,2,3))].">
      <j1 rule="para" parents="15245 15317"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(u,w,z)) = a(x,y,a(w,z,u) * z)
    ]]></literal>
    <justification jstring="[hyper(325,a,14291,a(flip),b,15318,a),flip(a)].">
      <j1 rule="hyper" parents="325 14291 15318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15320">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(u,w,z)) = a(x,y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14470,a(flip),b,15319,a),flip(a)].">
      <j1 rule="hyper" parents="325 14470 15319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      a(x,x,L(L(y,z,x),u,w)) * a(x,x,a(u,w,L(y,z,x))) = a(x,x,y * a(u,L(y,z,x),w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14771,a(flip),b,15320,a),flip(a)].">
      <j1 rule="hyper" parents="325 14771 15320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * a(x,x,a(z,u,L(y,w,x))) = a(x,x,y * a(z,L(y,w,x),u))
    ]]></literal>
    <justification jstring="[para(11810(a,1),15321(a,1,1))].">
      <j1 rule="para" parents="11810 15321"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      a(x,x,y * a(z,L(y,u,x),w)) = a(x,x,L(y,z,w)) * a(x,x,a(z,w,y))
    ]]></literal>
    <justification jstring="[para(14847(a,1),15322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14847 15322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      a(x,x,y * a(z,L(y,u,x),w)) = a(x,x,y * a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15320,a(flip),b,15324,a),flip(a)].">
      <j1 rule="hyper" parents="325 15320 15324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      a(x,x,((y * L(z,u,x)) \ w) \ (y \ w)) = a(x,x,z * a(y,L(z,u,x),L(z,u,x) * (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(10137,a,14772,a)].">
      <j1 rule="hyper" parents="10137 14772"/>
    </justification>
  </clause>

  <clause id="15328">
    <literal><![CDATA[
      L(x,L(y,(z \ 1) \ u,w) * (w * ((1 / z) \ u)),v5) = L(x,w * ((z * u) * (a(z,z,u) * y)),v5)
    ]]></literal>
    <justification jstring="[para(10824(a,1),15274(a,1,2,1))].">
      <j1 rule="para" parents="10824 15274"/>
    </justification>
  </clause>

  <clause id="15329">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * w) * (u / (z \ 1))) = a(x,y,(u * z) * (z \ L(w,z,z)))
    ]]></literal>
    <justification jstring="[para(13564(a,1),15308(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="13564 15308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * w) * (u / (z \ 1))) = a(x,y,(z * w) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10482,a(flip),b,15329,a),flip(a)].">
      <j1 rule="hyper" parents="325 10482 15329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * w) * ((z \ 1) \ u)) = a(x,y,(z * w) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(10154,a,15330,a)].">
      <j1 rule="hyper" parents="10154 15330"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      a(x,y,(z \ u) * (L(z,z,u) * w)) = a(x,y,(z * w) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(10641,a,15332,a)].">
      <j1 rule="hyper" parents="10641 15332"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      a(x,x,((y * L(z,u,x)) \ w) * (y \ w)) = a(x,x,z * a(y,L(z,u,x),L(z,u,x) * (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14704,a(flip),b,15327,a)].">
      <j1 rule="hyper" parents="65 14704 15327"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      L(x,L(y,(z \ 1) \ u,w) * (w * ((z \ 1) \ u)),v5) = L(x,w * ((z * u) * (a(z,z,u) * y)),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10991,a(flip),b,15328,a)].">
      <j1 rule="hyper" parents="65 10991 15328"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      L(x,y * ((z * u) * (a(z,z,u) * w)),v5) = L(x,y * (((z \ 1) \ u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(10889,a,15335,a),flip(a)].">
      <j1 rule="hyper" parents="10889 15335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      L(x,y * (((1 / z) \ u) * w),v5) = L(x,y * (((z \ 1) \ u) * w),v5)
    ]]></literal>
    <justification jstring="[para(15271(a,1),15336(a,1,2,2))].">
      <j1 rule="para" parents="15271 15336"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ (z * y))) * u,w) = L(x,u * (((y \ 1) \ (y \ z)) * y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15277,a,b,15337,a)].">
      <j1 rule="hyper" parents="65 15277 15337"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ (z * y))) * u,w) = L(x,u * ((y \ z) * (y * y)),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10988,a(flip),b,15338,a),flip(a)].">
      <j1 rule="hyper" parents="325 10988 15338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ (z * y))) * u,w) = L(x,u * ((y \ 1) \ z),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11133,a(flip),b,15339,a),flip(a)].">
      <j1 rule="hyper" parents="325 11133 15339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      a(x,x,(y * z) * ((z / (u / (w * w))) * (u * y))) = a(x,x,a(z / (u / (w * w)),u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,10499,a(flip),b,14945,a)].">
      <j1 rule="hyper" parents="65 10499 14945"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      a(x,x,(y * z) * (((u / (w * w)) \ z) * (u * y))) = a(x,x,a(z / (u / (w * w)),u,y))
    ]]></literal>
    <justification jstring="[hyper(10277,a,15341,a)].">
      <j1 rule="hyper" parents="10277 15341"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,(z * u) * (z / (u \ 1)),z / (u \ 1))) = a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[hyper(11035,a,15041,a)].">
      <j1 rule="hyper" parents="11035 15041"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,(z * u) * (z / (u \ 1)),(u \ 1) \ z)) = a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[para(1551(a,1),15344(a,1,3))].">
      <j1 rule="para" parents="1551 15344"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,(z * u) * (z / (u \ 1)),u \ z)) = a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[para(5127(a,1),15345(a,1,3))].">
      <j1 rule="para" parents="5127 15345"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,(z * u) * ((u \ 1) \ z),u \ z)) = a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[para(10864(a,1),15346(a,1,3))].">
      <j1 rule="para" parents="10864 15346"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,(u \ z) * (z * u),u \ z)) = a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12188,a(flip),b,15347,a)].">
      <j1 rule="hyper" parents="65 12188 15347"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,a(u,u,z),u \ z)) = a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14246,a(flip),b,15348,a)].">
      <j1 rule="hyper" parents="65 14246 15348"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      a(x,y,a(z,u,u) \ ((z / (u \ 1)) \ w)) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(15242(a,1),15349(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15242 15349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      a(x,y,a(z,u,u) \ (((u \ 1) \ z) \ w)) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(10282,a,15350,a)].">
      <j1 rule="hyper" parents="10282 15350"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      a(x,y,a(z,u,u) \ ((u \ z) \ w)) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(10727,a,15351,a)].">
      <j1 rule="hyper" parents="10727 15351"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * ((u \ z) \ w)) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14291,a(flip),b,15353,a)].">
      <j1 rule="hyper" parents="65 14291 15353"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w))) = (x \ L(x,y,z)) * (x * a(w,u,x * L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(1752(a,1),15046(a,2,1))].">
      <j1 rule="para" parents="1752 15046"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w))) = x * (a(w,u,x * L(x,y,z)) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,8512,a(flip),b,15355,a),flip(a)].">
      <j1 rule="hyper" parents="325 8512 15355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w))) = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14437(a,1),15356(a,2,2))].">
      <j1 rule="para" parents="14437 15356"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x * a(u,w,x * L(x,y,z)))) = x * L(x \ L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(15044(a,1),15357(a,1,2,2))].">
      <j1 rule="para" parents="15044 15357"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,x * L(x,y,z)) = x * L(x \ L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(520,a,15358,a)].">
      <j1 rule="hyper" parents="520 15358"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(z,y,x)) = x * L(x \ L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(14681(a,1),15359(a,1,2))].">
      <j1 rule="para" parents="14681 15359"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,L(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(132,a,14930,a(flip),b,15361,a)].">
      <j1 rule="hyper" parents="132 14930 15361"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,L(z,u \ w,v5)) = a(v5,(u \ 1) \ w,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,12214,a,b,15362,a),flip(a)].">
      <j1 rule="hyper" parents="325 12214 15362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,a(z,y,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,15178,a,b,15362,a)].">
      <j1 rule="hyper" parents="137 15178 15362"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,z) = L(x,u,L(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15024,a(flip),b,15364,a)].">
      <j1 rule="hyper" parents="65 15024 15364"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      L(x,y,L(z,u,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12916(a,1),15365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12916 15365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15368">
    <literal><![CDATA[
      L(R(x,y,z),u,L(w,v5,x)) = L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(12923(a,1),15365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12923 15365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15370">
    <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(15229(a,1),15365(a,1,1))].">
      <j1 rule="para" parents="15229 15365"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,L(z,v5,x)) = L(x \ R(x,u,w),y,L(z,v5,x))
    ]]></literal>
    <justification jstring="[para(15367(a,1),11548(a,1,1))].">
      <j1 rule="para" parents="15367 11548"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,11989,a(flip),b,15370,a),flip(a)].">
      <j1 rule="hyper" parents="325 11989 15370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,L(z,u * w,w)) = a(w,(w \ 1) \ u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(15019(a,1),15363(a,1,2))].">
      <j1 rule="para" parents="15019 15363"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      a(x,(x \ 1) \ y,a(z,u,w)) = a(x,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15362,a(flip),b,15376,a),flip(a)].">
      <j1 rule="hyper" parents="65 15362 15376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      a(x,x \ y,a(z,u,w)) = a(x,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12214,a(flip),b,15377,a)].">
      <j1 rule="hyper" parents="65 12214 15377"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      a(x,y \ x,a(z,u,w)) = a(x,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15086,a,b,15378,a)].">
      <j1 rule="hyper" parents="65 15086 15378"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      a(x,y * x,a(z,u,L(w,x,y))) = a(z,u,a(x,x \ y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15223,a(flip),b,15378,a),flip(a)].">
      <j1 rule="hyper" parents="65 15223 15378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      a(x,y \ x,a(z,u,w)) = a(z,y * x,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,15188,a,b,15379,a),flip(a)].">
      <j1 rule="hyper" parents="325 15188 15379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      L(x,y,a(z,(z \ u) \ 1,w)) = x * a(z,u * z,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(15379(a,1),15222(a,2,2))].">
      <j1 rule="para" parents="15379 15222"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      a(x,(y \ z) * z,a(u,w,z)) = a(z,y,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(10150,a,15381,a),flip(a)].">
      <j1 rule="hyper" parents="10150 15381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,z)) = a(x,y * z,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15188,a,b,15381,a)].">
      <j1 rule="hyper" parents="65 15188 15381"/>
    </justification>
  </clause>

  <clause id="15385">
    <literal><![CDATA[
      a(x,y * (z \ y),a(u,w,y)) = a(y,z,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(10160,a,15383,a)].">
      <j1 rule="hyper" parents="10160 15383"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      a(x,y * (z \ y),a(y,u,w)) = a(y,z,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15209,a,b,15383,a)].">
      <j1 rule="hyper" parents="65 15209 15383"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      a(x,y \ z,a(u,u,z)) = a(z,y,a(x,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14983,a(flip),b,15385,a)].">
      <j1 rule="hyper" parents="65 14983 15385"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      a(x,y * z,a(u,u,z)) = a(z,y,a(x,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15384,a(flip),b,15387,a)].">
      <j1 rule="hyper" parents="65 15384 15387"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      a(x,y * x,a(z,u,u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15197,a,b,15388,a)].">
      <j1 rule="hyper" parents="65 15197 15388"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      a(x,x,a(y,z * y,u)) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15163,a,b,15388,a)].">
      <j1 rule="hyper" parents="65 15163 15388"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      a(x,y * z,a(z,u,u)) = a(z,y,a(x,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,15388,a)].">
      <j1 rule="hyper" parents="65 12836 15388"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,a(w,w,y \ u)) = a(y \ u,R(y,z,z),a(x,w,w))
    ]]></literal>
    <justification jstring="[para(14557(a,1),15388(a,1,2))].">
      <j1 rule="para" parents="14557 15388"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      a(x,y * (a(z,z,y) * u),a(w,w,u)) = a(u,y * a(z,z,y),a(x,w,w))
    ]]></literal>
    <justification jstring="[para(14720(a,1),15388(a,1,2))].">
      <j1 rule="para" parents="14720 15388"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      a(x,x,L(y,z * u,u)) = a(u,z,a(y,x,x)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(15388(a,1),15214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15388 15214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,w)) = a(x,y,a(z,u * z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15224,a(flip),b,15380,a),flip(a)].">
      <j1 rule="hyper" parents="65 15224 15380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      a(x,y * (z \ y),a(y,u * y,w)) = a(y,z,a(w,y \ u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15386,a(flip),b,15395,a),flip(a)].">
      <j1 rule="hyper" parents="65 15386 15395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      (a(x,x,y) * (z / u)) * a(x,x,a(u,z * u,y)) = (a(x,x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(15395(a,1),15267(a,1,2))].">
      <j1 rule="para" parents="15395 15267"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      ((x / y) \ (x * a(z,z,a(y,u * y,w)))) \ (u * a(z,z,w)) = T(a(z,z,w) * (T(u,a(z,z,w)) / y),y)
    ]]></literal>
    <justification jstring="[para(15395(a,1),15268(a,1,1,2,2))].">
      <j1 rule="para" parents="15395 15268"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      a(x,x,L(y,z * u,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14818,a(flip),b,15394,a),flip(a)].">
      <j1 rule="hyper" parents="325 14818 15394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      a(x,x,L(y,z * u,z)) = a(x,x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(11035,a,15399,a)].">
      <j1 rule="hyper" parents="11035 15399"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      (x * K(x \ y,x)) \ (a(z,z,u) \ y) = a(z,z,L(u,y,x)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(15400(a,1),15040(a,2,1))].">
      <j1 rule="para" parents="15400 15040"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      a(x,x,L(y,z,z * u)) \ u = (z / u) \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(15400(a,1),15070(a,1,1))].">
      <j1 rule="para" parents="15400 15070"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      (x / y) \ (a(z,z,u) \ x) = x * ((a(z,z,u) * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15288,a(flip),b,15402,a),flip(a)].">
      <j1 rule="hyper" parents="65 15288 15402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      a(x,x,L(y,z,u * z)) \ z = u * ((a(x,x,y) * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13447,a,b,15403,a)].">
      <j1 rule="hyper" parents="65 13447 15403"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      (a(x,x,L(y,z,u * z)) \ z) / u = z / (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(135,a,15404,a,b,13271,a)].">
      <j1 rule="hyper" parents="135 15404 13271"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      L(x,y,a(z,(z \ u) \ 1,w)) = L(x,y,a(z,u * z,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15168,a(flip),b,15382,a),flip(a)].">
      <j1 rule="hyper" parents="325 15168 15382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,w)) = L(x,y,a(z,u * z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14008,a(flip),b,15406,a)].">
      <j1 rule="hyper" parents="65 14008 15406"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      L(x,y,a(z,u \ z,w)) = L(x,y,a(z,u * z,w))
    ]]></literal>
    <justification jstring="[para(15084(a,1),15406(a,1,3))].">
      <j1 rule="para" parents="15084 15406"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (z * w))) = L(x,y,a(u,w * u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13890,a,b,15407,a)].">
      <j1 rule="hyper" parents="65 13890 15407"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      L(x,y,a(z,(u \ z) * z,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(9992(a,1),15408(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9992 15408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      a(x,y,a(z,x \ u,w)) = a(x,y,a(z,u * x,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15386,a(flip),b,15396,a),flip(a)].">
      <j1 rule="hyper" parents="65 15386 15396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,a(y,u * z,w))) = L(y,z \ u,a(z,z,w))
    ]]></literal>
    <justification jstring="[para(15411(a,1),15266(a,1,2,2))].">
      <j1 rule="para" parents="15411 15266"/>
    </justification>
  </clause>

  <clause id="15414">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,u)) = (w / x) \ (w * a(x,z,a(y,y,u)))
    ]]></literal>
    <justification jstring="[para(15199(a,1),15412(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15199 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      R(x,y,L(a(z,z,u),x,w)) = L(x,z \ y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14915,a(flip),b,15414,a)].">
      <j1 rule="hyper" parents="325 14915 15414"/>
    </justification>
  </clause>

  <clause id="15416">
    <literal><![CDATA[
      R(x,y,a(z,z,L(u,x,w))) = L(x,z \ y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(12056(a,2),15415(a,1,3))].">
      <j1 rule="para" parents="12056 15415"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,u)) = L(x,z,a(y,y,L(u,x,w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,13374,a(flip),b,15416,a),flip(a)].">
      <j1 rule="hyper" parents="65 13374 15416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,u)) = L(x,z,a(y,y,u))
    ]]></literal>
    <justification jstring="[para(153(a,1),15417(a,2,3,3))].">
      <j1 rule="para" parents="153 15417"/>
    </justification>
  </clause>

  <clause id="15419">
    <literal><![CDATA[
      L(x,y * z,a(z,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(10897,a,15418,a),flip(a)].">
      <j1 rule="hyper" parents="10897 15418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      (x * (y * z)) * ((y * z) \ (z \ y)) = L(x,y,a(z,z,y)) * (z \ y)
    ]]></literal>
    <justification jstring="[para(15419(a,1),13389(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15419 13389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      (x * (y * z)) * ((y * z) \ (z \ y)) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(14597(a,1),15421(a,2,1))].">
      <j1 rule="para" parents="14597 15421"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      (x * (y * z)) * (z \ (y \ (z \ y))) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(14890(a,1),15424(a,1,2))].">
      <j1 rule="para" parents="14890 15424"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      ((x * y) * (z \ u)) / ((y * (u * z)) * (z \ (u \ (z \ u)))) = R(R(x,y,u * z),y * (u * z),z \ (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(15425(a,1),488(a,1,1))].">
      <j1 rule="para" parents="15425 488"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      K(x,x \ y) * (x \ (a(z,z,u) \ y)) = a(z,z,L(u,y,x)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(9579,a,15401,a)].">
      <j1 rule="hyper" parents="9579 15401"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ (z / u) = (a(x,x,y) \ z) / u
    ]]></literal>
    <justification jstring="[hyper(65,a,13276,a(flip),b,15427,a),flip(a)].">
      <j1 rule="hyper" parents="65 13276 15427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      a(x * a(y,x,z),x,u) \ (y / z) = (a(x,x,L(u,z,y)) \ y) / z
    ]]></literal>
    <justification jstring="[para(14952(a,2),15428(a,1,1))].">
      <j1 rule="para" parents="14952 15428"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,a(w,w,y * u)) = a(y \ u,R(y,z,z),a(x,w,w))
    ]]></literal>
    <justification jstring="[para(14704(a,1),15392(a,1,3))].">
      <j1 rule="para" parents="14704 15392"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      a(x,y * (a(z,z,y) * u),a(w,w,u)) = a(u,L(y,z,z),a(x,w,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14687,a(flip),b,15393,a),flip(a)].">
      <j1 rule="hyper" parents="325 14687 15393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      (a(x,x,y) * (z / u)) * a(u,z,a(y,x,x)) = (a(x,x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(15390(a,1),15397(a,1,2))].">
      <j1 rule="para" parents="15390 15397"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * (z / u) = (a(x,x,y) * z) / u
    ]]></literal>
    <justification jstring="[hyper(65,a,14846,a(flip),b,15432,a)].">
      <j1 rule="hyper" parents="65 14846 15432"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,x,y)) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[hyper(7209,a,15433,a)].">
      <j1 rule="hyper" parents="7209 15433"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      (x / y) * a(z,z,u * a(x,u,y)) = (a(z,z,L(u,y,x)) * x) / y
    ]]></literal>
    <justification jstring="[para(13081(a,1),15434(a,1,2))].">
      <j1 rule="para" parents="13081 15434"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      (x / y) * a(z * a(x,z,y),z,u) = (a(z,z,L(u,y,x)) * x) / y
    ]]></literal>
    <justification jstring="[para(14952(a,2),15434(a,1,2))].">
      <j1 rule="para" parents="14952 15434"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,a(w,w,y * u)) = a(y \ u,L(y,z,z),a(x,w,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10526,a(flip),b,15430,a),flip(a)].">
      <j1 rule="hyper" parents="325 10526 15430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,L(w,v5,x)) = L(x,u,w) \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(15368(a,1),15374(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15368 15374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,L(w,v5,x)) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11548,a(flip),b,15438,a),flip(a)].">
      <j1 rule="hyper" parents="325 11548 15438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w,v5,x)) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14596(a,2),15439(a,1,1))].">
      <j1 rule="para" parents="14596 15439"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,v5,x))) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14816,a,b,15441,a)].">
      <j1 rule="hyper" parents="65 14816 15441"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,v5,x))) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14596(a,2),15442(a,2,1))].">
      <j1 rule="para" parents="14596 15442"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,v5,x))) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14816,a,b,15443,a),flip(a)].">
      <j1 rule="hyper" parents="325 14816 15443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      a(x,y,L(z,z,x * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15104,a(flip),b,15444,a),flip(a)].">
      <j1 rule="hyper" parents="65 15104 15444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15447">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) \ a(x,y,z) = a(x * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(15445(a,1),14839(a,1,1))].">
      <j1 rule="para" parents="15445 14839"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      a(x * y,z,a(x,u,z)) = a(y,z,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14839,a(flip),b,15447,a),flip(a)].">
      <j1 rule="hyper" parents="65 14839 15447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15451">
    <literal><![CDATA[
      a(x,x,a(y,z,u * y)) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15194,a(flip),b,15448,a)].">
      <j1 rule="hyper" parents="65 15194 15448"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      ((x / y) \ (x * a(y,z,a(u,w,w)))) \ (z * a(w,w,u)) = T(a(w,w,u) * (T(z,a(w,w,u)) / y),y)
    ]]></literal>
    <justification jstring="[para(15390(a,1),15398(a,1,1,2,2))].">
      <j1 rule="para" parents="15390 15398"/>
    </justification>
  </clause>

  <clause id="15454">
    <literal><![CDATA[
      R(x,y,L(a(z,u,u),x,w)) \ (y * a(u,u,z)) = T(a(u,u,z) * (T(y,a(u,u,z)) / x),x)
    ]]></literal>
    <justification jstring="[para(14915(a,1),15453(a,1,1))].">
      <j1 rule="para" parents="14915 15453"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      R(x,y,a(z,u,L(u,x,w))) \ (y * a(u,u,z)) = T(a(u,u,z) * (T(y,a(u,u,z)) / x),x)
    ]]></literal>
    <justification jstring="[para(12665(a,2),15454(a,1,1,3))].">
      <j1 rule="para" parents="12665 15454"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      L(x,y,a(z,u,L(u,x,w))) \ (y * a(u,u,z)) = T(a(u,u,z) * (T(y,a(u,u,z)) / x),x)
    ]]></literal>
    <justification jstring="[para(13374(a,1),15455(a,1,1))].">
      <j1 rule="para" parents="13374 15455"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      T(a(x,x,y) * (T(z,a(x,x,y)) / u),u) = L(u,z,a(y,x,x)) \ (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(153(a,1),15456(a,1,1,3,3)),flip(a)].">
      <j1 rule="para" parents="153 15456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) \ (y * a(u,u,z)) = (x \ y) * a(u,u,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13427,a(flip),b,15457,a),flip(a)].">
      <j1 rule="hyper" parents="65 13427 15457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15459">
    <literal><![CDATA[
      (a(x,x,y) * (T(z,a(x,x,y)) * u)) / u = u * ((u \ z) * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(15458(a,1),14239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15458 14239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15460">
    <literal><![CDATA[
      x \ ((x * y) * a(z,z,u)) = x * ((x \ y) * a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13426,a(flip),b,15459,a)].">
      <j1 rule="hyper" parents="65 13426 15459"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      x \ (y * a(z,z,L(u,y,x))) = (x \ y) * a(z,z,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,14833,a(flip),b,15460,a(flip))].">
      <j1 rule="hyper" parents="132 14833 15460"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      (x * (y * a(z,z,L(u,y,1 / x)))) \ (((1 / x) \ y) * a(z,z,u)) = a(x,x,y * a(z,z,L(u,y,1 / x)))
    ]]></literal>
    <justification jstring="[para(15461(a,1),11638(a,1,2))].">
      <j1 rule="para" parents="15461 11638"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      (x * (y * a(z,z,L(u,y,x)))) \ (((1 / x) \ y) * a(z,z,u)) = a(x,x,y * a(z,z,L(u,y,1 / x)))
    ]]></literal>
    <justification jstring="[para(1490(a,1),15462(a,1,1,2,2,3))].">
      <j1 rule="para" parents="1490 15462"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      a(x,x,y * a(z,z,L(u,y,1 / x))) = ((x * y) * a(z,z,u)) \ (((1 / x) \ y) * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(14832(a,1),15463(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14832 15463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      a(x,x,y * a(z,z,L(u,y,1 / x))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,14574,a(flip),b,15464,a),flip(a)].">
      <j1 rule="hyper" parents="325 14574 15464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      a(x,x,y * a(z,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(448(a,1),15465(a,1,3,2,3))].">
      <j1 rule="para" parents="448 15465"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      a(x,x,a(y,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(10136,a,15467,a)].">
      <j1 rule="hyper" parents="10136 15467"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      a(x,x,L(y,z,a(u,u,w)) * z) = a(x,x,(a(u,u,w) * z) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,12636,a(flip),b,15467,a),flip(a)].">
      <j1 rule="hyper" parents="65 12636 15467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      a(x,x,y * L(z,u,u)) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(12749(a,1),15467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12749 15467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      a(x * a(y,y,z),u,a(w,w,v5)) = a(v5,u,a(w,w,x))
    ]]></literal>
    <justification jstring="[para(15467(a,1),15178(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15467 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      a(x,x,y * a(z,u,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,14470,a(flip),b,15468,a)].">
      <j1 rule="hyper" parents="65 14470 15468"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      a(x,x,L(a(y,y,z),u,w) * (R(w,u,a(y,y,z)) * u)) = a(x,x,w * u)
    ]]></literal>
    <justification jstring="[para(12892(a,2),15468(a,1,3))].">
      <j1 rule="para" parents="12892 15468"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      a(x,a(y,z,y * z) * u,a(w,w,u)) = 1
    ]]></literal>
    <justification jstring="[para(15468(a,1),14592(a,1,3))].">
      <j1 rule="para" parents="15468 14592"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,a(w,v5,v5)) = a(w,u,a(v5,v5,z))
    ]]></literal>
    <justification jstring="[para(15468(a,1),15188(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15468 15188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),a(v5,v5,w)) = a(a(z,z,u) * w,y,a(x,v5,v5))
    ]]></literal>
    <justification jstring="[para(15468(a,1),15388(a,1,3))].">
      <j1 rule="para" parents="15468 15388"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      a(x * a(y,z,z),u,a(w,w,v5)) = a(v5,u,a(w,w,x))
    ]]></literal>
    <justification jstring="[para(15473(a,1),15178(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15473 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15479">
    <literal><![CDATA[
      a(x,x,L(y,z,z) * u) = a(x,x,u * y)
    ]]></literal>
    <justification jstring="[hyper(10136,a,15471,a)].">
      <j1 rule="hyper" parents="10136 15471"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      a(x,a(y,z,y * z),a(u,w,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,15388,a(flip),b,15475,a)].">
      <j1 rule="hyper" parents="65 15388 15475"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      a(x,a(y,y,z),a(u,w,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,14249,a(flip),b,15480,a)].">
      <j1 rule="hyper" parents="65 14249 15480"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      a(x,y,a(y,a(z,z,u),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,15198,a,b,15482,a)].">
      <j1 rule="hyper" parents="65 15198 15482"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      L(x,y,a(y,a(z,z,u),w)) = x * 1
    ]]></literal>
    <justification jstring="[para(15483(a,1),13398(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15483 13398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15486">
    <literal><![CDATA[
      L(x,y,a(y,a(z,z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,8,a(flip),b,15485,a),flip(a)].">
      <j1 rule="hyper" parents="325 8 15485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      L(x,y,a(y,a(z,u,u),w)) = x
    ]]></literal>
    <justification jstring="[para(14233(a,2),15486(a,1,3))].">
      <j1 rule="para" parents="14233 15486"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,14217,a,b,15488,a)].">
      <j1 rule="hyper" parents="65 14217 15488"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      L(x,a(y,z,z),L(u,w,w)) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(15490(a,1),15365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15490 15365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      a(x,x,(y * z) * u) = a(x,x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10273,a(flip),b,15479,a)].">
      <j1 rule="hyper" parents="65 10273 15479"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,w) * v5)) = a(x,y,a(z,z,u * v5))
    ]]></literal>
    <justification jstring="[para(15479(a,2),10788(a,1,3))].">
      <j1 rule="para" parents="15479 10788"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      a(x,x,y * (z \ u)) = a(x,x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(10136,a,15492,a),flip(a)].">
      <j1 rule="hyper" parents="10136 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      a(x,x,(y \ z) * u) = a(x,x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10045,a,b,15492,a)].">
      <j1 rule="hyper" parents="325 10045 15492"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      a(x,x,((y * L(z,u,x)) \ w) * (y * w)) = a(x,x,z * a(y,L(z,u,x),L(z,u,x) * (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15334,a(flip),b,15494,a),flip(a)].">
      <j1 rule="hyper" parents="65 15334 15494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      a(x,x,y * ((z * u) * (u * (z * w)))) = a(x,x,y * L(K(u,z) * w,z,u))
    ]]></literal>
    <justification jstring="[para(5238(a,1),15494(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5238 15494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      a(a(x,x,y * (z * u)),w,v5) = a(x,x,a(v5,w,y * (z \ u)))
    ]]></literal>
    <justification jstring="[para(15494(a,1),15162(a,1,1))].">
      <j1 rule="para" parents="15494 15162"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      a(x,x,L((y \ z) * u,w,v5)) = L(a(x,x,(y * z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(15495(a,1),12056(a,2,1))].">
      <j1 rule="para" parents="15495 12056"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      a(x \ y,z,a(u,u,(w * v5) * v6)) = a(x * y,u,a((w \ v5) * v6,z,u))
    ]]></literal>
    <justification jstring="[para(15495(a,1),15215(a,1,3))].">
      <j1 rule="para" parents="15495 15215"/>
    </justification>
  </clause>

  <clause id="15501">
    <literal><![CDATA[
      L(x * a(L(y,z,z),x,a(u,w,w)),a(u,w,w),y) = L(x,L(y,z,z),a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12111,a(flip),b,15491,a),flip(a)].">
      <j1 rule="hyper" parents="65 12111 15491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      a(x * a(y,z,z),(u * w) \ u,a(v5,v5,v6)) = a(v6,u \ (w \ u),a(v5,v5,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,10260,a(flip),b,15478,a),flip(a)].">
      <j1 rule="hyper" parents="325 10260 15478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      a(x,y,a(L(z,u,u) * w,v5,v5)) = a(x,y,a(v5,v5,z * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,15493,a)].">
      <j1 rule="hyper" parents="65 12836 15493"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      a(x,x,a(y,z,u * (w \ v5))) = a(x,x,a(y,z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15162,a(flip),b,15498,a),flip(a)].">
      <j1 rule="hyper" parents="65 15162 15498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      a(x,x,L((y \ z) * u,w,v5)) = a(x,x,L((y * z) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,14816,a,b,15499,a),flip(a)].">
      <j1 rule="hyper" parents="325 14816 15499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      a(x,x,a(y,z,z * (y * (u * z)))) = a(x,x,a(y,z,y * u))
    ]]></literal>
    <justification jstring="[para(15249(a,1),15504(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15249 15504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      a(x,x,a(y,y,L(z,u,w)) * (R(w,u,a(y,y,z)) * u)) = a(x,x,w * u)
    ]]></literal>
    <justification jstring="[para(12056(a,2),15474(a,1,3,1))].">
      <j1 rule="para" parents="12056 15474"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),a(v5,v5,w)) = a(x,y,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15476,a(flip),b,15477,a),flip(a)].">
      <j1 rule="hyper" parents="325 15476 15477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,w,w)) = a(u,y,a(w,w,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15431,a(flip),b,15508,a)].">
      <j1 rule="hyper" parents="65 15431 15508"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,a(w,w,y * u)) = a(x,y,a(w,w,y \ u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15437,a,b,15510,a)].">
      <j1 rule="hyper" parents="65 15437 15510"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,a(w,w,y * u)) = a(x,y,a(w,w,y * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14899,a(flip),b,15512,a),flip(a)].">
      <j1 rule="hyper" parents="325 14899 15512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      a(x * y,y,a((z \ u) * w,v5,y)) = a((z * u) * w,v5,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15244,a(flip),b,15500,a),flip(a)].">
      <j1 rule="hyper" parents="65 15244 15500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,v5,v5)) = a((x * y) * z,u,a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15190,a(flip),b,15515,a)].">
      <j1 rule="hyper" parents="65 15190 15515"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,w,v5)) = a((x * y) * z,u,a(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,15516,a)].">
      <j1 rule="hyper" parents="65 12836 15516"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      a(x,x,a(y,y,L(z,u,w)) * (L(w,u,a(y,y,z)) * u)) = a(x,x,w * u)
    ]]></literal>
    <justification jstring="[hyper(11374,a,15507,a)].">
      <j1 rule="hyper" parents="11374 15507"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      a(x,x,L(y,z,a(u,u,w)) * z) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15468,a(flip),b,15518,a)].">
      <j1 rule="hyper" parents="65 15468 15518"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      a(x,x,(a(y,y,z) * u) * w) = a(x,x,w * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15470,a(flip),b,15519,a)].">
      <j1 rule="hyper" parents="65 15470 15519"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      a(x,x,(y * a(z,z,u)) * w) = a(x,x,w * y)
    ]]></literal>
    <justification jstring="[hyper(10139,a,15521,a)].">
      <j1 rule="hyper" parents="10139 15521"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      a(x,x,(R(y,y,z) * u) * w) = a(x,x,w * (y * u))
    ]]></literal>
    <justification jstring="[para(12248(a,1),15521(a,1,3,1))].">
      <j1 rule="para" parents="12248 15521"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      a(x,x,(L(y,y,z) * u) * w) = a(x,x,w * (y * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,11369,a(flip),b,15524,a)].">
      <j1 rule="hyper" parents="65 11369 15524"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      a(x,x,y * (z * (L(z,z,u) \ w))) = a(x,x,w * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15525(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 15525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      a(x,x,(L(y / z,y / z,u) * a(w,w,L(v5,y,z))) * v6) = a(x,x,v6 * ((a(w,w,v5) * y) / z))
    ]]></literal>
    <justification jstring="[para(15434(a,1),15525(a,2,3,2))].">
      <j1 rule="para" parents="15434 15525"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      a(x,x,y * (z * a(u,w,w))) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[para(12679(a,1),15526(a,1,3,2))].">
      <j1 rule="para" parents="12679 15526"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      a(x,x,(a(y,z,z) \ u) * w) = a(x,x,w * u)
    ]]></literal>
    <justification jstring="[hyper(10155,a,15528,a),flip(a)].">
      <j1 rule="hyper" parents="10155 15528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      a(x * (a(y,z,z) * u),w,a(v5,v6,w)) = a(v5,v6,a(w,w,u * x))
    ]]></literal>
    <justification jstring="[para(15528(a,1),15187(a,2,3))].">
      <j1 rule="para" parents="15528 15187"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      a(x,x,(a(y,z,z) * u) * w) = a(x,x,w * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15495,a(flip),b,15529,a)].">
      <j1 rule="hyper" parents="65 15495 15529"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      a(x,x,y * (L(z,z,u) * w)) = a(x,x,(z * w) * y)
    ]]></literal>
    <justification jstring="[para(12675(a,1),15531(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12675 15531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      a(x,x,y * (L(z * u,z * u,w) * (a(z,z,u) * v5))) = a(x,x,(((1 / z) \ u) * v5) * y)
    ]]></literal>
    <justification jstring="[para(15271(a,1),15532(a,2,3,1))].">
      <j1 rule="para" parents="15271 15532"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      a(x,y,a(y,z,u * (a(w,v5,v5) * v6))) = a(x,z,a(y,y,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15188,a,b,15530,a)].">
      <j1 rule="hyper" parents="65 15188 15530"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      a(x,x,y * ((z * u) * (u * (z * w)))) = a(x,x,y * L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10179,a(flip),b,15497,a),flip(a)].">
      <j1 rule="hyper" parents="325 10179 15497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      a(x,x,(y * (z * (z * (y * u)))) * L(u,y,z)) = a(x,x,a(y,z,(y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,14947,a(flip),b,15535,a),flip(a)].">
      <j1 rule="hyper" parents="65 14947 15535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      L(x * a(y,x,L(a(z,u,u),w,w)),a(z,u,u),y) = L(x,L(y,w,w),a(z,u,u))
    ]]></literal>
    <justification jstring="[para(14817(a,1),15501(a,1,1,2))].">
      <j1 rule="para" parents="14817 15501"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      a(x,x,(L(y * z,u,u) * y) * L(z,y,u)) = a(x,x,a(y,u,(y \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(10517,a,15537,a)].">
      <j1 rule="hyper" parents="10517 15537"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,L(u,w,w))),a(z,u,u),y) = L(x,L(y,w,w),a(z,u,u))
    ]]></literal>
    <justification jstring="[para(12665(a,2),15538(a,1,1,2,3))].">
      <j1 rule="para" parents="12665 15538"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,u)),a(z,u,u),y) = L(x,L(y,w,w),a(z,u,u))
    ]]></literal>
    <justification jstring="[para(15258(a,1),15540(a,1,1,2,3))].">
      <j1 rule="para" parents="15258 15540"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      L(x,L(y,z,z),a(u,w,w)) = L(x,y,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12111,a(flip),b,15541,a),flip(a)].">
      <j1 rule="hyper" parents="65 12111 15541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      L(x,(1 / y) * z,a(u,w,w)) = L(x,y \ z,a(u,w,w))
    ]]></literal>
    <justification jstring="[para(649(a,1),15542(a,1,2))].">
      <j1 rule="para" parents="649 15542"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      L(x,(y \ 1) * z,a(u,w,w)) = L(x,y \ z,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(10887,a,15544,a)].">
      <j1 rule="hyper" parents="10887 15544"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      L(x,y \ z,a(u,w,w)) = L(x,y * z,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,11184,a(flip),b,15545,a),flip(a)].">
      <j1 rule="hyper" parents="65 11184 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      x \ L(x,y * z,a(u,w,w)) = a(u,w,a(x,y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,15546,a(flip),b,15168,a)].">
      <j1 rule="hyper" parents="132 15546 15168"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,y)) = a(x,y,a(z,u * w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15175,a(flip),b,15547,a),flip(a)].">
      <j1 rule="hyper" parents="65 15175 15547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      a(x * y,y,a(z,u * w,y)) = a(z,u \ w,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15190,a(flip),b,15548,a),flip(a)].">
      <j1 rule="hyper" parents="65 15190 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,w)) = a(x,y * z,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15190,a(flip),b,15549,a),flip(a)].">
      <j1 rule="hyper" parents="65 15190 15549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      a(x,y \ z,a(u,u,w)) = a(x,y * z,a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,15550,a)].">
      <j1 rule="hyper" parents="65 12836 15550"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      a(x * a(y,z,z),(u * w) * u,a(v5,v6,v6)) = a(v5,u \ (w \ u),a(v6,v6,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15502,a(flip),b,15551,a),flip(a)].">
      <j1 rule="hyper" parents="65 15502 15551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      a(x * a(y,z,z),L(u,w,w),a(v5,v6,v6)) = a(v5,w \ (u \ w),a(v6,v6,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13392,a(flip),b,15552,a)].">
      <j1 rule="hyper" parents="65 13392 15552"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,u,w)) = a(x,z,a(u,u,w * a(v5,v6,v6)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15510,a(flip),b,15553,a),flip(a)].">
      <j1 rule="hyper" parents="65 15510 15553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,u,w)) = a(x,z,a(u,u,w))
    ]]></literal>
    <justification jstring="[para(127(a,1),15554(a,2,3,3))].">
      <j1 rule="para" parents="127 15554"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      a(x,y * (z \ y),a(u,w,w)) = a(x,z,a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15551,a(flip),b,15556,a)].">
      <j1 rule="hyper" parents="65 15551 15556"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      a(x,x,a(y,(z \ u) * u,w)) = a(y,z,a(x,x,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15170,a(flip),b,15557,a)].">
      <j1 rule="hyper" parents="65 15170 15557"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      a(x,(y \ z) * z,a(u,w,w)) = a(u,y,a(w,w,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15186,a,b,15558,a)].">
      <j1 rule="hyper" parents="65 15186 15558"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      a(x,x,a(y,(a(z,z,u) \ w) * 1,v5)) = a(y,a(z,z,u) / w,a(x,x,v5))
    ]]></literal>
    <justification jstring="[para(14744(a,1),15558(a,1,3,2,1))].">
      <j1 rule="para" parents="14744 15558"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u \ (x \ w),x,u))) = a(z,z,a(x,(y \ v5) * v5,x * (u \ w)))
    ]]></literal>
    <justification jstring="[para(14955(a,1),15558(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14955 15558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      a(x,y,a(z,z,L((u * x) * w,u,u))) = a(z,z,a(x,(y \ v5) * v5,x * (u \ w)))
    ]]></literal>
    <justification jstring="[para(15145(a,1),15558(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15145 15558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      a(x,a(y,y,z) / u,a(w,w,v5)) = a(w,w,a(x,a(y,y,z) \ u,v5))
    ]]></literal>
    <justification jstring="[para(8(a,1),15560(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8 15560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      a(x,a(y,y,z) / u,a(w,w,v5)) = a(w,w,a(x,a(z,y,y) * u,v5))
    ]]></literal>
    <justification jstring="[para(15078(a,1),15563(a,2,3))].">
      <j1 rule="para" parents="15078 15563"/>
    </justification>
  </clause>

  <clause id="15565">
    <literal><![CDATA[
      a(x,y \ a(z,z,u),a(w,w,v5)) = a(w,w,a(x,a(u,z,z) * y,v5))
    ]]></literal>
    <justification jstring="[hyper(10163,a,15564,a)].">
      <j1 rule="hyper" parents="10163 15564"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      a(x,y * a(z,z,u),a(w,v5,v5)) = a(v5,v5,a(x,a(u,z,z) * y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15551,a(flip),b,15565,a)].">
      <j1 rule="hyper" parents="65 15551 15565"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u \ (x \ w),x,u))) = a(z,z,a(x,(y \ v5) * v5,x * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,15504,a(flip),b,15561,a),flip(a)].">
      <j1 rule="hyper" parents="325 15504 15561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      a(x,y,a(z,z,L((u * x) * w,u,u))) = a(z,z,a(x,(y \ v5) * v5,x * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,15504,a(flip),b,15562,a),flip(a)].">
      <j1 rule="hyper" parents="325 15504 15562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u \ (x \ w),x,u))) = a(x,y,a(z,z,x * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,15558,a(flip),b,15567,a),flip(a)].">
      <j1 rule="hyper" parents="325 15558 15567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      a(x,y,a(z,z,L((x \ u) * w,x,w))) = a(x,y,a(z,z,x * (w * u)))
    ]]></literal>
    <justification jstring="[para(14703(a,1),15569(a,1,3))].">
      <j1 rule="para" parents="14703 15569"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      a(x,y,a(z,z,L((x * u) * w,x,w))) = a(x,y,a(z,z,x * (w * u)))
    ]]></literal>
    <justification jstring="[para(15505(a,1),15570(a,1,3))].">
      <j1 rule="para" parents="15505 15570"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,w,w)) = a(x,u,a(w,w,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15259,a(flip),b,15571,a)].">
      <j1 rule="hyper" parents="65 15259 15571"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      a(x,y,a(z,z,L((u * x) * w,u,u))) = a(x,y,a(z,z,x * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(325,a,15558,a(flip),b,15568,a),flip(a)].">
      <j1 rule="hyper" parents="325 15558 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      a(x,y,a(z,z,(u * x) * w)) = a(x,y,a(z,z,x * (u * w)))
    ]]></literal>
    <justification jstring="[para(14697(a,1),15574(a,1,3))].">
      <j1 rule="para" parents="14697 15574"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      a(x,x,((y * L(z,u,x)) * w) * (y * w)) = a(x,x,z * a(y,L(z,u,x),L(z,u,x) * (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15495,a(flip),b,15496,a)].">
      <j1 rule="hyper" parents="65 15495 15496"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      a(x,x,(L(y / z,z \ y,u) * a(w,w,L(v5,y,z))) * v6) = a(x,x,v6 * ((a(w,w,v5) * y) / z))
    ]]></literal>
    <justification jstring="[para(10814(a,1),15527(a,1,3,1,1))].">
      <j1 rule="para" parents="10814 15527"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      a(x,x,y * a(z,L(y,u,x),L(y,u,x) * (z \ w))) = a(x,x,L(L(y,u,x),z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14719,a(flip),b,15577,a),flip(a)].">
      <j1 rule="hyper" parents="65 14719 15577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      a(x,x,y * a(z,L(y,u,x),L(y,u,x) * (z \ w))) = a(x,x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14538,a(flip),b,15579,a),flip(a)].">
      <j1 rule="hyper" parents="325 14538 15579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      a(x,x,y * a(z,y,L(y,u,x) * (z \ w))) = a(x,x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15325,a(flip),b,15580,a)].">
      <j1 rule="hyper" parents="65 15325 15580"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      a(x,x,y * L(z / u,u \ z,w)) = a(x,x,y * ((a(v5,v5,v6) * z) / u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15522,a(flip),b,15578,a)].">
      <j1 rule="hyper" parents="65 15522 15578"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      a(x,x,y * L(z \ u,z \ u,w)) = a(x,x,y * ((a(v5,v5,v6) * u) / z))
    ]]></literal>
    <justification jstring="[hyper(10539,a,15584,a)].">
      <j1 rule="hyper" parents="10539 15584"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      a(x,x,y * ((a(z,z,u) * w) / v5)) = a(x,x,y * (v5 \ w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15471,a(flip),b,15585,a),flip(a)].">
      <j1 rule="hyper" parents="65 15471 15585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      a(x,x,y * ((a(z,z,u) * w) / v5)) = a(x,x,y * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15494,a(flip),b,15587,a),flip(a)].">
      <j1 rule="hyper" parents="325 15494 15587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      a(x,x,y * (z \ (a(u,u,w) * v5))) = a(x,x,y * (z * v5))
    ]]></literal>
    <justification jstring="[hyper(10154,a,15588,a)].">
      <j1 rule="hyper" parents="10154 15588"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      a(x,x,(y * (a(z,z,u) * w)) * v5) = a(x,x,v5 * (y * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15492,a,b,15589,a)].">
      <j1 rule="hyper" parents="65 15492 15589"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      a(x,x,y * (z * (a(u,u,w) * v5))) = a(x,x,y * (z * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15494,a(flip),b,15589,a)].">
      <j1 rule="hyper" parents="65 15494 15589"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      a(x,x,y * (z * a(u,u,w))) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,10311,a(flip),b,15590,a),flip(a)].">
      <j1 rule="hyper" parents="65 10311 15590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      a(x,x,y * (a(z,z,u) * w)) = a(x,x,w * y)
    ]]></literal>
    <justification jstring="[para(7190(a,2),15592(a,1,3,2))].">
      <j1 rule="para" parents="7190 15592"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      a(x,x,(L(y,z,z) * u) * w) = a(x,x,w * (y * u))
    ]]></literal>
    <justification jstring="[para(14569(a,1),15593(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14569 15593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      a(x,x,a(y,z,(y \ z) * u)) = a(x,x,L(u,y,z) * ((y * u) * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15539,a(flip),b,15594,a)].">
      <j1 rule="hyper" parents="65 15539 15594"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      a(x,x,y * (L(z * u,z * u,w) * v5)) = a(x,x,(((1 / z) \ u) * v5) * y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15533,a(flip),b,15591,a),flip(a)].">
      <j1 rule="hyper" parents="65 15533 15591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      a(x,x,a(y,z,(y \ z) * u)) = a(x,x,L(u,y,z) * L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,10645,a(flip),b,15595,a),flip(a)].">
      <j1 rule="hyper" parents="325 10645 15595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      a(x,x,a(y,z,(y \ z) * u)) = a(x,x,L(u,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,15471,a(flip),b,15598,a),flip(a)].">
      <j1 rule="hyper" parents="325 15471 15598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      a(x,x,a(y,z,(y \ z) * u)) = a(x,x,u * L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,10045,a,b,15599,a),flip(a)].">
      <j1 rule="hyper" parents="325 10045 15599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      a(x,x,a(y,z,(y \ z) * u)) = a(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14681,a(flip),b,15601,a),flip(a)].">
      <j1 rule="hyper" parents="325 14681 15601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      a(x,x,a(y,z,z * (y * u))) = a(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[para(14943(a,1),15602(a,1,3))].">
      <j1 rule="para" parents="14943 15602"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      a(x,x,a(y,z,u * y)) = a(x,x,a(z,y,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15506,a(flip),b,15603,a),flip(a)].">
      <j1 rule="hyper" parents="65 15506 15603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      a(x,x,a(y,z,y * u)) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15451,a(flip),b,15604,a),flip(a)].">
      <j1 rule="hyper" parents="65 15451 15604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      a(x,y,a(z,z,x * u)) = a(u,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15159,a,b,15605,a)].">
      <j1 rule="hyper" parents="65 15159 15605"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      a(x,x,(((1 / y) \ z) * u) * w) = a(x,x,((y * z) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15532,a(flip),b,15596,a),flip(a)].">
      <j1 rule="hyper" parents="65 15532 15596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      a(x,x,((y \ z) * u) * w) = a(x,x,((y * z) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11338,a(flip),b,15608,a)].">
      <j1 rule="hyper" parents="65 11338 15608"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      a(x,x,((y * z) * (a(u,u,w) * v5)) * v6) = a(x,x,v6 * ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15590,a(flip),b,15609,a),flip(a)].">
      <j1 rule="hyper" parents="65 15590 15609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      a(x,x,((y * T(z,u)) * (y * w)) * (T((y \ z) * y,u) * w)) = a(x,x,a(y \ T(z,u),y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14946,a(flip),b,15609,a),flip(a)].">
      <j1 rule="hyper" parents="65 14946 15609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      a(x,x,(((y / z) * y) * u) * w) = a(x,x,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(85(a,1),15609(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="85 15609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      a(x,x,(((y \ z) * z) * u) * w) = a(x,x,(y * u) * w)
    ]]></literal>
    <justification jstring="[hyper(10275,a,15612,a)].">
      <j1 rule="hyper" parents="10275 15612"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      a(x,x,y * ((z \ u) * w)) = a(x,x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15590,a(flip),b,15610,a),flip(a)].">
      <j1 rule="hyper" parents="65 15590 15610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      a(x,x,(y * z) * (((u / (w * w)) * z) * (u * y))) = a(x,x,a(z / (u / (w * w)),u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15342,a(flip),b,15614,a),flip(a)].">
      <j1 rule="hyper" parents="65 15342 15614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      a(x,x,(y * z) * ((((u * u) \ w) * z) * (w * y))) = a(x,x,a(z / (w / (u * u)),w,y))
    ]]></literal>
    <justification jstring="[hyper(10278,a,15615,a)].">
      <j1 rule="hyper" parents="10278 15615"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      a(x,x,a(y / (z / (u * u)),z,w)) = a(x,x,(w * y) * ((z * y) * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(11242,a,15616,a),flip(a)].">
      <j1 rule="hyper" parents="11242 15616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      a(x,x,(((y \ z) * y) * u) * ((y * T(z,w)) * (y * u))) = a(x,x,a(y \ T(z,w),y,u))
    ]]></literal>
    <justification jstring="[hyper(10394,a,15611,a)].">
      <j1 rule="hyper" parents="10394 15611"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      a(x,x,a(y \ T(z,u),y,w)) = a(x,x,((y * w) * (y * z)) * (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10504,a(flip),b,15618,a),flip(a)].">
      <j1 rule="hyper" parents="65 10504 15618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      a(x,x,a(y \ T(z,u),y,w)) = a(x,x,(z * w) * ((y * w) * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(325,a,10360,a(flip),b,15619,a),flip(a)].">
      <j1 rule="hyper" parents="325 10360 15619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15623">
    <literal><![CDATA[
      a(x,x,a(T(y,z) * u,u,w)) = a(x,x,(y * w) * ((u * w) * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14998,a(flip),b,15621,a)].">
      <j1 rule="hyper" parents="65 14998 15621"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      a(x,x,(y * z) * ((u * z) * (u * y))) = a(x,x,a(y * u,u,z))
    ]]></literal>
    <justification jstring="[para(112(a,1),15623(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="112 15623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      a(x,x,a(y / (z / (u * u)),z,w)) = a(x,x,a(w * z,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15617,a,b,15624,a)].">
      <j1 rule="hyper" parents="65 15617 15624"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      a(x,x,a(y * z,z,u)) = a(x,x,a(y,z,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13165,a(flip),b,15625,a),flip(a)].">
      <j1 rule="hyper" parents="65 13165 15625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      a(x,x,a(y * z,y,u)) = a(x,x,a(z,y,y * u))
    ]]></literal>
    <justification jstring="[hyper(7507,a,15626,a)].">
      <j1 rule="hyper" parents="7507 15626"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      a(x,x,a(y,z,z * (u * x))) = a(y * z,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15225,a(flip),b,15626,a),flip(a)].">
      <j1 rule="hyper" parents="65 15225 15626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      x * a(y,y,a(z,u,u * x)) = L(x,u,a(y,y,u * z))
    ]]></literal>
    <justification jstring="[para(15627(a,1),15193(a,1,2))].">
      <j1 rule="para" parents="15627 15193"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      a(x,x,a(y,z,z * u)) * y = a(x,x,u) * ((y / z) * (a(x,x,u) \ z))
    ]]></literal>
    <justification jstring="[para(15627(a,1),15243(a,1,1))].">
      <j1 rule="para" parents="15627 15243"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      a(x * y,y,a(z,u,u)) = a(x,y,a(u,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15164,a(flip),b,15628,a),flip(a)].">
      <j1 rule="hyper" parents="65 15164 15628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      a(x,y,a(z * y,u,u)) = a(z,y,a(u,u,y * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15206,a,b,15631,a)].">
      <j1 rule="hyper" parents="65 15206 15631"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      a(x,y \ 1,a(z,z,(y \ 1) * u)) = a(u,y \ 1,a(x * y,z,z))
    ]]></literal>
    <justification jstring="[para(1890(a,1),15632(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1890 15632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      a(x,a(x,y,y) * z,a(u,u,(a(x,y,y) * z) * w)) = a(w,a(x,y,y) * z,a(R(x,y,y) * z,u,u))
    ]]></literal>
    <justification jstring="[para(14561(a,1),15632(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14561 15632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      a(x,(y * x) \ 1,a(z,z,((y * x) \ 1) * u)) = a(u,(y * x) \ 1,a(y,z,L(z,x,x)))
    ]]></literal>
    <justification jstring="[para(14849(a,1),15633(a,2,3))].">
      <j1 rule="para" parents="14849 15633"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      a(x,x,y) * ((z / u) * (a(x,x,y) \ u)) = L(z,u,a(x,x,u * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15218,a(flip),b,15630,a),flip(a)].">
      <j1 rule="hyper" parents="65 15218 15630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      a(x,x,y) * (z * ((a(x,x,y) * z) \ u)) = L(u,z,a(x,x,z * y))
    ]]></literal>
    <justification jstring="[para(15291(a,1),15636(a,1,2))].">
      <j1 rule="para" parents="15291 15636"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      (a(x,x,y) * z) \ L(u,z,a(x,x,z * y)) = L((a(x,x,y) * z) \ u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,15637,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="132 15637 100"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      a(x,x,y) * (z * L(z \ u,z,a(x,x,y))) = L(a(x,x,y) * u,z,a(x,x,z * y))
    ]]></literal>
    <justification jstring="[para(102(a,2),15637(a,1,2,2))].">
      <j1 rule="para" parents="102 15637"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      a(x,x,y) * ((z \ u) * ((a(x,x,y) * (z \ u)) \ w)) = L(w,u / z,a(x,x,(u / z) * y))
    ]]></literal>
    <justification jstring="[para(9825(a,1),15637(a,1,2))].">
      <j1 rule="para" parents="9825 15637"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      (a(x,x,y) * z) \ L(u,z,a(x,x,z * y)) = z \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(325,a,13368,a(flip),b,15638,a),flip(a)].">
      <j1 rule="hyper" parents="325 13368 15638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(a(x,x,y) \ z,a(x,x,y)) * L(u,z / a(x,x,y),a(x,x,(z / a(x,x,y)) * y)) = z * ((z / a(x,x,y)) \ (a(x,x,y) \ u))
    ]]></literal>
    <justification jstring="[para(15641(a,1),2778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15641 2778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      L(a(x,x,y) * z,u,a(x,x,u * y)) = (a(x,x,y) * u) * (u \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13361,a(flip),b,15639,a),flip(a)].">
      <j1 rule="hyper" parents="65 13361 15639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      a(x,(y * x) \ 1,a(z,z,((y * x) \ 1) * u)) = a(u,(y * x) \ 1,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(15258(a,1),15635(a,2,3))].">
      <j1 rule="para" parents="15258 15635"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,((((y \ z) \ z) * x) \ 1) * w)) = a(w,(((y \ z) \ z) * x) \ 1,a(y,u,u))
    ]]></literal>
    <justification jstring="[para(1871(a,1),15644(a,2,3))].">
      <j1 rule="para" parents="1871 15644"/>
    </justification>
  </clause>

  <clause id="15647">
    <literal><![CDATA[
      L(x,y / a(z,z,u),a(z,z,(y / a(z,z,u)) * u)) = a(z,z,u) * ((a(z,z,u) \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[para(10(a,1),15640(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      L(x,y / a(z,z,u),a(z,z,(y / a(z,z,u)) * u)) = a(z,z,u) * (y * ((a(z,z,u) * y) \ x))
    ]]></literal>
    <justification jstring="[para(15289(a,1),15647(a,2,2))].">
      <j1 rule="para" parents="15289 15647"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      L(x,y / a(z,z,u),a(z,z,(y / a(z,z,u)) * u)) = L(x,y,a(z,z,y * u))
    ]]></literal>
    <justification jstring="[hyper(325,a,15637,a(flip),b,15648,a),flip(a)].">
      <j1 rule="hyper" parents="325 15637 15648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      a(x,a(x,y,y) * z,a(u,u,(a(x,y,y) * z) * w)) = a(w,a(x,y,y) * z,a(L(x,y,y) * z,u,u))
    ]]></literal>
    <justification jstring="[para(11285(a,1),15634(a,2,3))].">
      <j1 rule="para" parents="11285 15634"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      a(x,a(x,y,y) * z,a(u,u,(a(x,y,y) * z) * w)) = a(w,a(x,y,y) * z,a(u,u,x * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15503,a(flip),b,15650,a),flip(a)].">
      <j1 rule="hyper" parents="325 15503 15650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      a(x,a(x,y,y) * z,a(u,u,(a(x,y,y) * z) * w)) = a(w,x,a(u,u,x * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15514,a(flip),b,15651,a),flip(a)].">
      <j1 rule="hyper" parents="325 15514 15651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      a(x,a(x,y,y) * z,a(u,u,w * z)) = a(w,x,a(u,u,x * z))
    ]]></literal>
    <justification jstring="[para(15531(a,1),15653(a,1,3))].">
      <j1 rule="para" parents="15531 15653"/>
    </justification>
  </clause>

  <clause id="15657">
    <literal><![CDATA[
      R(R(x,y,z * u),y * (z * u),u \ (z \ (u \ z))) = ((x * y) * (u \ z)) / (y * (u \ z))
    ]]></literal>
    <justification jstring="[para(15425(a,1),15426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15425 15426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      R(R(x,y,z * u),y * (z * u),u \ (z \ (u \ z))) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(325,a,20,a,b,15657,a),flip(a)].">
      <j1 rule="hyper" parents="325 20 15657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      L(R(x,y,z * u),y * (z * u),a(u,u,z)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(65,a,13378,a(flip),b,15658,a)].">
      <j1 rule="hyper" parents="65 13378 15658"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,((((y \ z) \ z) * x) \ 1) * w)) = a(w,((y \ z) \ z) * x,a(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,12215,a(flip),b,15645,a),flip(a)].">
      <j1 rule="hyper" parents="325 12215 15645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,((((y \ z) \ z) * x) \ 1) * w)) = a(w,x * y,a(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,10210,a(flip),b,15661,a),flip(a)].">
      <j1 rule="hyper" parents="325 10210 15661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,((((y \ z) \ z) * x) \ 1) * w)) = a(y,x,a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,15391,a(flip),b,15662,a),flip(a)].">
      <j1 rule="hyper" parents="325 15391 15662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,(((y \ z) \ z) * x) * w)) = a(y,x,a(w,u,u))
    ]]></literal>
    <justification jstring="[para(10112(a,1),15664(a,1,3))].">
      <j1 rule="para" parents="10112 15664"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,(((y \ z) * z) * x) * w)) = a(y,x,a(w,u,u))
    ]]></literal>
    <justification jstring="[para(15609(a,1),15665(a,1,3))].">
      <j1 rule="para" parents="15609 15665"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,(y * x) * w)) = a(y,x,a(w,u,u))
    ]]></literal>
    <justification jstring="[para(15613(a,1),15666(a,1,3))].">
      <j1 rule="para" parents="15613 15666"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) * x) \ 1,a(u,u,x * (y * w))) = a(y,x,a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15575,a(flip),b,15667,a)].">
      <j1 rule="hyper" parents="65 15575 15667"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      a(x,((y \ z) \ z) * x,a(x * (y * u),w,w)) = a(y,x,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,12839,a(flip),b,15668,a)].">
      <j1 rule="hyper" parents="65 12839 15668"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      a(x,(y \ z) \ z,a(x * (y * u),w,w)) = a(y,x,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15389,a(flip),b,15670,a)].">
      <j1 rule="hyper" parents="65 15389 15670"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      a(x,(y \ z) * z,a(x * (y * u),w,w)) = a(y,x,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15550,a(flip),b,15671,a)].">
      <j1 rule="hyper" parents="65 15550 15671"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      a(x * (y * z),y,a(u,u,x)) = a(y,x,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15559,a(flip),b,15672,a)].">
      <j1 rule="hyper" parents="65 15559 15672"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      a(x,y,a(y,z,x * (z * u))) = a(z,x,a(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15186,a,b,15673,a)].">
      <j1 rule="hyper" parents="65 15186 15673"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      a(x * a(y,y,z),u,a(u,w,(w * v5) * (a(z,y,y) * x))) = a(w,x * a(y,y,z),a(v5,u,u))
    ]]></literal>
    <justification jstring="[para(14999(a,1),15674(a,1,3))].">
      <j1 rule="para" parents="14999 15674"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      a(x * a(y,y,z),u,a(w,w,x * (u * v5))) = a(u,x * a(y,y,z),a(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15534,a(flip),b,15675,a)].">
      <j1 rule="hyper" parents="65 15534 15675"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      a(x * (y * z),y,a(u,u,x)) = a(y,x * a(w,w,v5),a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15472,a(flip),b,15676,a)].">
      <j1 rule="hyper" parents="65 15472 15676"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      a(x,y * a(z,z,u),a(w,v5,v5)) = a(x,y,a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15673,a(flip),b,15678,a),flip(a)].">
      <j1 rule="hyper" parents="65 15673 15678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      a(x,x,a(y,a(z,u,u) * w,v5)) = a(y,w,a(v5,x,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15566,a(flip),b,15680,a)].">
      <j1 rule="hyper" parents="65 15566 15680"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,a(w,w,v5)) = a(x,u,a(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15159,a,b,15681,a)].">
      <j1 rule="hyper" parents="65 15159 15681"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      a(x,y,a(z * y,u,u)) = a(z,x,a(u,u,x * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15655,a(flip),b,15683,a),flip(a)].">
      <j1 rule="hyper" parents="65 15655 15683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) = a(z,z,a(x * u,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15186,a,b,15684,a),flip(a)].">
      <j1 rule="hyper" parents="65 15186 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      a(x,y,a(z * y,x,u)) = a(z,u,a(x,x,u * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15178,a,b,15684,a)].">
      <j1 rule="hyper" parents="65 15178 15684"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      a(x,x,L(y,z,u * z)) = a(u,y,a(x,x,y * z)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(15684(a,1),15217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15684 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) = a(z,z,a(x,u,u * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,15626,a(flip),b,15686,a),flip(a)].">
      <j1 rule="hyper" parents="325 15626 15686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      L(x,y,a(z,z,y * u)) = x * a(u,x,a(z,z,x * y))
    ]]></literal>
    <justification jstring="[para(15689(a,2),15629(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15689 15629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z) = R(x,y,z) \ (a(x,x \ 1,u) / (1 / R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12044(a,1),15138(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12044 15138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z) = (R(x,y,z) \ 1) * (R(x,y,z) * a(x,x \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,13655,a(flip),b,15691,a),flip(a)].">
      <j1 rule="hyper" parents="325 13655 15691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z) = (x \ 1) * (x * a(x,x \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,13559,a(flip),b,15692,a),flip(a)].">
      <j1 rule="hyper" parents="325 13559 15692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z) = (x \ 1) * R(x,x \ 1,u)
    ]]></literal>
    <justification jstring="[para(11652(a,1),15694(a,2,2))].">
      <j1 rule="para" parents="11652 15694"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      L(x \ R(x,R(x,y,z),u * R(x,y,z)),y,z) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(325,a,11596,a(flip),b,15696,a),flip(a)].">
      <j1 rule="hyper" parents="325 11596 15696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      L(x \ R(x,R(x,y,z),u * L(x,y,z)),y,z) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[para(13029(a,1),15697(a,1,1,2))].">
      <j1 rule="para" parents="13029 15697"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      L(x \ R(x,L(x,y,z),u * L(x,y,z)),y,z) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[para(9941(a,1),15698(a,1,1,2))].">
      <j1 rule="para" parents="9941 15698"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      L(a(x,x,L(y * L(x,z,u),z,u)),z,u) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(13514(a,1),15699(a,1,1))].">
      <j1 rule="para" parents="13514 15699"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      a(x,x,y * L(x,z,u)) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(65,a,14827,a(flip),b,15700,a)].">
      <j1 rule="hyper" parents="65 14827 15700"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      a(x,x,L(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(10136,a,15701,a)].">
      <j1 rule="hyper" parents="10136 15701"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      L((a(x,x,y) \ K(z,u)) \ (K(z,u) * (w \ v5)),a(x,x,y) \ 1,w / K(z,u)) = (K(z,u) * ((a(x,x,y) * K(z,u)) \ w)) \ v5
    ]]></literal>
    <justification jstring="[para(9571(a,1),15292(a,1,1,2))].">
      <j1 rule="para" parents="9571 15292"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      L(T(a(x,x,y) \ 1,K(z,u)) \ (w \ v5),a(x,x,y) \ 1,w / K(z,u)) = (K(z,u) * ((a(x,x,y) * K(z,u)) \ w)) \ v5
    ]]></literal>
    <justification jstring="[para(7536(a,1),15705(a,1,1))].">
      <j1 rule="para" parents="7536 15705"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      L((a(x,x,y) \ 1) \ (z \ u),a(x,x,y) \ 1,z / K(w,v5)) = (K(w,v5) * ((a(x,x,y) * K(w,v5)) \ z)) \ u
    ]]></literal>
    <justification jstring="[para(8495(a,1),15706(a,1,1,1))].">
      <j1 rule="para" parents="8495 15706"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      L(a(x,x,y) * (z \ u),a(x,x,y) \ 1,z / K(w,v5)) = (K(w,v5) * ((a(x,x,y) * K(w,v5)) \ z)) \ u
    ]]></literal>
    <justification jstring="[para(14280(a,1),15707(a,1,1))].">
      <j1 rule="para" parents="14280 15707"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      L(a(x,x,y) * (z \ u),a(x,x,y) \ 1,z) = (K(w,v5) * ((a(x,x,y) * K(w,v5)) \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(2864,a,15709,a)].">
      <j1 rule="hyper" parents="2864 15709"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      L(a(x,x,y) * (z \ u),a(y,x,x),z) = (K(w,v5) * ((a(x,x,y) * K(w,v5)) \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(65,a,13069,a(flip),b,15710,a)].">
      <j1 rule="hyper" parents="65 13069 15710"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      L(a(x,x,y) * (z \ u),a(y,x,x),z) = (a(x,x,y) \ z) \ u
    ]]></literal>
    <justification jstring="[para(9570(a,1),15711(a,2,1))].">
      <j1 rule="para" parents="9570 15711"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      L(a(x,x,y * x) * (y \ z),a(y * x,x,x),y) = (x * ((1 / x) * y)) \ z
    ]]></literal>
    <justification jstring="[para(12264(a,1),15712(a,2,1))].">
      <j1 rule="para" parents="12264 15712"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      L(a(x,x,y * x) * (y \ z),a(x,x,y),y) = (x * ((1 / x) * y)) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,14203,a(flip),b,15713,a)].">
      <j1 rule="hyper" parents="65 14203 15713"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      L(a(x,x,y * x) * (y \ z),y,a(x,x,y)) = (x * ((1 / x) * y)) \ z
    ]]></literal>
    <justification jstring="[hyper(65,a,10605,a(flip),b,15714,a)].">
      <j1 rule="hyper" parents="65 10605 15714"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      a(x,x,y * x) * (y \ z) = (x * ((1 / x) * y)) \ z
    ]]></literal>
    <justification jstring="[hyper(14600,a,15715,a)].">
      <j1 rule="hyper" parents="14600 15715"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      a(x * y,y,(y * ((1 / y) * x)) \ z) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[para(15716(a,1),15299(a,1,3))].">
      <j1 rule="para" parents="15716 15299"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      a(x * y,y,(y * ((y \ 1) * x)) \ z) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,10446,a(flip),b,15718,a)].">
      <j1 rule="hyper" parents="65 10446 15718"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      a(x * y,y,L(x,y \ 1,y) \ z) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[para(261(a,1),15719(a,1,3,1))].">
      <j1 rule="para" parents="261 15719"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      a(x * y,y,L(x,y,y) \ z) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12498,a(flip),b,15720,a)].">
      <j1 rule="hyper" parents="65 12498 15720"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      a(x * y,y,L(x,y,y) * z) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15031,a(flip),b,15721,a)].">
      <j1 rule="hyper" parents="65 15031 15721"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      a(x * y,y,L(z,y,y) * x) = a(x * y,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15149,a,b,15722,a)].">
      <j1 rule="hyper" parents="65 15149 15722"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      a(T(((x \ 1) * y) * x,z),x,L(u,x,x) * ((x \ 1) * T(y,z))) = a(((x \ 1) * T(y,z)) * x,x,((x \ 1) * T(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(5188(a,2),15723(a,1,1))].">
      <j1 rule="para" parents="5188 15723"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      a(T(((x \ 1) * y) * x,z),x,(y * (x \ 1)) * L(u,x,x)) = a(((x \ 1) * T(y,z)) * x,x,((x \ 1) * T(y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(10395,a,15724,a)].">
      <j1 rule="hyper" parents="10395 15724"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      a(T(((x \ 1) * y) * x,z),x,(y * x) * L(u,x,x)) = a(((x \ 1) * T(y,z)) * x,x,((x \ 1) * T(y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,10644,a(flip),b,15725,a)].">
      <j1 rule="hyper" parents="65 10644 15725"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      a(((x \ 1) * T(y,z)) * x,x,((x \ 1) * T(y,z)) * u) = a(((x \ 1) * y) * x,x,(y * x) * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(1876,a,15726,a),flip(a)].">
      <j1 rule="hyper" parents="1876 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      a(((x \ 1) * T(y,z)) * x,x,((x \ 1) * T(y,z)) * u) = a((x * y) * x,x,(y * x) * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,6904,a(flip),b,15727,a),flip(a)].">
      <j1 rule="hyper" parents="325 6904 15727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      a(((x \ 1) * T(y,z)) * x,x,((x \ 1) * T(y,z)) * u) = a(y,x,L((y * x) * L(u,x,x),x,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,14851,a(flip),b,15729,a),flip(a)].">
      <j1 rule="hyper" parents="325 14851 15729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      a(((x \ 1) * T(y,z)) * x,x,((x \ 1) * T(y,z)) * u) = a(y,x,x * (y \ L(u,x,x)))
    ]]></literal>
    <justification jstring="[hyper(325,a,15126,a(flip),b,15730,a),flip(a)].">
      <j1 rule="hyper" parents="325 15126 15730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      a(T(((x \ 1) * y) * x,z),x,((x \ 1) * T(y,z)) * u) = a(y,x,x * (y \ L(u,x,x)))
    ]]></literal>
    <justification jstring="[para(5188(a,2),15731(a,1,1))].">
      <j1 rule="para" parents="5188 15731"/>
    </justification>
  </clause>

  <clause id="15733">
    <literal><![CDATA[
      a(T(((x \ 1) * y) * x,z),x,((x \ 1) * y) * u) = a(y,x,x * (y \ L(u,x,x)))
    ]]></literal>
    <justification jstring="[hyper(10274,a,15732,a)].">
      <j1 rule="hyper" parents="10274 15732"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      a(T(((x \ 1) * y) * x,z),x,(x * y) * u) = a(y,x,x * (y \ L(u,x,x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,10437,a(flip),b,15733,a)].">
      <j1 rule="hyper" parents="65 10437 15733"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      a(((x \ 1) * y) * x,x,(x * y) * z) = a(y,x,x * (y \ L(z,x,x)))
    ]]></literal>
    <justification jstring="[hyper(1876,a,15734,a)].">
      <j1 rule="hyper" parents="1876 15734"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      a((x * y) * x,x,(x * y) * z) = a(y,x,x * (y \ L(z,x,x)))
    ]]></literal>
    <justification jstring="[hyper(65,a,6904,a(flip),b,15735,a)].">
      <j1 rule="hyper" parents="65 6904 15735"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      a(x,y,L((y * x) * z,y,y)) = a(x,y,y * (x \ L(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14851,a(flip),b,15736,a)].">
      <j1 rule="hyper" parents="65 14851 15736"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      a(x,y,y * (x \ L(z,y,y))) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15145,a(flip),b,15737,a),flip(a)].">
      <j1 rule="hyper" parents="65 15145 15737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      a(x,R(y,z,y),x * (z * y)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15313,a,b,15738,a)].">
      <j1 rule="hyper" parents="65 15313 15738"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      a(x,y,x * (y \ z)) = a(x,y,x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(10220,a,15739,a),flip(a)].">
      <j1 rule="hyper" parents="10220 15739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      L(x,y,a(z,u,u * (z \ w))) = L(x,y,a(z,u,z * (w * u)))
    ]]></literal>
    <justification jstring="[para(15740(a,1),15269(a,2,3))].">
      <j1 rule="para" parents="15740 15269"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      a((K(x,y * x) * a(y,x,x)) \ z,u,(x * (y \ (x \ y))) * K(y * x,x)) = a(a(y,x,x) * (K(y * x,x) * z),u,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(2618(a,1),15063(a,1,1,1))].">
      <j1 rule="para" parents="2618 15063"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      a((a(x,y,y) * K(y,x * y)) \ z,u,(y * (x \ (y \ x))) * K(x * y,y)) = a(a(x,y,y) * (K(x * y,y) * z),u,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(6072(a,1),15743(a,1,1,1))].">
      <j1 rule="para" parents="6072 15743"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      a((x \ (y * (x * (y \ 1)))) \ z,u,(y * (x \ (y \ x))) * K(x * y,y)) = a(a(x,y,y) * (K(x * y,y) * z),u,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(14950(a,1),15744(a,1,1,1))].">
      <j1 rule="para" parents="14950 15744"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      a((x \ (y * (x * (y \ 1)))) \ z,u,y * (x \ (y \ x))) = a(a(x,y,y) * (K(x * y,y) * z),u,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(10142,a,15745,a)].">
      <j1 rule="hyper" parents="10142 15745"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      a(a(x,y,y) * (K(x * y,y) * z),u,a(x,y,y)) = a((x \ (y * (x * (y \ 1)))) \ z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,11683,a(flip),b,15746,a),flip(a)].">
      <j1 rule="hyper" parents="65 11683 15746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      a(a(x,y,y) * (K(x * y,y) * z),u,a(x,y,y)) = a((x \ (y * (x * (y \ 1)))) * z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,14871,a(flip),b,15748,a),flip(a)].">
      <j1 rule="hyper" parents="325 14871 15748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      a(x * (L(T(x,y * x),x,y) \ z),u,a(y,x,x)) = a((y \ (x * (y * (x \ 1)))) * z,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(12763(a,1),15749(a,1,1))].">
      <j1 rule="para" parents="12763 15749"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      a((x \ (y * (x * (y \ 1)))) * z,u,a(y,y,x)) = a(x,u,a(y,y,L(T(y,x * y),y,x) \ z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15211,a(flip),b,15750,a),flip(a)].">
      <j1 rule="hyper" parents="65 15211 15750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      a((x \ (y * (x * (y \ 1)))) * z,u,a(y,y,x)) = a(x,u,a(y,y,L(T(y,x * y),y,x) * z))
    ]]></literal>
    <justification jstring="[para(14704(a,1),15751(a,2,3))].">
      <j1 rule="para" parents="14704 15751"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      a((x \ (y * (x * (y \ 1)))) * z,u,a(y,y,x)) = a(x,u,a(y,y,L(y,y,x) * z))
    ]]></literal>
    <justification jstring="[para(10044(a,1),15752(a,2,3))].">
      <j1 rule="para" parents="10044 15752"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      a((x \ (y * (x * (y \ 1)))) * z,u,a(y,y,x)) = a(x,u,a(y,y,z * y))
    ]]></literal>
    <justification jstring="[para(15702(a,1),15753(a,2,3))].">
      <j1 rule="para" parents="15702 15753"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      a((x \ (y * (x * (y \ 1)))) * z,u,a(y,y,x)) = a(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13990,a(flip),b,15755,a),flip(a)].">
      <j1 rule="hyper" parents="325 13990 15755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      a((x * (y * (x * (y \ 1)))) * z,u,a(x,y,y)) = a(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15517,a(flip),b,15756,a)].">
      <j1 rule="hyper" parents="65 15517 15756"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      a(x,y,a(z,z,x * (u * (z * (x * (z \ 1)))))) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15572,a(flip),b,15758,a)].">
      <j1 rule="hyper" parents="65 15572 15758"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      a(x * (y * (z * (y \ 1))),y,a(u,z,y)) = a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15606,a(flip),b,15759,a)].">
      <j1 rule="hyper" parents="65 15606 15759"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (y * (z \ 1)))) = a(y,x,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15263,a(flip),b,15760,a)].">
      <j1 rule="hyper" parents="65 15263 15760"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (y * z))) = a(y,x,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(10643(a,1),15761(a,1,3))].">
      <j1 rule="para" parents="10643 15761"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      a(x,y,a(z,z,u * y)) = a(y,x,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13992,a(flip),b,15763,a)].">
      <j1 rule="hyper" parents="65 13992 15763"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) = a(y,x,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(10789,a,15764,a)].">
      <j1 rule="hyper" parents="10789 15764"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      a(x,y,a(z * y,x,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15687,a,b,15765,a)].">
      <j1 rule="hyper" parents="65 15687 15765"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      L(x,y,a(z,z,y * u)) = x * a(x,u,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(15765(a,1),15690(a,2,2))].">
      <j1 rule="para" parents="15765 15690"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      a(x,x,L(y,z,u * z)) = a(y,u,a(x,x,z)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(15765(a,1),15688(a,2,1))].">
      <j1 rule="para" parents="15765 15688"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      L(x,y,a(z,z,y * u)) = L(x,u,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,14606,a(flip),b,15767,a),flip(a)].">
      <j1 rule="hyper" parents="325 14606 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      a(x,x,L(y,z,u * z)) = a(x,x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15214,a(flip),b,15768,a),flip(a)].">
      <j1 rule="hyper" parents="325 15214 15768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ u) / z = u / (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(15770(a,1),15405(a,1,1,1))].">
      <j1 rule="para" parents="15770 15405"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      K(a(x,x,y) \ z,a(x,x,y)) * L(u,z / a(x,x,y),a(x,x,(z / a(x,x,y)) * y)) = z * ((a(x,x,y) \ z) \ (a(x,x,y) \ u))
    ]]></literal>
    <justification jstring="[para(7194(a,1),15642(a,2,2,1))].">
      <j1 rule="para" parents="7194 15642"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      1 * L(x,y / a(z,z,u),a(z,z,(y / a(z,z,u)) * u)) = y * ((a(z,z,u) \ y) \ (a(z,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(7175(a,1),15772(a,1,1))].">
      <j1 rule="para" parents="7175 15772"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      x * ((a(y,y,z) \ x) \ (a(y,y,z) \ u)) = 1 * L(u,x,a(y,y,x * z))
    ]]></literal>
    <justification jstring="[para(15649(a,1),15773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15649 15773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      x * ((a(y,y,z) \ x) \ (a(y,y,z) \ u)) = L(u,x,a(y,y,x * z))
    ]]></literal>
    <justification jstring="[hyper(325,a,7,a(flip),b,15775,a),flip(a)].">
      <j1 rule="hyper" parents="325 7 15775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      L(a(x,x,y) * z,u,a(x,x,u * y)) = u * ((a(x,x,y) \ u) \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),15776(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      (a(x,x,y) * z) * (z \ u) = z * ((a(x,x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15643,a(flip),b,15777,a)].">
      <j1 rule="hyper" parents="65 15643 15777"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      (a(x,x,y) * z) * (z \ (z * u)) = z * L(a(x,x,y) * u,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(14396(a,2),15778(a,2,2))].">
      <j1 rule="para" parents="14396 15778"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      x * L(a(y,y,z) * u,a(y,y,z),x) = (a(y,y,z) * x) * u
    ]]></literal>
    <justification jstring="[hyper(520,a,15779,a),flip(a)].">
      <j1 rule="hyper" parents="520 15779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      (x \ 1) * L(a(y,y,z) * u,a(y,y,z),x) = (a(y,y,z) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(1499(a,1),15780(a,1,2))].">
      <j1 rule="para" parents="1499 15780"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      (x \ 1) * L(a(y,y,z) * u,a(y,y,z),x) = (x \ a(y,y,z)) * u
    ]]></literal>
    <justification jstring="[para(14698(a,1),15782(a,2,1))].">
      <j1 rule="para" parents="14698 15782"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),a(w,z,y) * u,a(w,z,y)) = u \ L(u * L(x,a(w,z,y),u),a(w,z,y),a(w,z,y))
    ]]></literal>
    <justification jstring="[para(14279(a,1),15260(a,2,1))].">
      <j1 rule="para" parents="14279 15260"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),a(w,z,y) * u,a(w,z,y)) = u \ (u * L(x,a(w,z,y),u))
    ]]></literal>
    <justification jstring="[para(14279(a,1),15784(a,2,2))].">
      <j1 rule="para" parents="14279 15784"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),a(w,z,y) * u,a(w,z,y)) = L(x,a(w,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(325,a,9,a(flip),b,15785,a),flip(a)].">
      <j1 rule="hyper" parents="325 9 15785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15789">
    <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(65,a,15231,a(flip),b,15786,a)].">
      <j1 rule="hyper" parents="65 15231 15786"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      L(x * a(y,z \ (u * y),a(w,x,z)),z \ (u * y),a(y,w,z)) = L(x,a(z,(z \ u) * y,y),w)
    ]]></literal>
    <justification jstring="[para(14965(a,1),15789(a,2,2))].">
      <j1 rule="para" parents="14965 15789"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      (x * L(L(y,a(z,u,w),x),x,a(z,u,w))) / (a(z,u,w) \ (T(a(z,u,w),x) * y)) = L(x,T(a(z,u,w),x) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(13360(a,1),14510(a,1,1))].">
      <j1 rule="para" parents="13360 14510"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      (x * L(L(y,a(z,u,w),x),x,a(z,u,w))) / (a(z,u,w) \ (a(z,u,w) * y)) = L(x,T(a(z,u,w),x) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(7186(a,1),15792(a,1,2,2,1))].">
      <j1 rule="para" parents="7186 15792"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      (x * L(L(y,a(z,u,w),x),x,a(z,u,w))) / y = L(x,T(a(z,u,w),x) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),15793(a,1,2))].">
      <j1 rule="para" parents="9 15793"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      (x * L(L(y,a(z,u,w),x),x,a(z,u,w))) / y = L(x,a(z,u,w) * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,10808,a(flip),b,15794,a),flip(a)].">
      <j1 rule="hyper" parents="325 10808 15794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      (x * L(L(y,a(z,u,w),x),x,a(z,u,w))) / y = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,14428,a(flip),b,15796,a),flip(a)].">
      <j1 rule="hyper" parents="325 14428 15796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = (a(x,y,z) * a(x,y,z)) \ ((x \ (a(x,y,z) * x)) * L(a(x,y,z) * x,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(7207(a,1),14238(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7207 14238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = (a(x,y,z) * a(x,y,z)) \ (a(x,y,z) * L(a(x,y,z) * x,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(7207(a,1),15803(a,2,2,1))].">
      <j1 rule="para" parents="7207 15803"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = (a(x,y,z) * a(x,y,z)) \ (a(x,y,z) * (a(x,y,z) * x))
    ]]></literal>
    <justification jstring="[para(13411(a,1),15804(a,2,2,2))].">
      <j1 rule="para" parents="13411 15804"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = (a(x,y,z) * a(x,y,z)) \ (x * (a(x,y,z) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(11650(a,1),15807(a,2,2))].">
      <j1 rule="para" parents="11650 15807"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = (a(x,y,z) * a(x,y,z)) \ R(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(13491(a,1),15808(a,2,2))].">
      <j1 rule="para" parents="13491 15808"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = R((a(x,y,z) * a(x,y,z)) \ R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(325,a,1054,a,b,15810,a),flip(a)].">
      <j1 rule="hyper" parents="325 1054 15810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = R(R((a(x,y,z) * a(x,y,z)) \ x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(1054(a,2),15811(a,2,1))].">
      <j1 rule="para" parents="1054 15811"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = R(R(x * (z \ L(L(z,y,x),y,x)),y,z),y,z)
    ]]></literal>
    <justification jstring="[para(12545(a,1),15812(a,2,1,1))].">
      <j1 rule="para" parents="12545 15812"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      L(a(a(x,y,z),x,x \ (a(x,y,z) * x)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = R(x * (R(x,y,z) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(13494(a,1),15813(a,2,1))].">
      <j1 rule="para" parents="13494 15813"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      L(a(a(x,y,z),x,a(x,y,z)) \ x,a(x,y,z),x \ (a(x,y,z) * x)) = R(x * (R(x,y,z) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(7207(a,1),15814(a,1,1,1,3))].">
      <j1 rule="para" parents="7207 15814"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      L(1 \ x,a(x,y,z),x \ (a(x,y,z) * x)) = R(x * (R(x,y,z) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(7248(a,1),15815(a,1,1,1))].">
      <j1 rule="para" parents="7248 15815"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      L(x,a(x,y,z),x \ (a(x,y,z) * x)) = R(x * (R(x,y,z) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(67(a,1),15816(a,1,1))].">
      <j1 rule="para" parents="67 15816"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      R(x * (R(x,y,z) \ x),y,z) = L(x,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1575,a,15818,a),flip(a)].">
      <j1 rule="hyper" parents="1575 15818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      R(x * (R(x,y,z) \ x),y,z) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,14279,a(flip),b,15821,a),flip(a)].">
      <j1 rule="hyper" parents="325 14279 15821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      R(a(x,y,z) \ x,y,z) = x
    ]]></literal>
    <justification jstring="[para(14710(a,1),15822(a,1,1))].">
      <j1 rule="para" parents="14710 15822"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      R(a(x,y,a(z * y,x,u)) \ z,u,a(x,x,u * y)) = z
    ]]></literal>
    <justification jstring="[para(15687(a,2),15826(a,1,1,1))].">
      <j1 rule="para" parents="15687 15826"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      R(a(x,y,a(z * y,x,u)) * z,u,a(x,x,u * y)) = z
    ]]></literal>
    <justification jstring="[para(14302(a,1),15827(a,1,1))].">
      <j1 rule="para" parents="14302 15827"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      L(a(x,y,a(z * y,x,u)) * z,u,a(x,x,u * y)) = z
    ]]></literal>
    <justification jstring="[hyper(65,a,13374,a(flip),b,15828,a)].">
      <j1 rule="hyper" parents="65 13374 15828"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)) * y,x,a(z,z,x * u)) = y
    ]]></literal>
    <justification jstring="[para(15766(a,1),15829(a,1,1,1))].">
      <j1 rule="para" parents="15766 15829"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)) * y,u,a(z,z,x)) = y
    ]]></literal>
    <justification jstring="[hyper(65,a,15769,a(flip),b,15830,a)].">
      <j1 rule="hyper" parents="65 15769 15830"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      L(x,a(y,y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,15201,a(flip),b,15831,a)].">
      <j1 rule="hyper" parents="65 15201 15831"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      L(x,a(y,z,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,14187,a,b,15832,a)].">
      <j1 rule="hyper" parents="65 14187 15832"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      (a(x,x,y) \ z) * u = z * (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(137,a,15832,a(flip),b,14397,a)].">
      <j1 rule="hyper" parents="137 15832 14397"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      (a(x,x,y) * z) * u = z * (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[para(15832(a,1),15780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15832 15780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      (x \ 1) * (a(y,y,z) * u) = (x \ a(y,y,z)) * u
    ]]></literal>
    <justification jstring="[para(15832(a,1),15783(a,1,2))].">
      <j1 rule="para" parents="15832 15783"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      (x * a(y,z,z)) * u = x * (a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(989,a,15838,a),flip(a)].">
      <j1 rule="hyper" parents="989 15838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      a(x,a(y,z,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,15838,a,b,14595,a),flip(a)].">
      <j1 rule="hyper" parents="133 15838 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15855">
    <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(15838(a,1),450(a,1,2,2,1))].">
      <j1 rule="para" parents="15838 450"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      x * a(y,a(z,u,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,15852,a,b,69,a)].">
      <j1 rule="hyper" parents="137 15852 69"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      a(x * a(y,x,z),x,u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14491,a(flip),b,15859,a)].">
      <j1 rule="hyper" parents="65 14491 15859"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ u) / z = a(x,x,y) \ (u / z)
    ]]></literal>
    <justification jstring="[para(15860(a,1),15429(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15860 15429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) * u) / z = (u / z) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(15860(a,1),15436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15860 15436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * (a(z,z,u) \ y)) * w) = a(x,a(z,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(15839(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="15839 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      (x * (a(y,y,z) \ (u * w))) \ (((a(y,y,z) \ x) * u) * w) = a(a(y,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(15839(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15839 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      R(x,y,(z * u) * (a(w,w,u) * v5)) = R(x,y,v5 * (z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(15843(a,1),15114(a,1,3))].">
      <j1 rule="para" parents="15843 15114"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      a(x,y,(z * u) * (a(w,w,u) * v5)) = a(x,y,(z * L(u,w,w)) * v5)
    ]]></literal>
    <justification jstring="[para(15843(a,1),15151(a,1,3))].">
      <j1 rule="para" parents="15843 15151"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      x / (a(y,y,z) * u) = a(y,y,z) \ (x / u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15771,a(flip),b,15862,a)].">
      <j1 rule="hyper" parents="65 15771 15862"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      x / (y * a(z,z,u)) = a(z,z,u) \ (x / y)
    ]]></literal>
    <justification jstring="[para(7190(a,1),15870(a,1,2))].">
      <j1 rule="para" parents="7190 15870"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      (a(x,x,y) \ ((z * (u * (a(x,x,y) * w))) / w)) \ (z * u) = a(z,u,a(x,x,y) * w)
    ]]></literal>
    <justification jstring="[para(15870(a,1),11710(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15870 11710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,15435,a,b,15863,a(flip))].">
      <j1 rule="hyper" parents="36 15435 15863"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(65,a,15582,a(flip),b,15874,a)].">
      <j1 rule="hyper" parents="65 15582 15874"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(131,a,15877,a,b,15166,a),flip(a)].">
      <j1 rule="hyper" parents="131 15877 15166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) = a(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(15877(a,1),13518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15877 13518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      (a(x,x,y) * z) / u = (z / u) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(15877(a,1),15434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15877 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      a(a(x,y,z),u,y) = 1
    ]]></literal>
    <justification jstring="[hyper(65,a,15210,a,b,15888,a)].">
      <j1 rule="hyper" parents="65 15210 15888"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      L(a(x,y,z),u,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,15888,a)].">
      <j1 rule="hyper" parents="54 15888"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      L(x,y,a(z,x,u)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,15911,a)].">
      <j1 rule="hyper" parents="54 15911"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,15227,a,b,15919,a)].">
      <j1 rule="hyper" parents="65 15227 15919"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(15919(a,1),15365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15919 15365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,14816,a,b,15915,a)].">
      <j1 rule="hyper" parents="65 14816 15915"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),w,v5)) = a(x,y,u \ (L(z,w,v5) \ u))
    ]]></literal>
    <justification jstring="[para(15924(a,1),12696(a,1,3,1))].">
      <j1 rule="para" parents="15924 12696"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10508,a,15935,a)].">
      <j1 rule="hyper" parents="10508 15935"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      a(x,y,(z * u) * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10174,a,15935,a)].">
      <j1 rule="hyper" parents="10174 15935"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      a(x,y,L((z * u) * z,w,v5)) = a(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,10122,a,b,15935,a)].">
      <j1 rule="hyper" parents="65 10122 15935"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      a(x \ y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14864,a(flip),b,15935,a),flip(a)].">
      <j1 rule="hyper" parents="65 14864 15935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      a(x,y,L(z \ u,w,v5)) = a(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,12063,a(flip),b,15935,a)].">
      <j1 rule="hyper" parents="65 12063 15935"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      a(x,y,(z \ u) * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,12025,a(flip),b,15935,a)].">
      <j1 rule="hyper" parents="65 12025 15935"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      a(x,y,z \ u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,11996,a(flip),b,15935,a)].">
      <j1 rule="hyper" parents="65 11996 15935"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      a(x,y,L(z * u,u,w)) = a(x,y,(u * w) \ (z * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10630,a(flip),b,15935,a)].">
      <j1 rule="hyper" parents="65 10630 15935"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ y),u,w) = a(z * L(y,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14974,a,b,15959,a)].">
      <j1 rule="hyper" parents="65 14974 15959"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      a(x * y,z,L(u,y,x)) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,14860,a,b,15959,a)].">
      <j1 rule="hyper" parents="65 14860 15959"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,v5,x)) = a(x,v5,a(y \ (x * z),u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15270,a(flip),b,15959,a),flip(a)].">
      <j1 rule="hyper" parents="65 15270 15959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      a(L(x,y,y) * (z \ (y * x)),u,w) = a(x \ (z \ (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15054,a(flip),b,15959,a),flip(a)].">
      <j1 rule="hyper" parents="65 15054 15959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      x * R(x \ y,z,u) = y * a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(137,a,15959,a(flip),b,14616,a),flip(a)].">
      <j1 rule="hyper" parents="137 15959 14616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      a(x,y,L(z * a(u * w,z,v5),v5,u \ w)) = a(x,y,L(z,u \ w,v5))
    ]]></literal>
    <justification jstring="[para(15959(a,1),11797(a,1,3,1,2))].">
      <j1 rule="para" parents="15959 11797"/>
    </justification>
  </clause>

  <clause id="15987">
    <literal><![CDATA[
      L(x * a(y * z,x,a(u,w,v5)),a(u,w,v5),y \ z) = L(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(15959(a,1),12111(a,1,1,2))].">
      <j1 rule="para" parents="15959 12111"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * ((u \ z) \ w)) = a(x,y,w * (z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15354,a,b,15965,a)].">
      <j1 rule="hyper" parents="65 15354 15965"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (u * z)))) = a(x,y,(u * z) * ((z * w) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15111,a(flip),b,15965,a)].">
      <j1 rule="hyper" parents="65 15111 15965"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * (L(z,z,u * w) * u)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14750,a(flip),b,15965,a),flip(a)].">
      <j1 rule="hyper" parents="65 14750 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) * (w * z)) = a(x,y,a(u * z,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13147,a(flip),b,15965,a),flip(a)].">
      <j1 rule="hyper" parents="65 13147 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      a(x,y,(z * u) * ((w \ z) * (w * u))) = a(x,y,a(z * w,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13145,a(flip),b,15965,a),flip(a)].">
      <j1 rule="hyper" parents="65 13145 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (x \ v5))) = a(x,y,a(z,u,v5 * (x * w)))
    ]]></literal>
    <justification jstring="[para(15965(a,1),14900(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15965 14900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (x * v5))) = a(x,y,a(z,u,v5 * (x \ w)))
    ]]></literal>
    <justification jstring="[para(15965(a,1),14901(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15965 14901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,14594,a,b,15897,a),flip(a)].">
      <j1 rule="hyper" parents="325 14594 15897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,15365,a(flip),b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="43 15365 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,14096,a(flip),b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="43 14096 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,14217,a,b,16014,a)].">
      <j1 rule="hyper" parents="65 14217 16014"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      R(x,y,z \ u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15659,a(flip),b,16014,a)].">
      <j1 rule="hyper" parents="65 15659 16014"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      (x * a(y,y,z)) \ u = x \ (a(y,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(65,a,13369,a(flip),b,16014,a),flip(a)].">
      <j1 rule="hyper" parents="65 13369 16014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      a(x,x,y) \ (z * u) = z * (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(136,a,16014,a(flip),b,14509,a),flip(a)].">
      <j1 rule="hyper" parents="136 16014 14509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * (w * v5)) = R(x,y,v5 * (a(z,z,u) * w))
    ]]></literal>
    <justification jstring="[para(16014(a,1),8692(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="16014 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      (x * y) * a(z,z,u) = x * (a(z,z,u) * y)
    ]]></literal>
    <justification jstring="[para(16014(a,1),13272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16014 13272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      a(x,x,y) * (z * (a(x,x,y) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(16014(a,1),14421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16014 14421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      L(x,y,z \ u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(16014(a,1),15375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16014 15375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      x * (y * a(x,z,u)) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,14662,a(flip),b,16015,a)].">
      <j1 rule="hyper" parents="65 14662 16015"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      R(x,y,(z \ (u * w)) * (u * (z \ w))) = L(x,y,a(z,w * z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15409,a(flip),b,16025,a),flip(a)].">
      <j1 rule="hyper" parents="65 15409 16025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) * (u * (z * w))) = L(x,y,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13376,a(flip),b,16025,a),flip(a)].">
      <j1 rule="hyper" parents="65 13376 16025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(65,a,11582,a,b,16051,a)].">
      <j1 rule="hyper" parents="65 11582 16051"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      (x * (y / x)) \ ((R(x,z,u) * (y / x)) * w) = y \ ((y * a(x,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(16077(a,1),14149(a,1,2,1))].">
      <j1 rule="para" parents="16077 14149"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      x \ ((y * R(y \ x,z,u)) * w) = w * a(w * (x \ (y * w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,1814,a(flip),b,15984,a)].">
      <j1 rule="hyper" parents="65 1814 15984"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      (x * (a(y,y,z) \ u)) * w = (x * u) * (a(y,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(16028(a,1),15839(a,1,1))].">
      <j1 rule="para" parents="16028 15839"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      (((x * (y * z)) * a(u,u,w)) * v5) / ((y * (a(u,u,w) * z)) * v5) = R(R(x,y * z,a(u,u,w)),(y * z) * a(u,u,w),v5)
    ]]></literal>
    <justification jstring="[para(16034(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="16034 488"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      (a(x,x,y) * (z * u)) * w = (z * (a(x,x,y) * u)) * w
    ]]></literal>
    <justification jstring="[para(16034(a,1),7211(a,2,1))].">
      <j1 rule="para" parents="16034 7211"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      (a(x,x,y) * (z * u)) / w = (z * (a(x,x,y) * u)) / w
    ]]></literal>
    <justification jstring="[para(16034(a,1),7222(a,2,1))].">
      <j1 rule="para" parents="16034 7222"/>
    </justification>
  </clause>

  <clause id="16097">
    <literal><![CDATA[
      (x * (a(y,y,z) * (u * w))) / v5 = (x * (u * (a(y,y,z) * w))) / v5
    ]]></literal>
    <justification jstring="[para(16034(a,1),7302(a,2,1,2))].">
      <j1 rule="para" parents="16034 7302"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      a(x,a(y,y,z) * (u * w),v5) = a(x,u * (a(y,y,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(16034(a,1),9995(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16034 9995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      L(x,a(y,y,z) * (u * w),v5) = L(x,u * (a(y,y,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(16034(a,1),10813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16034 10813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      x / (y * (a(z,z,u) * w)) = a(z,z,u) \ (x / (y * w))
    ]]></literal>
    <justification jstring="[para(16034(a,1),15872(a,1,2))].">
      <j1 rule="para" parents="16034 15872"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      (x * (a(y,y,z) * u)) \ w = (x * u) \ (a(y,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(16034(a,1),16026(a,1,1))].">
      <j1 rule="para" parents="16034 16026"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      a(x * ((y * z) * (z \ x)),u,w) = a(y,u,L(w,z,z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14994,a,b,15951,a)].">
      <j1 rule="hyper" parents="65 14994 15951"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      a(x,y,L(z * u,u,w)) = a(x,y,(z * w) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15965,a(flip),b,15966,a),flip(a)].">
      <j1 rule="hyper" parents="325 15965 15966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      a(x,y,L(z \ (u * ((z * w) / u)),u * (((z \ 1) \ w) / u),v5)) = a(x,y,((z \ 1) * v5) * ((u * (((z \ 1) \ w) / u)) * v5))
    ]]></literal>
    <justification jstring="[para(1795(a,1),16111(a,1,3,1))].">
      <j1 rule="para" parents="1795 16111"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      (x * (a(y,y,z) * u)) * w = (x * u) * (a(y,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15843,a(flip),b,16095,a),flip(a)].">
      <j1 rule="hyper" parents="65 15843 16095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      (x * (a(y,y,z) * u)) / w = ((x * u) / w) * a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,15905,a(flip),b,16096,a),flip(a)].">
      <j1 rule="hyper" parents="65 15905 16096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      (x * y) \ (a(z,z,u) \ (x * (y * (a(z,z,u) * w)))) = L(L(w,a(z,z,u),y),a(z,z,u) * y,x)
    ]]></literal>
    <justification jstring="[hyper(65,a,7233,a(flip),b,16101,a),flip(a)].">
      <j1 rule="hyper" parents="65 7233 16101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      ((x * y) * (a(z,z,u) * w)) / (x * ((a(z,z,u) * y) * w)) = a(x,a(z,z,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(135,a,16114,a(flip),b,7223,a)].">
      <j1 rule="hyper" parents="135 16114 7223"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      ((x * y) * (a(z,z,u) * w)) / ((a(z,z,u) * y) * w) = R(x,a(z,z,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(135,a,16114,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="135 16114 109"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      L(x,(y * z) * (a(u,u,w) * v5),v6) = L(x,v5 * (y * (a(u,u,w) * z)),v6)
    ]]></literal>
    <justification jstring="[para(16114(a,1),10813(a,1,2))].">
      <j1 rule="para" parents="16114 10813"/>
    </justification>
  </clause>

  <clause id="16120">
    <literal><![CDATA[
      a(x,x,y) \ ((z * (a(x,x,y) * u)) / w) = (z * u) / w
    ]]></literal>
    <justification jstring="[hyper(132,a,16115,a,b,7190,a)].">
      <j1 rule="hyper" parents="132 16115 7190"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),w,v5)) = a(x,y,(L(z,w,v5) \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,15965,a(flip),b,15948,a),flip(a)].">
      <j1 rule="hyper" parents="325 15965 15948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(325,a,15963,a(flip),b,16121,a),flip(a)].">
      <j1 rule="hyper" parents="325 15963 16121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      a(x,y,L(z,z * u,w)) = a(x,y,u \ (w \ (z \ (w * u))))
    ]]></literal>
    <justification jstring="[hyper(65,a,15110,a(flip),b,16124,a),flip(a)].">
      <j1 rule="hyper" parents="65 15110 16124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16130">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,v5,x)) = a(x,v5,a(y * (x * z),u,w))
    ]]></literal>
    <justification jstring="[para(15959(a,1),15979(a,2,3))].">
      <j1 rule="para" parents="15959 15979"/>
    </justification>
  </clause>

  <clause id="16131">
    <literal><![CDATA[
      a(x,y,a(z,u,(x \ w) * v5)) = a(x,y,a(z,u,w * (x * v5)))
    ]]></literal>
    <justification jstring="[para(15965(a,1),16010(a,1,3))].">
      <j1 rule="para" parents="15965 16010"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      a(x,y,a(z,u,(x * w) * v5)) = a(x,y,a(z,u,w * (x \ v5)))
    ]]></literal>
    <justification jstring="[para(15965(a,1),16011(a,1,3))].">
      <j1 rule="para" parents="15965 16011"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      a(x,y,a(z * (x \ u),w,v5)) = a(x,w,a(u * (x * z),y,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15196,a(flip),b,16130,a)].">
      <j1 rule="hyper" parents="65 15196 16130"/>
    </justification>
  </clause>

  <clause id="16134">
    <literal><![CDATA[
      a(L(x,y,y) * (z \ (y * x)),u,w) = a(x * (z \ (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,15959,a(flip),b,15980,a),flip(a)].">
      <j1 rule="hyper" parents="325 15959 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16135">
    <literal><![CDATA[
      a(x,y,(z * u) * ((u * w) * z)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15333,a(flip),b,16001,a)].">
      <j1 rule="hyper" parents="65 15333 16001"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (u * z)))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16000,a,b,16135,a)].">
      <j1 rule="hyper" parents="65 16000 16135"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      a(x,y,L(z,z * u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16127,a,b,16136,a)].">
      <j1 rule="hyper" parents="65 16127 16136"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      a(x,y,L(z,u \ z,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15278,a,b,16137,a)].">
      <j1 rule="hyper" parents="65 15278 16137"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(w,z * u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16137(a,1),14839(a,1,1))].">
      <j1 rule="para" parents="16137 14839"/>
    </justification>
  </clause>

  <clause id="16143">
    <literal><![CDATA[
      a(x,y * z,a(u,w,y)) = a(x,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,14839,a(flip),b,16142,a),flip(a)].">
      <j1 rule="hyper" parents="65 14839 16142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      a(x,y * z,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15209,a,b,16143,a)].">
      <j1 rule="hyper" parents="65 15209 16143"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      a(x,y,a(z,u * w,u)) = a(z,w,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15159,a,b,16143,a)].">
      <j1 rule="hyper" parents="65 15159 16143"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      a(x,y,a(z,u * (z * w),u)) = a(x,w * u,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15216,a(flip),b,16143,a)].">
      <j1 rule="hyper" parents="65 15216 16143"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      a(x,y * x,a(z,u,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15206,a,b,16144,a)].">
      <j1 rule="hyper" parents="65 15206 16144"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      a(x,y,a(z,u * w,u)) = a(z,w,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,12836,a,b,16145,a),flip(a)].">
      <j1 rule="hyper" parents="325 12836 16145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      a(x,y,a(z,u * (z * w),u)) = a(z,w,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,16144,a(flip),b,16147,a),flip(a)].">
      <j1 rule="hyper" parents="325 16144 16147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      a(x,x * y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16145,a(flip),b,16153,a)].">
      <j1 rule="hyper" parents="65 16145 16153"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      a(x,x * y,a(z,u,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15198,a,b,16154,a),flip(a)].">
      <j1 rule="hyper" parents="325 15198 16154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16156">
    <literal><![CDATA[
      a(x,y * z,a(u,w,z)) = a(z,y,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15209,a,b,16154,a)].">
      <j1 rule="hyper" parents="65 15209 16154"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      a(x,y * z,a(y,u,w)) = a(y,z,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,15188,a(flip),b,16154,a)].">
      <j1 rule="hyper" parents="65 15188 16154"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      L(x,y * z,a(u,w,y)) = x * a(y,z,a(u,w,x))
    ]]></literal>
    <justification jstring="[para(16154(a,1),15204(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16154 15204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      a(x,y,a(z,x * u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15205,a,b,16155,a)].">
      <j1 rule="hyper" parents="65 15205 16155"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      a(x,y,a(z,u * x,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15186,a,b,16156,a)].">
      <j1 rule="hyper" parents="65 15186 16156"/>
    </justification>
  </clause>

  <clause id="16166">
    <literal><![CDATA[
      (x * y) \ ((y * R(T(x,y),z,u)) * w) = w * a(w * ((x * y) \ (y * w)),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),16087(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 16087"/>
    </justification>
  </clause>

  <clause id="16167">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) * w))) / v5 = ((x * (y * w)) / v5) * a(z,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16115,a(flip),b,16097,a),flip(a)].">
      <j1 rule="hyper" parents="65 16115 16097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      a(x,y,L(z * a(u * w,z,v5),v5,u * w)) = a(x,y,L(z,u \ w,v5))
    ]]></literal>
    <justification jstring="[para(16042(a,1),15986(a,1,3))].">
      <j1 rule="para" parents="16042 15986"/>
    </justification>
  </clause>

  <clause id="16169">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,v5)) = a(x,y,L(z,u * w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,11797,a(flip),b,16168,a),flip(a)].">
      <j1 rule="hyper" parents="65 11797 16168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      a(x,y,L(z,u * w,v5)) \ a(x,y,z) = a(v5,u \ w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16169(a,1),14839(a,1,1))].">
      <j1 rule="para" parents="16169 14839"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,v5)) = a(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,14839,a(flip),b,16172,a),flip(a)].">
      <j1 rule="hyper" parents="65 14839 16172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      a(x,y * ((z * z) \ u),a(w,v5,v6)) = a(v6,v5,a(x,y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15176,a(flip),b,16173,a),flip(a)].">
      <j1 rule="hyper" parents="65 15176 16173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16178">
    <literal><![CDATA[
      L(x * a(y,z * (u * y),a(w,x,z)),z \ (u * y),a(y,w,z)) = L(x,a(z,(z \ u) * y,y),w)
    ]]></literal>
    <justification jstring="[para(16173(a,1),15791(a,1,1,2))].">
      <j1 rule="para" parents="16173 15791"/>
    </justification>
  </clause>

  <clause id="16179">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,v5)) = a(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15177,a(flip),b,16177,a),flip(a)].">
      <j1 rule="hyper" parents="65 15177 16177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      L(x * a(y * z,x,a(u,w,v5)),a(u,w,v5),y * z) = L(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,16042,a(flip),b,15987,a)].">
      <j1 rule="hyper" parents="65 16042 15987"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      ((x * y) * (a(z,z,u) * w)) / (y * (a(z,z,u) * w)) = R(x,a(z,z,u) * y,w)
    ]]></literal>
    <justification jstring="[para(15843(a,1),16118(a,1,2))].">
      <j1 rule="para" parents="15843 16118"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      (x * y) \ ((R(x,z,u) * y) * w) = w * a(w * ((x * y) \ (y * w)),z,u)
    ]]></literal>
    <justification jstring="[para(243(a,1),16166(a,1,2,1))].">
      <j1 rule="para" parents="243 16166"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      L(x,y \ z,a(u,w,v5)) = L(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,12111,a(flip),b,16183,a),flip(a)].">
      <j1 rule="hyper" parents="65 12111 16183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16190">
    <literal><![CDATA[
      R(x,a(y,y,z) * u,w) = R(x,u,a(y,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(490,a,16184,a),flip(a)].">
      <j1 rule="hyper" parents="490 16184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * y) * (a(z,z,u) \ w)) = a(x,a(z,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(16093(a,1),15864(a,1,2))].">
      <j1 rule="para" parents="16093 15864"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ (((a(z,z,u) \ x) * y) * w) = a(a(z,z,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(16028(a,1),15865(a,1,1,2))].">
      <j1 rule="para" parents="16028 15865"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      (a(x,x,y) \ (((z * (u * w)) / w) * a(x,x,y))) \ (z * u) = a(z,u,a(x,x,y) * w)
    ]]></literal>
    <justification jstring="[para(16167(a,1),15873(a,1,1,2))].">
      <j1 rule="para" parents="16167 15873"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      ((x * y) * (a(z,z,u) * w)) / (x * (y * (a(z,z,u) * w))) = a(x,a(z,z,u) * y,w)
    ]]></literal>
    <justification jstring="[para(15843(a,1),16117(a,1,2,2))].">
      <j1 rule="para" parents="15843 16117"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      a(x,a(y,y,z) \ u,w) = a(x,u,a(y,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(709,a,16191,a),flip(a)].">
      <j1 rule="hyper" parents="709 16191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      a(x,a(y,y,z) \ u,w) = a(x,u,w * a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,15965,a(flip),b,16195,a),flip(a)].">
      <j1 rule="hyper" parents="325 15965 16195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,w) = a(x,u,w * a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15078,a(flip),b,16196,a)].">
      <j1 rule="hyper" parents="65 15078 16196"/>
    </justification>
  </clause>

  <clause id="16198">
    <literal><![CDATA[
      L(x,y,a(z,u * a(w,w,v5),v6)) = L(x,y,a(z,u,v6 * a(w,w,v5)))
    ]]></literal>
    <justification jstring="[para(16196(a,1),14010(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16196 14010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      a(x,L(y,z,z) \ u,w * a(z,z,y)) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14567,a(flip),b,16197,a),flip(a)].">
      <j1 rule="hyper" parents="65 14567 16197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      L(x,y,a(z,u \ w,v5 * a(u,u,w))) = L(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,14014,a(flip),b,16198,a),flip(a)].">
      <j1 rule="hyper" parents="65 14014 16198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * (a(z,z,u) \ y)) * w) = a(a(z,z,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(15839(a,1),16192(a,1,2,1))].">
      <j1 rule="para" parents="15839 16192"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * w) = ((x * (y * w)) / w) \ (x * y)
    ]]></literal>
    <justification jstring="[para(7193(a,1),16193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7193 16193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,11710,a,b,16202,a),flip(a)].">
      <j1 rule="hyper" parents="325 11710 16202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      a(x,y,z * a(u,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10136,a,16203,a)].">
      <j1 rule="hyper" parents="10136 16203"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(14569(a,1),16203(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14569 16203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14470,a,b,16205,a)].">
      <j1 rule="hyper" parents="65 14470 16205"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      a(x,L(y,z,z) \ u,w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16199,a(flip),b,16205,a),flip(a)].">
      <j1 rule="hyper" parents="65 16199 16205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(16034(a,1),16205(a,1,3))].">
      <j1 rule="para" parents="16034 16205"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      L(x,y,a(z,u \ w,v5)) = L(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(16205(a,1),16200(a,1,3))].">
      <j1 rule="para" parents="16205 16200"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      a(x,y,(z \ u) \ w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15999,a(flip),b,16216,a),flip(a)].">
      <j1 rule="hyper" parents="65 15999 16216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(10344,a,16210,a)].">
      <j1 rule="hyper" parents="10344 16210"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      a(x,y,(z \ u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12027,a(flip),b,16210,a)].">
      <j1 rule="hyper" parents="65 12027 16210"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      a(x,((y * z) * z) \ u,w) = a(x,(y * (z * z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13791,a(flip),b,16218,a)].">
      <j1 rule="hyper" parents="65 13791 16218"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15965,a(flip),b,16224,a)].">
      <j1 rule="hyper" parents="65 15965 16224"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(10141,a,16233,a)].">
      <j1 rule="hyper" parents="10141 16233"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      a(x,y,((z * u) * (w \ z)) * (u * w)) = a(x,y,a(z * w,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16002,a(flip),b,16233,a),flip(a)].">
      <j1 rule="hyper" parents="65 16002 16233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * x) * v5)) = a(x,y,a(z,u,w * (x * v5)))
    ]]></literal>
    <justification jstring="[para(16233(a,1),16131(a,1,3))].">
      <j1 rule="para" parents="16233 16131"/>
    </justification>
  </clause>

  <clause id="16248">
    <literal><![CDATA[
      a(x,y,((z * u) \ (z * w)) * (w * u)) = a(x,y,a(z,u,u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14716,a(flip),b,16239,a),flip(a)].">
      <j1 rule="hyper" parents="65 14716 16239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      a(x,y,z * (L(u * w,w,w) * v5)) = a(x,y,z * (v5 \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,14417,a(flip),b,16239,a),flip(a)].">
      <j1 rule="hyper" parents="65 14417 16239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),z,u)) = L(x,y,a(u,z,u * (z * w)))
    ]]></literal>
    <justification jstring="[para(16239(a,1),14924(a,2,3))].">
      <j1 rule="para" parents="16239 14924"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      L(x,y,a(z,u,u * (w * z))) = L(x,y,a(z,u,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(16239(a,1),14976(a,2,3))].">
      <j1 rule="para" parents="16239 14976"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (x * v5))) = a(z,u,a(x,y,x * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(16239(a,1),15282(a,1,3))].">
      <j1 rule="para" parents="16239 15282"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      L(x,y,a(z,u,u * (w * z))) = L(x,y,a(z,u,z * (w * u)))
    ]]></literal>
    <justification jstring="[para(16239(a,1),15742(a,1,3))].">
      <j1 rule="para" parents="16239 15742"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      a(x,y,a(z,u,(x * w) * v5)) = a(x,y,a(z,u,w * (v5 * x)))
    ]]></literal>
    <justification jstring="[para(16239(a,1),16132(a,2,3))].">
      <j1 rule="para" parents="16239 16132"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,w)) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,15867,a(flip),b,16221,a)].">
      <j1 rule="hyper" parents="65 15867 16221"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,w) * v5)) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[para(14569(a,1),16221(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14569 16221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) * v5) = a(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11380,a(flip),b,16259,a),flip(a)].">
      <j1 rule="hyper" parents="65 11380 16259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      a(x,((y * z) * z) \ u,w) = a(x,y \ ((z * z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,10391,a(flip),b,16237,a),flip(a)].">
      <j1 rule="hyper" parents="325 10391 16237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) * v5) = a(x,y,(z * (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,10307,a(flip),b,16265,a)].">
      <j1 rule="hyper" parents="65 10307 16265"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      a(x,(T(y,z) \ u) \ ((y * y) \ w),v5) = a(x,(u * y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11176,a(flip),b,16268,a),flip(a)].">
      <j1 rule="hyper" parents="65 11176 16268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) = a(v5,w,a(x,y,x * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,16253,a)].">
      <j1 rule="hyper" parents="65 12836 16253"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      a(x,y,((z * u) * (z * w)) * (u * w)) = a(x,y,a(z * w,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16270,a(flip),b,16243,a)].">
      <j1 rule="hyper" parents="65 16270 16243"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      a(x,y,((z * u) * (z * w)) * (u * w)) = a(x,y,a(z,w,w * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16233,a(flip),b,16248,a)].">
      <j1 rule="hyper" parents="65 16233 16248"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ v5))) = a(x,y,z * ((v5 * w) * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16260,a(flip),b,16249,a),flip(a)].">
      <j1 rule="hyper" parents="65 16260 16249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,16239,a(flip),b,16275,a)].">
      <j1 rule="hyper" parents="65 16239 16275"/>
    </justification>
  </clause>

  <clause id="16278">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * w) * (w * u))) = a(x,y,a(z * w,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16003,a(flip),b,16277,a),flip(a)].">
      <j1 rule="hyper" parents="65 16003 16277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16279">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(z,u,u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16273,a(flip),b,16274,a)].">
      <j1 rule="hyper" parents="65 16273 16274"/>
    </justification>
  </clause>

  <clause id="16280">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * w) * (w * u))) = a(x,y,a(w,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10304,a(flip),b,16274,a)].">
      <j1 rule="hyper" parents="65 10304 16274"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) = a(x,y,a(u,z,z * w))
    ]]></literal>
    <justification jstring="[hyper(7507,a,16279,a)].">
      <j1 rule="hyper" parents="7507 16279"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      x * a(x,y,a(z,u,u * w)) = R(x,y,a(z * u,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,16279,a(flip),b,14596,a(flip))].">
      <j1 rule="hyper" parents="137 16279 14596"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(z,u,a(y,x,x * w))
    ]]></literal>
    <justification jstring="[para(16279(a,1),15181(a,2,2))].">
      <j1 rule="para" parents="16279 15181"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      R(x,y,a(z * u,u,w)) = L(x,y,a(z,u,u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,14606,a(flip),b,16283,a),flip(a)].">
      <j1 rule="hyper" parents="65 14606 16283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      L(L(x,y,a(z * y,u,w)),u,a(z,y,y * w)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,15235,a(flip),b,16287,a),flip(a)].">
      <j1 rule="hyper" parents="65 15235 16287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      L(x,y,a(z * u,u,w)) = L(x,y,a(z,u,u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,13374,a(flip),b,16287,a)].">
      <j1 rule="hyper" parents="65 13374 16287"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      L(x,y,a(z * u,z,w)) = L(x,y,a(u,z,z * w))
    ]]></literal>
    <justification jstring="[para(2337(a,1),16289(a,1,3))].">
      <j1 rule="para" parents="2337 16289"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      L(x,y,a(z * u,w,w * z)) = L(x,y,a(z,w,z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,16251,a(flip),b,16290,a),flip(a)].">
      <j1 rule="hyper" parents="65 16251 16290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = L(y,x,a(z,u,x * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,15168,a(flip),b,16284,a),flip(a)].">
      <j1 rule="hyper" parents="325 15168 16284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      x * a(y,z,a(u,w,w * x)) = L(x,w,a(u,z,w * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15192,a(flip),b,16292,a)].">
      <j1 rule="hyper" parents="65 15192 16292"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      x * a(y * x,y,a(z,u,w)) = L(x,y,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,13417,a(flip),b,16292,a)].">
      <j1 rule="hyper" parents="65 13417 16292"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = L(u,w,a(z,y,w * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14420,a,b,16295,a)].">
      <j1 rule="hyper" parents="65 14420 16295"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      L(x,y,a(z * u,w,y * z)) = L(x,w,a(z,y,z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(65,a,15227,a,b,16291,a)].">
      <j1 rule="hyper" parents="65 15227 16291"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(u,w,w * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16278,a(flip),b,16280,a)].">
      <j1 rule="hyper" parents="65 16278 16280"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      a(x,y,a(z,u,u * w)) = a(x,y,a(w,z,z * u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16279,a(flip),b,16298,a),flip(a)].">
      <j1 rule="hyper" parents="65 16279 16298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      L(x,y,a(z,u,y * w)) = x * a(w,u,a(y,x,x * z))
    ]]></literal>
    <justification jstring="[para(16299(a,2),16294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16299 16294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      L(x,y * z,a(u,w,y)) = x * a(z,w,a(y * z,x,x * u))
    ]]></literal>
    <justification jstring="[para(15952(a,1),16300(a,1,3))].">
      <j1 rule="para" parents="15952 16300"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      a(x,y,a(z * x,u,u * w)) = a(z,x,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,16159,a(flip),b,16301,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 16159 16301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      a(x,y,a(z * (u * x),z,w)) = a(u,x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16281,a,b,16302,a)].">
      <j1 rule="hyper" parents="65 16281 16302"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      a(x,y,a(z,x * u,u * (w * x))) = a(w,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16160,a,b,16303,a)].">
      <j1 rule="hyper" parents="65 16160 16303"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      a(x,y,a(z,x * u,(x * u) * w)) = a(w,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16255,a,b,16305,a)].">
      <j1 rule="hyper" parents="65 16255 16305"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      a(x,a(y,y,z) * u,w) = a(x,u,a(y,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(7298,a,16194,a),flip(a)].">
      <j1 rule="hyper" parents="7298 16194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      a(x,y \ ((y \ 1) \ z),u) = a(x,z,a(y,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11978,a,b,16308,a)].">
      <j1 rule="hyper" parents="65 11978 16308"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),v5) = a(x,y * w,a(z,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,16098,a(flip),b,16308,a)].">
      <j1 rule="hyper" parents="65 16098 16308"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      a(x,y \ ((y \ 1) \ z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,16203,a(flip),b,16309,a),flip(a)].">
      <j1 rule="hyper" parents="325 16203 16309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      a(x,(y \ 1) * z,u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),16311(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 16311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      L(x,a(y,z \ u,w),v5) = L(x,a(y,z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(16313(a,1),11318(a,1,2))].">
      <j1 rule="para" parents="16313 11318"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,16203,a(flip),b,16310,a),flip(a)].">
      <j1 rule="hyper" parents="325 16203 16310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      a(x,(y \ a(z,z,u)) * w,v5) = a(x,(y \ 1) * w,v5)
    ]]></literal>
    <justification jstring="[para(15844(a,1),16316(a,1,2))].">
      <j1 rule="para" parents="15844 16316"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      a(x,(y \ (z \ y)) * u,w) = a(x,(z \ 1) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11753,a(flip),b,16319,a)].">
      <j1 rule="hyper" parents="65 11753 16319"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      a(x,((y \ z) \ 1) * u,w) = a(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11169,a(flip),b,16320,a),flip(a)].">
      <j1 rule="hyper" parents="65 11169 16320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      a(x,(y \ z) \ u,w) = a(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16313,a(flip),b,16322,a)].">
      <j1 rule="hyper" parents="65 16313 16322"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      a(x,(y \ T(z,u)) * ((z * z) \ w),v5) = a(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,16271,a(flip),b,16324,a),flip(a)].">
      <j1 rule="hyper" parents="65 16271 16324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      a(x,(y \ z) * ((z * z) \ u),w) = a(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10125,a(flip),b,16325,a)].">
      <j1 rule="hyper" parents="65 10125 16325"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      L(x,a(y,(z * u) \ w,v5),v6) = L(x,a(y,(z \ u) * w,v5),v6)
    ]]></literal>
    <justification jstring="[para(16327(a,1),11298(a,1,2))].">
      <j1 rule="para" parents="16327 11298"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      L(x,a(y,(z \ u) * w,v5),v6) = L(x,a(y,(z * u) * w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,16315,a(flip),b,16328,a),flip(a)].">
      <j1 rule="hyper" parents="65 16315 16328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * y) * (a(z,z,u) \ w)) = a(a(z,z,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(16093(a,1),16201(a,1,2))].">
      <j1 rule="para" parents="16093 16201"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      a(a(x,x,y) \ z,u,w) = a(z,u,a(x,x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(709,a,16330,a),flip(a)].">
      <j1 rule="hyper" parents="709 16330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      a(a(x,x,y) \ z,u,w) = a(z,u,w * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,15965,a(flip),b,16331,a),flip(a)].">
      <j1 rule="hyper" parents="325 15965 16331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,w) = a(z,u,w * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,15959,a(flip),b,16332,a)].">
      <j1 rule="hyper" parents="65 15959 16332"/>
    </justification>
  </clause>

  <clause id="16335">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,16205,a(flip),b,16334,a),flip(a)].">
      <j1 rule="hyper" parents="325 16205 16334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16336">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,w) = a(z,u,w * a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,13810,a,b,16334,a)].">
      <j1 rule="hyper" parents="65 13810 16334"/>
    </justification>
  </clause>

  <clause id="16338">
    <literal><![CDATA[
      a(L(x,y,y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(14569(a,1),16335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14569 16335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      a(x * L(y,z,z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(14761(a,1),16335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14761 16335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      a(x \ y,z,u * a(y,y,w)) = a(x * L(y,y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15976,a(flip),b,16336,a),flip(a)].">
      <j1 rule="hyper" parents="65 15976 16336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      a(x * y,z,u * a(y,y,w)) = a(x * L(y,y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,15959,a(flip),b,16342,a)].">
      <j1 rule="hyper" parents="65 15959 16342"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      a(x * L(y,y,z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16205,a(flip),b,16343,a),flip(a)].">
      <j1 rule="hyper" parents="65 16205 16343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      a(x * L(y \ z,z,z),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12492,a(flip),b,16344,a)].">
      <j1 rule="hyper" parents="65 12492 16344"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      a(x * (y \ z),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16339,a(flip),b,16346,a)].">
      <j1 rule="hyper" parents="65 16339 16346"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      a(L(x,y,y) * (z * (y * x)),u,w) = a(x * (z \ (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16134,a(flip),b,16348,a),flip(a)].">
      <j1 rule="hyper" parents="65 16134 16348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) = a(x,w,a(u * (x * z),y,v5))
    ]]></literal>
    <justification jstring="[para(16348(a,1),16133(a,1,3))].">
      <j1 rule="para" parents="16348 16133"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      (x * y) \ ((R(x,z,u) * y) * w) = w * a(w * ((x * y) * (y * w)),z,u)
    ]]></literal>
    <justification jstring="[para(16348(a,1),16185(a,2,2))].">
      <j1 rule="para" parents="16348 16185"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      a(x,x * y,a(y * (x * z),u,w)) = a(x,u,a(z,x * y,(x * y) * w))
    ]]></literal>
    <justification jstring="[hyper(325,a,16279,a(flip),b,16351,a),flip(a)].">
      <j1 rule="hyper" parents="325 16279 16351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      a(x * (y \ (z \ x)),u,w) = a(x * (y * (z * x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16338,a(flip),b,16350,a),flip(a)].">
      <j1 rule="hyper" parents="65 16338 16350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      a(x * (y * (z \ x)),u,w) = a(x * (y * (z * x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16348,a(flip),b,16354,a)].">
      <j1 rule="hyper" parents="65 16348 16354"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      a(x * ((y * z) * (z * x)),u,w) = a(y,u,L(w,z,z * x))
    ]]></literal>
    <justification jstring="[hyper(65,a,16102,a(flip),b,16356,a),flip(a)].">
      <j1 rule="hyper" parents="65 16102 16356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      (x * y) \ ((R(x,z,u) * y) * w) = w * a(x,z,L(u,y,y * w))
    ]]></literal>
    <justification jstring="[para(16357(a,1),16352(a,2,2))].">
      <j1 rule="para" parents="16357 16352"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      (x * y) \ ((R(x,z,u) * y) * w) = (a(x,z,u) * y) * (y \ w)
    ]]></literal>
    <justification jstring="[hyper(325,a,14837,a(flip),b,16358,a),flip(a)].">
      <j1 rule="hyper" parents="325 14837 16358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      (a(x,y,z) * (u / x)) * ((u / x) \ w) = u \ ((u * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16084,a(flip),b,16359,a),flip(a)].">
      <j1 rule="hyper" parents="65 16084 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      a(x,y,z) \ (u \ ((u * a(x,y,z)) * w)) = w * a(a(x,y,z),u / x,(u / x) * w)
    ]]></literal>
    <justification jstring="[para(16360(a,1),13191(a,1,2))].">
      <j1 rule="para" parents="16360 13191"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      a(x,y,a(z,x * u,(x * u) * w)) = a(x,u,a(u * (x * z),y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16154,a(flip),b,16353,a),flip(a)].">
      <j1 rule="hyper" parents="65 16154 16353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      a(x,y,a(y * (x * z),u,w)) = a(w,x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16306,a(flip),b,16362,a),flip(a)].">
      <j1 rule="hyper" parents="65 16306 16362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (x * w))) = a(z,x,a(w,u,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,12836,a,b,16363,a)].">
      <j1 rule="hyper" parents="65 12836 16363"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (w * u))) = a(x,z,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16272,a(flip),b,16363,a)].">
      <j1 rule="hyper" parents="65 16272 16363"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      R(x,y,a(z,u,z * (w * u))) = x * a(x,z,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(137,a,16365,a(flip),b,14596,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 16365 14596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      a(x,y,a(z \ u,((z \ u) * z) \ w,(u / z) * (z * (u \ w)))) = a(x,z \ u,a(z,y,((z \ u) * z) \ w))
    ]]></literal>
    <justification jstring="[para(11526(a,1),16365(a,1,3,3))].">
      <j1 rule="para" parents="11526 16365"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      a(x * y,z,a(u,x,w)) \ y = ((y / x) * (x * a(z,w,z * (u * w)))) / a(z,w,z * (u * w))
    ]]></literal>
    <justification jstring="[para(16365(a,1),13153(a,1,1))].">
      <j1 rule="para" parents="16365 13153"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      R(x,y,a(z,u,z * (w * u))) = L(x,z,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(325,a,14606,a(flip),b,16366,a),flip(a)].">
      <j1 rule="hyper" parents="325 14606 16366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (w * u))) = L(x,z,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,13374,a(flip),b,16369,a)].">
      <j1 rule="hyper" parents="65 13374 16369"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      L(x,y,a(z,u,u * (w * z))) = L(x,z,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16254,a,b,16370,a)].">
      <j1 rule="hyper" parents="65 16254 16370"/>
    </justification>
  </clause>

  <clause id="16373">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (u * w))) = L(x,z,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16252,a(flip),b,16371,a)].">
      <j1 rule="hyper" parents="65 16252 16371"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      L(x,y,a(z * u,w,y * z)) = L(x,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16297,a,b,16373,a)].">
      <j1 rule="hyper" parents="65 16297 16373"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      x * a(a(y,z,u),w / y,(w / y) * x) = L(1 / x,a(y,z,u),w) \ 1
    ]]></literal>
    <justification jstring="[hyper(65,a,12356,a(flip),b,16361,a),flip(a)].">
      <j1 rule="hyper" parents="65 12356 16361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      x * a(a(y,z,u),w / y,(w / y) * x) = L((1 / x) \ 1,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,14160,a,b,16375,a),flip(a)].">
      <j1 rule="hyper" parents="325 14160 16375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      x * a(a(y,z,u),w / y,(w / y) * x) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(85(a,1),16376(a,2,1))].">
      <j1 rule="para" parents="85 16376"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      x * a(a(y,z,u),w / y,(w * y) * x) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(16241(a,1),16377(a,1,2))].">
      <j1 rule="para" parents="16241 16377"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      x * a(a(y,z,u),y \ w,(w * y) * x) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(9996(a,1),16378(a,1,2))].">
      <j1 rule="para" parents="9996 16378"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      x * a(y,z,a((u * y) * x,y \ u,w)) = L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[para(15162(a,1),16379(a,1,2))].">
      <j1 rule="para" parents="15162 16379"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      x * a(y,z,a((u * y) * x,u * y,w)) = L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[para(15411(a,1),16380(a,1,2))].">
      <j1 rule="para" parents="15411 16380"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      x * a(y,z,a(u,w,(z * y) * x)) = L(x,a(y,w,u),z)
    ]]></literal>
    <justification jstring="[para(16161(a,1),16381(a,1,2))].">
      <j1 rule="para" parents="16161 16381"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      x * a(y,z,a(u,w,z * (y * x))) = L(x,a(y,w,u),z)
    ]]></literal>
    <justification jstring="[para(16245(a,1),16382(a,1,2))].">
      <j1 rule="para" parents="16245 16382"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,a(z,u,y),w)
    ]]></literal>
    <justification jstring="[para(16364(a,1),16383(a,1,2))].">
      <j1 rule="para" parents="16364 16383"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,z,a(u,y,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15168,a(flip),b,16384,a),flip(a)].">
      <j1 rule="hyper" parents="65 15168 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      L(x,a(y,x,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,15921,a(flip),b,16385,a),flip(a)].">
      <j1 rule="hyper" parents="325 15921 16385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16390">
    <literal><![CDATA[
      L(x,a(y * z,u,w),v5) = L(x,u,a(z * y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,14192,a,b,16385,a)].">
      <j1 rule="hyper" parents="65 14192 16385"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      (x * L(L(y,z,a(u,w,x)),x,a(w,z,u))) / y = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(16385(a,1),15798(a,1,1,2,1))].">
      <j1 rule="para" parents="16385 15798"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      (a(x,y,z) * y) * u = y * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16387(a,1),13423(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16387 13423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16395">
    <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(15845(a,1),15855(a,1,2))].">
      <j1 rule="para" parents="15845 15855"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,z,u) \ (y * (a(z,z,u) * w)))) = L(L(w,a(z,z,u),y),a(z,z,u) * y,x)
    ]]></literal>
    <justification jstring="[para(16028(a,1),16116(a,1,2))].">
      <j1 rule="para" parents="16028 16116"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      L(x * a(y,z * y,a(u,x,w)),w \ (z * y),a(y,u,w)) = L(x,a(w,(w \ z) * y,y),u)
    ]]></literal>
    <justification jstring="[para(16143(a,1),16178(a,1,1,2))].">
      <j1 rule="para" parents="16143 16178"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),y \ (z * w),a(w,u,y)) = L(x,a(y,(y \ z) * w,w),u)
    ]]></literal>
    <justification jstring="[para(16149(a,1),16397(a,1,1,2))].">
      <j1 rule="para" parents="16149 16397"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),y * (z * w),a(w,u,y)) = L(x,a(y,(y \ z) * w,w),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16186,a(flip),b,16398,a)].">
      <j1 rule="hyper" parents="65 16186 16398"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,z * (w * u)))) / a(z,u,z * (w * u)) = a(y * x,z,a(w,y,u)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,14302,a(flip),b,16368,a),flip(a)].">
      <j1 rule="hyper" parents="65 14302 16368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16401">
    <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(774,a,16395,a)].">
      <j1 rule="hyper" parents="774 16395"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      L(x,L(y,a(z,u,u),w),w * a(z,u,u)) = L(x,a(z,u,u) * y,w)
    ]]></literal>
    <justification jstring="[para(16024(a,1),16401(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16024 16401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      L(x,a(y,z,z) * u,w) = L(x,u,w * a(y,z,z))
    ]]></literal>
    <justification jstring="[para(15838(a,1),16402(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15838 16402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      L(x,a(y,y,z) * u,w * a(z,y,y)) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15028,a(flip),b,16403,a),flip(a)].">
      <j1 rule="hyper" parents="65 15028 16403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      L(x,a(y,y,z) * u,w) = L(x,u,w * a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14473,a(flip),b,16404,a)].">
      <j1 rule="hyper" parents="65 14473 16404"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      L(x,y * (a(z,z,u) * w),v5) = L(x,y * w,v5 * a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16099,a(flip),b,16405,a)].">
      <j1 rule="hyper" parents="65 16099 16405"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      L(x,y * (z * (a(u,u,w) * v5)),v6) = L(x,(z * v5) * y,v6 * a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16119,a(flip),b,16406,a)].">
      <j1 rule="hyper" parents="65 16119 16406"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ z)) * u,w * a(v5,v5,v6)) = L(x,(a(v5,v5,v6) * u) * (a(y,y,z) * z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,12035,a(flip),b,16406,a),flip(a)].">
      <j1 rule="hyper" parents="65 12035 16406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,z,u) * (y * (a(z,z,u) \ w)))) = L(L(w,a(z,z,u),y),a(z,z,u) * y,x)
    ]]></literal>
    <justification jstring="[para(14419(a,1),16396(a,1,2,2))].">
      <j1 rule="para" parents="14419 16396"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      a(x,y,x * (z * y)) \ ((u / w) * (w * a(x,y,x * (z * y)))) = a(w * u,x,a(z,w,y)) * u
    ]]></literal>
    <justification jstring="[hyper(7210,a,16400,a)].">
      <j1 rule="hyper" parents="7210 16400"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      L(L(x,a(y,y,z),u),a(y,y,z) * u,w) = (w * u) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[para(16037(a,1),16409(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16037 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      L(L(x,a(y,y,z),u),a(y,y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(325,a,18,a,b,16411,a),flip(a)].">
      <j1 rule="hyper" parents="325 18 16411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      L(x,a(y,y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(15832(a,1),16412(a,1,1))].">
      <j1 rule="para" parents="15832 16412"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      L(x,y \ ((y \ 1) \ z),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(65,a,11982,a,b,16414,a)].">
      <j1 rule="hyper" parents="65 11982 16414"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      L(x,y,z * a(u,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16405,a(flip),b,16414,a)].">
      <j1 rule="hyper" parents="65 16405 16414"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      L(x,L(y,y,z) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15029,a(flip),b,16414,a),flip(a)].">
      <j1 rule="hyper" parents="65 15029 16414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      L(x,y * (z * (a(u,u,w) * v5)),v6) = L(x,(z * v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,16407,a,b,16416,a)].">
      <j1 rule="hyper" parents="65 16407 16416"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      L(x,(a(y,y,z) * u) * (a(w,w,v5) * v5),v6) = L(x,(w \ ((w \ 1) \ v5)) * u,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,16408,a(flip),b,16416,a)].">
      <j1 rule="hyper" parents="65 16408 16416"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      L(x,y * ((z * u) / z),w) = L(x,(u \ 1) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(11503,a,16415,a),flip(a)].">
      <j1 rule="hyper" parents="11503 16415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),16415(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 16415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = L(x,y \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(10969,a,16425,a)].">
      <j1 rule="hyper" parents="10969 16425"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(10884,a,16425,a)].">
      <j1 rule="hyper" parents="10884 16425"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z) \ u,w) = L(x,(y \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13819,a(flip),b,16417,a)].">
      <j1 rule="hyper" parents="65 13819 16417"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      L(x,y \ ((z * z) \ u),w) = L(x,z \ (z \ (y \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(10986,a,16426,a)].">
      <j1 rule="hyper" parents="10986 16426"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(10886,a,16423,a),flip(a)].">
      <j1 rule="hyper" parents="10886 16423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      L(x,((y \ z) \ 1) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15095,a(flip),b,16430,a),flip(a)].">
      <j1 rule="hyper" parents="65 15095 16430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      L(x,(y \ z) \ u,w) = L(x,u * (z \ y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16432,a(flip),b,16436,a),flip(a)].">
      <j1 rule="hyper" parents="65 16432 16436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      L(x,y * (a(z,z,u) * (a(w,w,v5) * v5)),v6) = L(x,(w \ ((w \ 1) \ v5)) * y,v6)
    ]]></literal>
    <justification jstring="[para(15843(a,1),16421(a,1,2))].">
      <j1 rule="para" parents="15843 16421"/>
    </justification>
  </clause>

  <clause id="16443">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ z)) * u,w) = L(x,(a(v5,v5,v6) * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16420,a(flip),b,16442,a),flip(a)].">
      <j1 rule="hyper" parents="65 16420 16442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      L(x,(y \ ((y \ 1) \ z)) * u,w) = L(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(7890(a,1),16443(a,2,2,1))].">
      <j1 rule="para" parents="7890 16443"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ u),w) = L(x,(u * z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15340,a(flip),b,16446,a)].">
      <j1 rule="hyper" parents="65 15340 16446"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) * u,w) = L(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(10884,a,16447,a)].">
      <j1 rule="hyper" parents="10884 16447"/>
    </justification>
  </clause>

  <clause id="16450">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) * (u \ 1),w) = L(x,u \ (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(325,a,16427,a(flip),b,16448,a),flip(a)].">
      <j1 rule="hyper" parents="325 16427 16448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16451">
    <literal><![CDATA[
      L(x,(y * (z \ a(u,w,u))) * v5,v6) = L(x,(z \ y) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,11516,a(flip),b,16448,a),flip(a)].">
      <j1 rule="hyper" parents="65 11516 16448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16452">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) \ u),w) = L(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16427,a(flip),b,16450,a)].">
      <j1 rule="hyper" parents="65 16427 16450"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      L(x,y \ ((z \ K(u,w)) \ v5),v6) = L(x,y \ (v5 * z),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10930,a,b,16452,a)].">
      <j1 rule="hyper" parents="65 10930 16452"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      L(x,y \ (z * (u \ a(w,v5,w))),v6) = L(x,y \ (u \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,10960,a(flip),b,16452,a),flip(a)].">
      <j1 rule="hyper" parents="65 10960 16452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      L(x,y * (z * (u \ 1)),w) = L(x,(u \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11159,a(flip),b,16451,a)].">
      <j1 rule="hyper" parents="65 11159 16451"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      L(x,(a(y,y \ z,u \ w) * (y \ z)) * (w * (u \ 1)),v5) = L(x,y \ (z * T(u \ w,y \ z)),v5)
    ]]></literal>
    <justification jstring="[para(11697(a,1),16455(a,2,2))].">
      <j1 rule="para" parents="11697 16455"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) * u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,10933,a(flip),b,16454,a)].">
      <j1 rule="hyper" parents="65 10933 16454"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      L(x,y \ ((z * z) \ u),w) = L(x,y \ (z \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11000,a(flip),b,16457,a)].">
      <j1 rule="hyper" parents="65 11000 16457"/>
    </justification>
  </clause>

  <clause id="16460">
    <literal><![CDATA[
      L(x,y \ (z \ (z \ u)),w) = L(x,z \ (z \ (y \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16431,a(flip),b,16459,a),flip(a)].">
      <j1 rule="hyper" parents="65 16431 16459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      L(x,(y / z) \ ((y / z) \ (u \ w)),v5) = L(x,u \ ((y / z) \ ((z \ y) \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11002,a(flip),b,16460,a),flip(a)].">
      <j1 rule="hyper" parents="65 11002 16460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      L(x,(y / z) \ ((y / z) \ (u \ w)),v5) = L(x,u \ ((z \ y) \ ((z \ y) \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,10929,a(flip),b,16461,a),flip(a)].">
      <j1 rule="hyper" parents="325 10929 16461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16463">
    <literal><![CDATA[
      L(x,(K(y,z) / u) \ ((K(y,z) / u) \ (w \ v5)),v6) = L(x,w \ ((u \ K(y,z)) \ ((u \ 1) \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,11003,a(flip),b,16462,a),flip(a)].">
      <j1 rule="hyper" parents="325 11003 16462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16464">
    <literal><![CDATA[
      a(x * y,z,a(u,x,w)) * y = a(z,w,z * (u * w)) * ((y / x) * (a(z,w,z * (u * w)) \ x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14418,a(flip),b,16410,a),flip(a)].">
      <j1 rule="hyper" parents="65 14418 16410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      L(x,(K(y,z) / u) \ ((K(y,z) / u) \ (w \ v5)),v6) = L(x,w \ (((u \ 1) \ v5) * u),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,16453,a(flip),b,16463,a),flip(a)].">
      <j1 rule="hyper" parents="325 16453 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      L(x,(K(y,z) / T(u,w)) \ ((K(y,z) / T(u,w)) \ (v5 \ v6)),v7) = L(x,v5 \ (((T(u,w) \ 1) \ v6) * u),v7)
    ]]></literal>
    <justification jstring="[hyper(325,a,10866,a(flip),b,16465,a),flip(a)].">
      <j1 rule="hyper" parents="325 10866 16465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),w,y * z)) = a(y * x,z,a(u,y,w)) * x
    ]]></literal>
    <justification jstring="[hyper(325,a,16296,a(flip),b,16464,a)].">
      <j1 rule="hyper" parents="325 16296 16464"/>
    </justification>
  </clause>

  <clause id="16469">
    <literal><![CDATA[
      L(x,y,a(z * u,u,w)) = a(w * x,y,a(z,w,u)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,16374,a(flip),b,16468,a)].">
      <j1 rule="hyper" parents="65 16374 16468"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      L(x,y,a(z,u,u * w)) = a(w * x,y,a(z,w,u)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,16289,a(flip),b,16469,a)].">
      <j1 rule="hyper" parents="65 16289 16469"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      L(x,(a(y,y \ z,u * w) * (y \ z)) * (u * (w \ 1)),v5) = L(x,y \ (z * T(w \ u,y \ z)),v5)
    ]]></literal>
    <justification jstring="[para(15965(a,1),16456(a,1,2,1,1))].">
      <j1 rule="para" parents="15965 16456"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      L(x,(y \ z) * ((u * (w \ 1)) * a(y,y \ z,u * w)),v5) = L(x,y \ (z * T(w \ u,y \ z)),v5)
    ]]></literal>
    <justification jstring="[para(16394(a,1),16472(a,1,2))].">
      <j1 rule="para" parents="16394 16472"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      L(x,(y \ z) * (L(R(u / w,w,u),y \ z,y) \ 1),v5) = L(x,y \ (z * T(u \ w,y \ z)),v5)
    ]]></literal>
    <justification jstring="[para(15001(a,1),16473(a,1,2,2))].">
      <j1 rule="para" parents="15001 16473"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      L(x,y \ (z * T(u \ w,y \ z)),v5) = L(x,y \ (z * (R(u / w,w,u) \ 1)),v5)
    ]]></literal>
    <justification jstring="[para(13002(a,1),16474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13002 16474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      L(x,y \ (z * T(u \ w,y \ z)),v5) = L(x,y \ (z * (w * (u \ 1))),v5)
    ]]></literal>
    <justification jstring="[para(1011(a,1),16475(a,2,2,2,2))].">
      <j1 rule="para" parents="1011 16475"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      L(x,y \ (z * (u * (w \ 1))),v5) = L(x,y \ (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(10903,a,16476,a),flip(a)].">
      <j1 rule="hyper" parents="10903 16476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      L(x,y \ (((z \ 1) * u) * w),v5) = L(x,y \ (w * (z \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(11045,a,16477,a)].">
      <j1 rule="hyper" parents="11045 16477"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,w \ v5),v6) = L(x,(y * ((w * w) \ v5)) \ ((w \ v5) * (w \ y)),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,11529,a,b,16478,a)].">
      <j1 rule="hyper" parents="65 11529 16478"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      L(x,y \ (z * ((u \ 1) \ w)),v5) = L(x,y \ ((w * u) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11124,a(flip),b,16478,a),flip(a)].">
      <j1 rule="hyper" parents="65 11124 16478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      L(x,y \ (((z \ 1) \ u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(10904,a,16481,a)].">
      <j1 rule="hyper" parents="10904 16481"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      L(x,y \ (((z * T(z,u)) * (T(z,u) \ w)) * v5),v6) = L(x,y \ ((w * z) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,11311,a,b,16482,a)].">
      <j1 rule="hyper" parents="65 11311 16482"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      L(x,y \ (((z * z) * (z \ u)) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(9633(a,1),16483(a,1,2,2,1))].">
      <j1 rule="para" parents="9633 16483"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      L(x,y \ ((z * z) * ((z \ u) * w)),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),16484(a,1,2,2))].">
      <j1 rule="para" parents="33 16484"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      L(x,(K(y,z) / T(u,w)) \ ((K(y,z) / T(u,w)) \ (v5 \ v6)),v7) = L(x,(u * u) * (v5 \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(325,a,11099,a(flip),b,16467,a),flip(a)].">
      <j1 rule="hyper" parents="325 11099 16467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      L(x,(K(y,z) / T(u,w)) \ ((T(u,w) \ K(y,z)) \ (v5 \ v6)),v7) = L(x,(u * u) * (v5 \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(10972,a,16486,a)].">
      <j1 rule="hyper" parents="10972 16486"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      L(x,(T(y,z) \ K(u,w)) \ ((T(y,z) \ K(u,w)) \ (v5 \ v6)),v7) = L(x,(y * y) * (v5 \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(10891,a,16487,a)].">
      <j1 rule="hyper" parents="10891 16487"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      L(x,(T(y,z) \ K(u,w)) \ ((v5 \ v6) * T(y,z)),v7) = L(x,(y * y) * (v5 \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(65,a,16453,a(flip),b,16489,a)].">
      <j1 rule="hyper" parents="65 16453 16489"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      L(x,(T(y,z) \ K(u,w)) \ ((v5 \ v6) * y),v7) = L(x,(y * y) * (v5 \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(10903,a,16490,a)].">
      <j1 rule="hyper" parents="10903 16490"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      L(x,((y \ z) * u) * (K(w,v5) \ T(u,v6)),v7) = L(x,(u * u) * (y \ z),v7)
    ]]></literal>
    <justification jstring="[hyper(65,a,16439,a(flip),b,16491,a)].">
      <j1 rule="hyper" parents="65 16439 16491"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      L(x,((y \ z) * u) * (K(w,v5) * T(u,v6)),v7) = L(x,(u * u) * (y \ z),v7)
    ]]></literal>
    <justification jstring="[para(2618(a,1),16494(a,1,2,2))].">
      <j1 rule="para" parents="2618 16494"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      L(x,(y * K(z,u)) * ((w \ v5) * y),v6) = L(x,(y * y) * (w \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(11014,a,16495,a)].">
      <j1 rule="hyper" parents="11014 16495"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      L(x,(y * y) * (z \ u),w) = L(x,y * ((z \ u) * y),w)
    ]]></literal>
    <justification jstring="[para(6188(a,1),16496(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6188 16496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      L(x,y \ ((z * z) * u),w) = L(x,z * ((y \ u) * z),w)
    ]]></literal>
    <justification jstring="[hyper(11046,a,16497,a)].">
      <j1 rule="hyper" parents="11046 16497"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) \ w,v5) = L(x,z * (((y * u) \ w) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,11121,a,b,16497,a)].">
      <j1 rule="hyper" parents="65 11121 16497"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      L(x,y * ((z \ ((y \ u) * w)) * y),v5) = L(x,z \ ((u * y) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,16485,a(flip),b,16498,a),flip(a)].">
      <j1 rule="hyper" parents="65 16485 16498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,w \ v5),v6) = L(x,w * (((y * v5) \ ((w \ v5) * (w \ y))) * w),v6)
    ]]></literal>
    <justification jstring="[hyper(65,a,16480,a,b,16499,a)].">
      <j1 rule="hyper" parents="65 16480 16499"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,w \ v5),v6) = L(x,(y * v5) \ ((v5 * w) * (w \ y)),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,16500,a(flip),b,16501,a),flip(a)].">
      <j1 rule="hyper" parents="325 16500 16501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,w \ v5),v6) = L(x,K(v5,y) * a(v5,w,w * y),v6)
    ]]></literal>
    <justification jstring="[para(13187(a,1),16502(a,2,2))].">
      <j1 rule="para" parents="13187 16502"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,w \ v5),v6) = L(x,a(v5,w,w * y),v6)
    ]]></literal>
    <justification jstring="[hyper(325,a,10802,a(flip),b,16503,a),flip(a)].">
      <j1 rule="hyper" parents="325 10802 16503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16506">
    <literal><![CDATA[
      L(x,a(y,a(z,u,z) / w,v5 * w),v6) = L(x,a(v5,w,w * y),v6)
    ]]></literal>
    <justification jstring="[para(15965(a,1),16504(a,1,2))].">
      <j1 rule="para" parents="15965 16504"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      L(x,a(y,z \ 1,u * z),w) = L(x,a(u,z,z * y),w)
    ]]></literal>
    <justification jstring="[para(1784(a,1),16506(a,1,2,2))].">
      <j1 rule="para" parents="1784 16506"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      L(x,a(y,z,u * z),w) = L(x,a(u,z,z * y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,11294,a(flip),b,16507,a)].">
      <j1 rule="hyper" parents="65 11294 16507"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      L(x,a(y,z,z * u),w) = L(x,z,a(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16385,a(flip),b,16508,a),flip(a)].">
      <j1 rule="hyper" parents="65 16385 16508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      L(x,y,a(z * y,u,w)) = L(x,y,a(y * u,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16385,a(flip),b,16509,a),flip(a)].">
      <j1 rule="hyper" parents="65 16385 16509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      a(x,y,a(z \ u,((z \ u) * z) \ w,(u * z) * (z * (u \ w)))) = a(x,z \ u,a(z,y,((z \ u) * z) \ w))
    ]]></literal>
    <justification jstring="[para(16241(a,1),16367(a,1,3))].">
      <j1 rule="para" parents="16241 16367"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      ((x * (a(y,y,z) * (u * w))) * v5) / ((u * (a(y,y,z) * w)) * v5) = R(R(x,u * w,a(y,y,z)),(u * w) * a(y,y,z),v5)
    ]]></literal>
    <justification jstring="[para(16034(a,1),16094(a,1,1,1))].">
      <j1 rule="para" parents="16034 16094"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      ((x * (y * z)) * (a(u,u,w) * v5)) / ((y * (a(u,u,w) * z)) * v5) = R(R(x,y * z,a(u,u,w)),(y * z) * a(u,u,w),v5)
    ]]></literal>
    <justification jstring="[para(16114(a,1),16512(a,1,1))].">
      <j1 rule="para" parents="16114 16512"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      ((x * (y * z)) * (a(u,u,w) * v5)) / ((y * z) * (a(u,u,w) * v5)) = R(R(x,y * z,a(u,u,w)),(y * z) * a(u,u,w),v5)
    ]]></literal>
    <justification jstring="[para(16114(a,1),16513(a,1,2))].">
      <j1 rule="para" parents="16114 16513"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      a(x,x,y) \ (((z * (u * w)) * (a(x,x,y) * v5)) / ((u * w) * v5)) = R(R(z,u * w,a(x,x,y)),(u * w) * a(x,x,y),v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,16100,a(flip),b,16514,a)].">
      <j1 rule="hyper" parents="65 16100 16514"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      R(R(x,y * z,a(u,u,w)),(y * z) * a(u,u,w),v5) = ((x * (y * z)) * v5) / ((y * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(65,a,16120,a(flip),b,16515,a),flip(a)].">
      <j1 rule="hyper" parents="65 16120 16515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      R(R(x,y * z,a(u,u,w)),(y * z) * a(u,u,w),v5) = R(x,y * z,v5)
    ]]></literal>
    <justification jstring="[hyper(325,a,20,a,b,16516,a),flip(a)].">
      <j1 rule="hyper" parents="325 20 16516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      R(L(x,y * z,a(u,u,w)),(y * z) * a(u,u,w),v5) = R(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(13374(a,1),16518(a,1,1))].">
      <j1 rule="para" parents="13374 16518"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      R(x,(y * z) * a(u,u,w),v5) = R(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(16014(a,1),16519(a,1,1))].">
      <j1 rule="para" parents="16014 16519"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) = R(x,a(v5,v5,v6) * u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9911,a(flip),b,16520,a),flip(a)].">
      <j1 rule="hyper" parents="65 9911 16520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      R(x,a(y,y,z) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,9896,a(flip),b,16521,a),flip(a)].">
      <j1 rule="hyper" parents="65 9896 16521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16190,a(flip),b,16522,a)].">
      <j1 rule="hyper" parents="65 16190 16522"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      R(x,y,z * (a(u,u,w) * v5)) = R(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(65,a,16033,a(flip),b,16524,a)].">
      <j1 rule="hyper" parents="65 16033 16524"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      R(x,y,L(z,u,u) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(14569(a,1),16524(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14569 16524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      R(x,y,(z \ u) * w) = R(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(65,a,13227,a(flip),b,16529,a)].">
      <j1 rule="hyper" parents="65 13227 16529"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      R(x,y,z * (u * L(w,v5,v5))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15866,a(flip),b,16528,a)].">
      <j1 rule="hyper" parents="65 15866 16528"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      R(x,y,z * (u * (w / v5))) = R(x,y,z * (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(65,a,11404,a(flip),b,16534,a),flip(a)].">
      <j1 rule="hyper" parents="65 11404 16534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      R(x,y,z * (u * (w \ v5))) = R(x,y,z * (u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(65,a,8722,a(flip),b,16536,a)].">
      <j1 rule="hyper" parents="65 8722 16536"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      R(x,y,(z \ (u * w)) * (u * (z * w))) = L(x,y,a(z,w * z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16065,a(flip),b,16538,a),flip(a)].">
      <j1 rule="hyper" parents="65 16065 16538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) * (u * (z * w))) = L(x,y,a(z,w * z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16530,a(flip),b,16539,a)].">
      <j1 rule="hyper" parents="65 16530 16539"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      L(x,y,a(z,u * z,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16066,a(flip),b,16540,a),flip(a)].">
      <j1 rule="hyper" parents="65 16066 16540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      L(x,y,a(z,z * u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14012,a,b,16541,a)].">
      <j1 rule="hyper" parents="65 14012 16541"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      L(x,y,a(z,u \ w,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,15410,a(flip),b,16541,a),flip(a)].">
      <j1 rule="hyper" parents="65 15410 16541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      L(x,y,a(z,u * w,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16222,a(flip),b,16543,a)].">
      <j1 rule="hyper" parents="65 16222 16543"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      L(x,y,a(z,u * w,u)) = L(x,y,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,14012,a,b,16545,a)].">
      <j1 rule="hyper" parents="65 14012 16545"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      L(x,y * z,a(y,u,w)) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15226,a,b,16546,a)].">
      <j1 rule="hyper" parents="65 15226 16546"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      L(x,y * (z * u),a(y,w,z)) = L(x,w,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,16546,a(flip),b,16547,a),flip(a)].">
      <j1 rule="hyper" parents="325 16546 16547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      L(x,y * (z * u),a(u,w,y)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15264,a,b,16548,a)].">
      <j1 rule="hyper" parents="65 15264 16548"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),u,a(y,z,w)) = L(x,a(y,(y \ z) * w,w),u)
    ]]></literal>
    <justification jstring="[hyper(65,a,16399,a(flip),b,16549,a),flip(a)].">
      <j1 rule="hyper" parents="65 16399 16549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16551">
    <literal><![CDATA[
      L(x,a(y,(y \ z) * u,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,15180,a(flip),b,16550,a),flip(a)].">
      <j1 rule="hyper" parents="65 15180 16550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      L(x,a(y,(y * z) * u,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16329,a(flip),b,16551,a)].">
      <j1 rule="hyper" parents="65 16329 16551"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      L(x,a(y,z * (y * u),z),w) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[para(9995(a,1),16552(a,1,2))].">
      <j1 rule="para" parents="9995 16552"/>
    </justification>
  </clause>

  <clause id="16554">
    <literal><![CDATA[
      L(x,a(y,z * (u * y),z),w) = L(x,a(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,14969,a,b,16553,a)].">
      <j1 rule="hyper" parents="65 14969 16553"/>
    </justification>
  </clause>

  <clause id="16555">
    <literal><![CDATA[
      L(x,y * (z * u),a(y,z,w)) = L(x,a(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16385,a(flip),b,16553,a)].">
      <j1 rule="hyper" parents="65 16385 16553"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      L(x,y * (z * u),a(y,u,w)) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16385,a(flip),b,16554,a)].">
      <j1 rule="hyper" parents="65 16385 16554"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      L(x,y,a(z,y * u,w)) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16547,a(flip),b,16555,a)].">
      <j1 rule="hyper" parents="65 16547 16555"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      L(x,y,a(z,y * u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,16385,a(flip),b,16557,a),flip(a)].">
      <j1 rule="hyper" parents="325 16385 16557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      L(x,y,a(z,u * y,w)) = L(x,a(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(65,a,16547,a(flip),b,16556,a)].">
      <j1 rule="hyper" parents="65 16547 16556"/>
    </justification>
  </clause>

  <clause id="16562">
    <literal><![CDATA[
      L(x,y,a(z,u * y,w)) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,16385,a(flip),b,16559,a),flip(a)].">
      <j1 rule="hyper" parents="325 16385 16559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      a(x,y,L(z \ (u * ((z * w) / u)),(z \ 1) \ w,v5)) = a(x,y,((z \ 1) * v5) * ((u * (((z \ 1) \ w) / u)) * v5))
    ]]></literal>
    <justification jstring="[para(10816(a,1),16112(a,1,3))].">
      <j1 rule="para" parents="10816 16112"/>
    </justification>
  </clause>

  <clause id="16565">
    <literal><![CDATA[
      a(x,y,L(z \ (u * ((z * w) / u)),z \ w,v5)) = a(x,y,((z \ 1) * v5) * ((u * (((z \ 1) \ w) / u)) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,11455,a(flip),b,16564,a)].">
      <j1 rule="hyper" parents="65 11455 16564"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      a(x,y,L((z * ((u * w) / z)) * u,u \ w,v5)) = a(x,y,((u \ 1) * v5) * ((z * (((u \ 1) \ w) / z)) * v5))
    ]]></literal>
    <justification jstring="[hyper(65,a,15961,a(flip),b,16565,a)].">
      <j1 rule="hyper" parents="65 15961 16565"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      a(x,y,L((z * u) * z,z \ u,w)) = a(x,y,((z \ 1) * w) * ((v5 * (((z \ 1) \ u) / v5)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,10423,a(flip),b,16567,a)].">
      <j1 rule="hyper" parents="65 10423 16567"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      a(x,y,L(z,u \ z,w)) = a(x,y,((u \ 1) * w) * ((v5 * (((u \ 1) \ z) / v5)) * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,15957,a(flip),b,16568,a)].">
      <j1 rule="hyper" parents="65 15957 16568"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * ((w * (((z \ 1) \ v5) / w)) * u)) = a(x,y,L(v5,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16141,a(flip),b,16570,a),flip(a)].">
      <j1 rule="hyper" parents="65 16141 16570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * (((z \ 1) \ w) * u)) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[para(179(a,1),16572(a,1,3,2,1))].">
      <j1 rule="para" parents="179 16572"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) * ((u \ 1) * z)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,10771,a(flip),b,16573,a)].">
      <j1 rule="hyper" parents="65 10771 16573"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      a(x,y,(z * u) * (u * (z \ w))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,10438,a(flip),b,16574,a)].">
      <j1 rule="hyper" parents="65 10438 16574"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      a(x,y,a(z \ u,((z \ u) * z) \ w,L(w,u,z))) = a(x,z \ u,a(z,y,((z \ u) * z) \ w))
    ]]></literal>
    <justification jstring="[para(16575(a,1),16511(a,1,3))].">
      <j1 rule="para" parents="16575 16511"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,((y \ z) * y) \ w)) = a(x,u,a(y \ z,z \ w,L(w,z,y)))
    ]]></literal>
    <justification jstring="[para(10005(a,1),16576(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10005 16576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,((y \ z) * y) \ w)) = a(x,u,a(y * z,z \ w,L(w,z,y)))
    ]]></literal>
    <justification jstring="[para(15959(a,1),16577(a,2,3))].">
      <j1 rule="para" parents="15959 16577"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,((y \ z) * y) \ w)) = a(x,u,a(z * y,z \ w,w))
    ]]></literal>
    <justification jstring="[para(15977(a,1),16579(a,2,3))].">
      <j1 rule="para" parents="15977 16579"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,((y \ z) * y) \ w)) = a(x,u,a(z * y,w * z,w))
    ]]></literal>
    <justification jstring="[hyper(325,a,16179,a(flip),b,16580,a),flip(a)].">
      <j1 rule="hyper" parents="325 16179 16580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,((y \ z) * y) \ w)) = a(z * y,z,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,16150,a(flip),b,16581,a),flip(a)].">
      <j1 rule="hyper" parents="325 16150 16581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,w * ((y \ z) * y))) = a(z * y,z,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(15965(a,1),16582(a,1,3))].">
      <j1 rule="para" parents="15965 16582"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,w * ((z * y) * y))) = a(z * y,z,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(16277(a,1),16583(a,1,3))].">
      <j1 rule="para" parents="16277 16583"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      a(x,y \ z,a(y,u,z * w)) = a(z * y,z,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(16226(a,1),16584(a,1,3))].">
      <j1 rule="para" parents="16226 16584"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      a(x,y * z,a(y,u,z * w)) = a(z * y,z,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,16173,a(flip),b,16585,a)].">
      <j1 rule="hyper" parents="65 16173 16585"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) = a(y,x,a(x * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16157,a(flip),b,16586,a),flip(a)].">
      <j1 rule="hyper" parents="65 16157 16586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      a(x * y,z,a(u,x,w)) = a(y,x,a(x * w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,15198,a,b,16588,a)].">
      <j1 rule="hyper" parents="65 15198 16588"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) * v5 = a(x,y,a(y * w,u,z)) * v5
    ]]></literal>
    <justification jstring="[para(16588(a,1),12862(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16588 12862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      L(x,y,a(z,u,u * w)) = a(x,w,a(w * u,y,z)) * x
    ]]></literal>
    <justification jstring="[para(16589(a,1),16471(a,2,1))].">
      <j1 rule="para" parents="16589 16471"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      R(x,y,a(y * z,u,w)) = L(x,u,a(w,z,z * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,14602,a,b,16591,a)].">
      <j1 rule="hyper" parents="325 14602 16591"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      L(x,y,a(y * z,u,w)) = L(x,u,a(w,z,z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,13374,a(flip),b,16592,a)].">
      <j1 rule="hyper" parents="65 13374 16592"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / a(z,u,w) = a(x,y,a(y * w,u,z)) * x
    ]]></literal>
    <justification jstring="[hyper(65,a,14346,a,b,16590,a)].">
      <j1 rule="hyper" parents="65 14346 16590"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / a(z,u,w) = R(x,y,a(y * w,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,14602,a,b,16594,a),flip(a)].">
      <j1 rule="hyper" parents="325 14602 16594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / a(z,u,w) = L(x,y,a(y * w,u,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,13374,a(flip),b,16595,a),flip(a)].">
      <j1 rule="hyper" parents="325 13374 16595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      a(x,y,z) \ ((u / w) * (w * a(x,y,z))) = L(u,w,a(w * z,y,x))
    ]]></literal>
    <justification jstring="[hyper(7210,a,16596,a)].">
      <j1 rule="hyper" parents="7210 16596"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = L(u,w,a(w * z,y,x))
    ]]></literal>
    <justification jstring="[hyper(65,a,14418,a(flip),b,16597,a)].">
      <j1 rule="hyper" parents="65 14418 16597"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      L(x,y,a(y * z,u,w)) = L(x,y,a(z,u,y * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16296,a(flip),b,16598,a),flip(a)].">
      <j1 rule="hyper" parents="65 16296 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      L(x,y,a(z * y,u,w)) = L(x,y,a(u,z,y * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16510,a,b,16600,a)].">
      <j1 rule="hyper" parents="65 16510 16600"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      L(x,a(y * z,z,u),w) = L(x,z,a(y,u,z * w))
    ]]></literal>
    <justification jstring="[hyper(65,a,16390,a,b,16600,a)].">
      <j1 rule="hyper" parents="65 16390 16600"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      L(x,y,a(z,u,u * w)) = L(x,w,a(u,y,w * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16593,a(flip),b,16600,a)].">
      <j1 rule="hyper" parents="65 16593 16600"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      L(x,a(y * z,z,y * u),w) = L(x,z,a(z * w,u,y))
    ]]></literal>
    <justification jstring="[hyper(325,a,16542,a(flip),b,16602,a),flip(a)].">
      <j1 rule="hyper" parents="325 16542 16602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      L(x,a(y * z,z,y * u),w) = L(x,z,a(w,u,z * y))
    ]]></literal>
    <justification jstring="[hyper(325,a,16600,a(flip),b,16604,a),flip(a)].">
      <j1 rule="hyper" parents="325 16600 16604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      L(x,y,a(z * u,z * y,w)) = L(x,y,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16385,a(flip),b,16605,a)].">
      <j1 rule="hyper" parents="65 16385 16605"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      L(x,y,a(z,y * u,w)) = L(x,z,a(w,u,z * y))
    ]]></literal>
    <justification jstring="[hyper(65,a,16562,a(flip),b,16606,a)].">
      <j1 rule="hyper" parents="65 16562 16606"/>
    </justification>
  </clause>

  <clause id="16608">
    <literal><![CDATA[
      L(x,y,a(z,u,y * w)) = L(x,u,a(y,w,z))
    ]]></literal>
    <justification jstring="[hyper(65,a,16558,a(flip),b,16607,a),flip(a)].">
      <j1 rule="hyper" parents="65 16558 16607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      L(x,y,a(z,u,u * w)) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16603,a,b,16608,a)].">
      <j1 rule="hyper" parents="65 16603 16608"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      L(x,y,a(z * y,u,w)) = L(x,z,a(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(65,a,16601,a,b,16608,a)].">
      <j1 rule="hyper" parents="65 16601 16608"/>
    </justification>
  </clause>

  <clause id="16615">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),w,a(y,z,z * u)) = x
    ]]></literal>
    <justification jstring="[para(16611(a,1),16288(a,1,1))].">
      <j1 rule="para" parents="16611 16288"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),w,a(u,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(65,a,16610,a(flip),b,16615,a)].">
      <j1 rule="hyper" parents="65 16610 16615"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = (x * y) / y
    ]]></literal>
    <justification jstring="[para(16616(a,1),16391(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16616 16391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(325,a,11,a(flip),b,16618,a),flip(a)].">
      <j1 rule="hyper" parents="325 11 16618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,16622,a,b,14595,a),flip(a)].">
      <j1 rule="hyper" parents="133 16622 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aa1")
    ]]></attribute>
    <justification jstring="[resolve(16650,a,66,a)].">
      <j1 rule="resolve" parents="16650 66"/>
    </justification>
  </clause>

</proof>

</proofs>
